lass::prim Namespace Reference

set of geometrical primitives More...

Namespaces
namespace	impl
	implementation details of lass::prim
Data Structures
class	Aabb2D
	your momma's axis aligned bounding box. More...
class	Aabb3D
	your momma's axis aligned bounding box. More...
struct	ColorRGBA
	an [0, 1] floating point RGB colour with Alpha channel. More...
class	DegenerationError
struct	NoDegenerate
	This is the default policy. More...
struct	StrictNoDegenerate
	This is the default policy. More...
struct	AllowDegenerate
	AllowDegenerate puts the responsibility on the user. More...
class	Cartesian
	policy for an implementation based on the cartesian equation. More...
class	Parametric
	policy for an implementation based on the parametric equation. More...
class	Combined
	policy for an implementation based on both the cartesian and parametric equation. More...
class	Line2D
	2D Line More...
class	Line3D
	3D Line More...
class	LineSegment2D
	2D Line Segment More...
class	LineSegment3D
	3D Line Segment More...
class	MinMaxError
	Exception thrown by StrictMinMax. More...
struct	StrictMinMax
	MinMaxPolicy enforcing strict rules for the minima and maxima. More...
struct	AutoMinMax
	MinMaxPolicy automatically correcting wrong minima and maxima. More...
struct	UncheckedMinMax
	MinMaxPolicy that makes it your responsibility to behave well. More...
struct	Normalized
	Policy to auto-normalize normals. More...
struct	Unnormalized
	Policy to keep normals unnormalized. More...
struct	IsAlreadyNormalized
class	Parallelogram3D
	A very simple 3D polygon :). More...
class	ParameterError
struct	Bounded
	Parameters supplied to functions must be in the range of the primitive. More...
struct	Unbounded
	Parameters supplied to functions can go out of the range of the primitive. More...
struct	Plane3D
	A 3D hyper plane. More...
struct	Point2D
struct	Point2DH
	homogenous 2D Point More...
struct	Point3D
	3D Point More...
struct	Point3DH
	homogenous 3D Point More...
class	SingularityError
class	Ray2D
	2D Ray More...
class	Ray3D
	3D Ray More...
class	SimplePolygon2D
	convex or concave polygon in 2D (not selfintersecting, no holes) More...
class	SimplePolygon3D
	convex or concave polygon in 3D (not selfintersecting, no holes) More...
struct	Sphere3D
	3D Sphere More...
class	Transformation2D
	a linear 2D transformation More...
class	Transformation3D
	a linear 3D transformation More...
class	Triangle2D
	A very simple 2D polygon :). More...
class	Triangle3D
	A very simple 3D polygon :). More...
struct	IndexTriangle
class	TriangleMesh3D
	One of the simplier meshes. More...
struct	Vector2D
	2D Vector More...
struct	Vector3D
	3D Vector More...
struct	Vector4D
	4D Vector More...
class	XY
	cyclic iterator over xy indices More...
class	XYZ
	cyclic iterator over xyz indices More...
class	XYZW
	cyclic iterator over xyzw indices More...
struct	Point_2d
	2D Point More...
Enumerations
enum	Orientation { oInvalid = 0, oClockWise = 1, oCounterClockWise = 2 }
	enumeration of clockwise versus counterclockwise More...
enum	Result {   rInvalid = 0, rNone = 1, rOne = 2, rTwo = 3,   rInfinite = 4 }
	meta information on the result you have from an operation like an intersection . More...
enum	Side {   sInvalid = 0x00, sFront = 0x01, sLeft = 0x01, sBack = 0x02,   sRight = 0x02, sInside = 0x04, sOutside = 0x08, sSurface = 0x10 }
	Different sides of a surface. More...
Functions
template<typename T , class MMPa , class MMPb >
const Aabb2D< T, MMPa >	operator+ (const Aabb2D< T, MMPa > &a, const Aabb2D< T, MMPb > &b)
template<typename T , class MMP >
const Aabb2D< T, MMP >	operator+ (const Aabb2D< T, MMP > &a, const Point2D< T > &b)
template<typename T , class MMP >
const Aabb2D< T, MMP >	operator+ (const Point2D< T > &a, const Aabb2D< T, MMP > &b)
template<typename T >
const Aabb2D< T >	aabb (const Point2D< T > &point)
template<typename T , class MMP >
T	distance (const Aabb2D< T, MMP > &a, const Point2D< T > &b)
template<typename T , class MMPa , class MMPb >
T	distance (const Aabb2D< T, MMPa > &a, const Aabb2D< T, MMPb > &b)
template<typename T , class MMPa , class MMPb , class MMPr >
Result	intersect (const Aabb2D< T, MMPa > &a, const Aabb2D< T, MMPb > &b, Aabb2D< T, MMPr > &result)
template<typename T , class MMPa , class MMPb >
const bool	intersects (const Aabb2D< T, MMPa > &a, const Aabb2D< T, MMPb > &b)
template<typename T , class MMP >
const bool	intersects (const Aabb2D< T, MMP > &a, const Point2D< T > &b)
template<typename T , class MMP >
const bool	intersects (const Point2D< T > &a, const Aabb2D< T, MMP > &b)
template<typename T , class MMPa , class MMPb >
const bool	collides (const Aabb2D< T, MMPa > &a, const Aabb2D< T, MMPb > &b)
template<typename T , class MMP >
const bool	collides (const Aabb2D< T, MMP > &a, const Point2D< T > &b)
template<typename T , class MMP >
const bool	collides (const Point2D< T > &a, const Aabb2D< T, MMP > &b)
template<typename T , class MMP >
std::ostream &	operator<< (std::ostream &ioOStream, const Aabb2D< T, MMP > &aabb)
template<typename T , class MMP >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Aabb2D< T, MMP > &aabb)
template<typename T , class MMP >
io::MatlabOStream &	operator<< (io::MatlabOStream &ioOStream, const Aabb2D< T, MMP > &aabb)
template<typename T , typename MMP >
const bool	intersects (const Triangle2D< T > &triangle, const Aabb2D< T, MMP > &box)
template<typename T , typename MMP >
const bool	intersects (const Aabb2D< T, MMP > &box, const Triangle2D< T > &triangle)
template<typename T , typename MMP >
const bool	collides (const Triangle2D< T > &triangle, const Aabb2D< T, MMP > &box)
template<typename T , typename MMP >
const bool	collides (const Aabb2D< T, MMP > &box, const Triangle2D< T > &triangle)
template<typename T , class MMPa , class MMPb >
const Aabb3D< T, MMPa >	operator+ (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b)
template<typename T , class MMP >
const Aabb3D< T, MMP >	operator+ (const Aabb3D< T, MMP > &a, const Point3D< T > &b)
template<typename T , class MMP >
const Aabb3D< T, MMP >	operator+ (const Point3D< T > &a, const Aabb3D< T, MMP > &b)
template<typename T >
const Aabb3D< T >	aabb (const Point3D< T > &point)
template<typename T , class MMP >
T	distance (const Aabb3D< T, MMP > &a, const Point3D< T > &b)
template<typename T , class MMPa , class MMPb >
T	distance (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b)
template<typename T , class MMPa , class MMPb , class MMPr >
Result	intersect (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b, Aabb3D< T, MMPr > &result)
template<typename T , class MMPa , class MMPb >
const bool	intersects (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b)
template<typename T , class MMP >
const bool	intersects (const Aabb3D< T, MMP > &a, const Point3D< T > &b)
template<typename T , class MMP >
const bool	intersects (const Point3D< T > &a, const Aabb3D< T, MMP > &b)
template<typename T , class MMPa , class MMPb >
const bool	collides (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b)
template<typename T , class MMP >
const bool	collides (const Aabb3D< T, MMP > &a, const Point3D< T > &b)
template<typename T , class MMP >
const bool	collides (const Point3D< T > &a, const Aabb3D< T, MMP > &b)
template<typename T , class MMP >
std::ostream &	operator<< (std::ostream &stream, const Aabb3D< T, MMP > &aabb)
template<typename T , class MMP >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Aabb3D< T, MMP > &aabb)
template<typename T , class DegeneratePolicy >
bool	triangulate (const SimplePolygon2D< T, DegenerationPolicy > &iPolygon, std::vector< Triangle2D< T > > &oTriangles)
ColorRGBA	over (const ColorRGBA &iA, const ColorRGBA &iB)
	placement of foreground iA in front of background iB.
ColorRGBA	in (const ColorRGBA &iA, const ColorRGBA &iB)
	part of iA inside iB.
ColorRGBA	out (const ColorRGBA &iA, const ColorRGBA &iB)
	iA held out by iB, part of iA outside iB.
ColorRGBA	atop (const ColorRGBA &iA, const ColorRGBA &iB)
	union of iA in iB and iB out iA.
ColorRGBA	plus (const ColorRGBA &iA, const ColorRGBA &iB)
ColorRGBA	through (const ColorRGBA &iA, const ColorRGBA &iB)
	iA seen through color filter iB.
ColorRGBA::TValue	distance (const ColorRGBA &iA, const ColorRGBA &iB)
	distance between non-non-premultiplied colours as 3D points (alpha channel is disregarded).
LASS_DLL ColorRGBA LASS_CALL	operator+ (const ColorRGBA &iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator- (const ColorRGBA &iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator* (const ColorRGBA &iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator/ (const ColorRGBA &iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator+ (ColorRGBA::TParam iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator- (ColorRGBA::TParam iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator* (ColorRGBA::TParam iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator/ (ColorRGBA::TParam iA, const ColorRGBA &iB)
LASS_DLL ColorRGBA LASS_CALL	operator+ (const ColorRGBA &iA, ColorRGBA::TParam iB)
LASS_DLL ColorRGBA LASS_CALL	operator- (const ColorRGBA &iA, ColorRGBA::TParam iB)
LASS_DLL ColorRGBA LASS_CALL	operator* (const ColorRGBA &iA, ColorRGBA::TParam iB)
LASS_DLL ColorRGBA LASS_CALL	operator/ (const ColorRGBA &iA, ColorRGBA::TParam iB)
template<typename T , class EP , class NP >
T	signedDistance (const Point2D< T > &iA, const Line2D< T, EP, NP > &iB)
template<typename T , class EPa , class NPa , class EPb , class NPb >
T	signedDistance (const Line2D< T, EPa, NPa > &iA, const Line2D< T, EPb, NPb > &iB)
template<typename T , class EPa , class NPa , class EPb , class NPb >
Result	intersect (const Line2D< T, EPa, NPa > &iA, const Line2D< T, EPb, NPb > &iB, T &oTa, T &oTb)
template<typename T , class EPa , class NPa , class EPb , class NPb >
Result	intersect (const Line2D< T, EPa, NPa > &iA, const Line2D< T, EPb, NPb > &iB, Point2D< T > &oPoint)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Line2D< T, Cartesian > &iLine)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Line2D< T, Parametric > &iLine)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Line2D< T, Combined > &iLine)
template<typename T , class NP >
std::ostream &	operator<< (std::ostream &oOStream, const Line3D< T, NP > &iB)
template<typename T , class NP >
io::XmlOStream &	operator<< (io::XmlOStream &oOStream, const Line3D< T, NP > &iB)
template<typename T , class PPa , class PPb >
bool	operator== (const LineSegment2D< T, PPa > &a, const LineSegment2D< T, PPb > &b)
template<typename T , class PPa , class PPb >
bool	operator!= (const LineSegment2D< T, PPa > &a, const LineSegment2D< T, PPb > &b)
template<typename T , class PP >
T	squaredDistance (const LineSegment2D< T, PP > &segment, const Point2D< T > &point)
template<typename T , class PP >
T	distance (const LineSegment2D< T, PP > &segment, const Point2D< T > &point)
template<typename T , class PPa , class PPb >
Result	intersect (const LineSegment2D< T, PPa > &a, const LineSegment2D< T, PPb > &b, T &tA, T &tB)
template<typename T , class PPa , class PPb >
Result	intersect (const LineSegment2D< T, PPa > &a, const LineSegment2D< T, PPb > &b, Point2D< T > &point)
template<typename T , class PP >
std::ostream &	operator<< (std::ostream &stream, const LineSegment2D< T, PP > &segment)
template<typename T , class PP >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const LineSegment2D< T, PP > &segment)
template<typename T , class PP >
lass::io::MatlabOStream &	operator<< (lass::io::MatlabOStream &stream, const LineSegment2D< T, PP > &segment)
template<typename T , class PPa , class PPb >
bool	operator== (const LineSegment3D< T, PPa > &iA, const LineSegment3D< T, PPb > &iB)
template<typename T , class PPa , class PPb >
bool	operator!= (const LineSegment3D< T, PPa > &iA, const LineSegment3D< T, PPb > &iB)
template<typename T , class PPa , class PPb >
Result	intersect (const LineSegment3D< T, PPa > &iA, const LineSegment3D< T, PPb > &iB, T &oTa, T &oTb)
template<typename T , class PPa , class PPb >
Result	intersect (const LineSegment3D< T, PPa > &iA, const LineSegment3D< T, PPb > &iB, Point3D< T > &oPoint)
template<typename T , class PP >
std::ostream &	operator<< (std::ostream &oOStream, const LineSegment3D< T, PP > &iB)
template<typename T , class PP >
io::XmlOStream &	operator<< (io::XmlOStream &oOStream, const LineSegment3D< T, PP > &iB)
template<typename T , class PP >
lass::io::MatlabOStream &	operator<< (lass::io::MatlabOStream &oOStream, const LineSegment3D< T, PP > &iLineSegment)
template<typename T , class PP1 , class NP2 , class PP2 >
T	distance (const LineSegment3D< T, PP1 > &lineSegment, const Ray3D< T, NP2, PP2 > &ray, const T &tMin=T())
template<typename T , class PP1 , class NP2 , class PP2 >
T	squaredDistance (const LineSegment3D< T, PP1 > &lineSegment, const Ray3D< T, NP2, PP2 > &ray, const T &tMin=T())
template<typename T , class PP1 , class NP2 , class PP2 >
T	closestsPoints (const LineSegment3D< T, PP1 > &lineSegment, const Ray3D< T, NP2, PP2 > &ray, T &tSeg, T &tRay, const T &tMin=T())
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Parallelogram3D< T > &iParallelogram)
template<typename T >
std::ostream &	operator<< (std::ostream &ioOStream, const Parallelogram3D< T > &iParallelogram)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Plane3D< T, Cartesian > &iPlane)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Plane3D< T, Parametric > &iPlane)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Plane3D< T, Combined > &iPlane)
template<typename T >
bool	operator== (const Point2D< T > &a, const Point2D< T > &b)
template<typename T >
bool	operator!= (const Point2D< T > &a, const Point2D< T > &b)
template<typename T >
Point2D< T >	operator+ (const Point2D< T > &a, const Vector2D< T > &b)
template<typename T >
Point2D< T >	operator+ (const Vector2D< T > &a, const Point2D< T > &b)
template<typename T >
Point2D< T >	operator- (const Point2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator- (const Point2D< T > &a, const Point2D< T > &b)
template<typename T >
Point2D< T >::TValue	distance (const Point2D< T > &a, const Point2D< T > &b)
template<typename T >
Point2D< T >::TValue	squaredDistance (const Point2D< T > &a, const Point2D< T > &b)
template<typename T >
Point2D< T >	pointwiseMin (const Point2D< T > &a, const Point2D< T > &b)
template<typename T >
Point2D< T >	pointwiseMax (const Point2D< T > &a, const Point2D< T > &b)
template<typename T >
Point2D< T >	lerp (const Point2D< T > &a, const Point2D< T > &b, typename Point2D< T >::TParam t)
template<typename T >
std::ostream &	operator<< (std::ostream &stream, const Point2D< T > &b)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Point2D< T > &b)
template<typename T >
std::istream &	operator>> (std::istream &stream, Point2D< T > &b)
template<typename T >
lass::io::MatlabOStream &	operator<< (lass::io::MatlabOStream &stream, const Point2D< T > &b)
template<typename T >
T	doubleTriangleArea (const Point2D< T > &a, const Point2D< T > &b, const Point2D< T > &c)
template<typename T >
bool	cw (const Point2D< T > &a, const Point2D< T > &b, const Point2D< T > &c)
template<typename T >
bool	ccw (const Point2D< T > &a, const Point2D< T > &b, const Point2D< T > &c)
template<typename T >
bool	weakCw (const Point2D< T > &a, const Point2D< T > &b, const Point2D< T > &c)
template<typename T >
bool	weakCcw (const Point2D< T > &a, const Point2D< T > &b, const Point2D< T > &c)
template<typename T >
bool	inCircle (const Point2D< T > &a, const Point2D< T > &b, const Point2D< T > &c, const Point2D< T > &d)
template<typename T >
T	preciseDoubleTriangleArea (const Point2D< T > &a, const Point2D< T > &b, const Point2D< T > &c)
template<typename T >
bool	operator== (const Point2DH< T > &iA, const Point2DH< T > &iB)
template<typename T >
bool	operator!= (const Point2DH< T > &iA, const Point2DH< T > &iB)
template<typename T >
Point2DH< T >	operator+ (const Point2DH< T > &iA, const Point2DH< T > &iB)
template<typename T >
Point2DH< T >	operator+ (const Point2DH< T > &iA, const Point2D< T > &iB)
template<typename T >
Point2DH< T >	operator+ (const Point2D< T > &iA, const Point2DH< T > &iB)
template<typename T >
Point2DH< T >	operator+ (const Point2D< T > &iA, const Point2D< T > &iB)
template<typename T >
Point2DH< T >	operator- (const Point2DH< T > &iA, const Point2DH< T > &iB)
template<typename T >
Point2DH< T >	operator* (const Point2DH< T > &iA, typename Point2DH< T >::TParam iB)
template<typename T >
Point2DH< T >	operator/ (const Point2DH< T > &iA, typename Point2DH< T >::TParam iB)
template<typename T >
Point2DH< T >	operator* (typename Point2DH< T >::TParam iA, const Point2DH< T > &iB)
template<typename T >
std::ostream &	operator<< (std::ostream &oOStream, const Point2DH< T > &iB)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &oOStream, const Point2DH< T > &iB)
template<typename T >
std::istream &	operator>> (std::istream &ioIStream, Point2DH< T > &oB)
template<typename T >
bool	operator== (const Point3D< T > &a, const Point3D< T > &b)
template<typename T >
bool	operator!= (const Point3D< T > &a, const Point3D< T > &b)
template<typename T >
Point3D< T >	operator+ (const Point3D< T > &a, const Vector3D< T > &b)
template<typename T >
Point3D< T >	operator+ (const Vector3D< T > &a, const Point3D< T > &b)
template<typename T >
Point3D< T >	operator- (const Point3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator- (const Point3D< T > &a, const Point3D< T > &b)
template<typename T >
Point3D< T >::TValue	distance (const Point3D< T > &a, const Point3D< T > &b)
template<typename T >
Point3D< T >::TValue	squaredDistance (const Point3D< T > &a, const Point3D< T > &b)
template<typename T >
Point3D< T >	pointwiseMin (const Point3D< T > &a, const Point3D< T > &b)
template<typename T >
Point3D< T >	pointwiseMax (const Point3D< T > &a, const Point3D< T > &b)
template<typename T >
Point3D< T >	lerp (const Point3D< T > &a, const Point3D< T > &b, typename Point3D< T >::TParam t)
template<typename T >
std::ostream &	operator<< (std::ostream &stream, const Point3D< T > &b)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Point3D< T > &b)
template<typename T >
std::istream &	operator>> (std::istream &stream, Point3D< T > &b)
template<typename T >
bool	operator== (const Point3DH< T > &iA, const Point3DH< T > &iB)
template<typename T >
bool	operator!= (const Point3DH< T > &iA, const Point3DH< T > &iB)
template<typename T >
Point3DH< T >	operator+ (const Point3DH< T > &iA, const Point3DH< T > &iB)
template<typename T >
Point3DH< T >	operator- (const Point3DH< T > &iA, Point3DH< T > &iB)
template<typename T >
Point3DH< T >	operator* (const Point3DH< T > &iA, typename Point3DH< T >::TParam iB)
template<typename T >
Point3DH< T >	operator/ (const Point3DH< T > &iA, typename Point3DH< T >::TParam iB)
template<typename T >
Point3DH< T >	operator* (typename Point3DH< T >::TParam iA, const Point3DH< T > &iB)
template<typename T >
std::ostream &	operator<< (std::ostream &oOStream, const Point3DH< T > &iB)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &oOStream, const Point3DH< T > &iB)
template<typename T >
std::istream &	operator>> (std::istream &ioIStream, Point3DH< T > &oB)
template<typename T >
Point3DH< T >	operator+ (const Point3D< T > &iA, const Point3D< T > &iB)
template<typename T >
Point3DH< T >	operator* (typename Point3D< T >::TParam iA, const Point3D< T > &iB)
template<typename T >
Point3DH< T >	operator* (const Point3D< T > &iA, typename Point3D< T >::TParam iB)
template<typename T , class NP , class PP >
std::ostream &	operator<< (std::ostream &oOStream, const Ray2D< T, NP, PP > &iB)
template<typename T , class NP , class PP >
io::XmlOStream &	operator<< (io::XmlOStream &oOStream, const Ray2D< T, NP, PP > &iB)
template<typename T , class NP , class PP >
std::ostream &	operator<< (std::ostream &oOStream, const Ray3D< T, NP, PP > &iB)
template<typename T , class NP , class PP >
io::XmlOStream &	operator<< (io::XmlOStream &oOStream, const Ray3D< T, NP, PP > &iB)
template<typename T , class DP >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const SimplePolygon2D< T, DP > &iPolygon)
template<typename T , class DP >
std::ostream &	operator<< (std::ostream &ioOStream, const SimplePolygon2D< T, DP > &iPolygon)
template<typename T , class DP >
lass::io::MatlabOStream &	operator<< (lass::io::MatlabOStream &oOStream, const SimplePolygon2D< T, DP > &iPolygon)
template<typename T , class DP >
bool	set_difference (const SimplePolygon2D< T, DP > &iPolygonA, const SimplePolygon2D< T, DP > &iPolygonB, std::vector< SimplePolygon2D< T, DP > > &oPolygonsC)
	C = A \ B.
template<typename T , class DP >
bool	set_union (const SimplePolygon2D< T, DP > &iPolygonA, const SimplePolygon2D< T, DP > &iPolygonB, std::vector< SimplePolygon2D< T, DP > > &oPolygonsC)
	C = A U B.
template<typename T , class DP >
bool	set_intersect (const SimplePolygon2D< T, DP > &iPolygonA, const SimplePolygon2D< T, DP > &iPolygonB, std::vector< SimplePolygon2D< T, DP > > &oPolygonsC)
	C = (A U B) \ (A \ B) \ (B \ A).
template<typename T , class DegeneratePolicy , typename OutputIterator >
OutputIterator	triangulate (const SimplePolygon2D< T, DegenerationPolicy > &polygon, OutputIterator triangles)
template<typename T , class EP , class NP , class PP >
Result	intersect (const SimplePolygon3D< T, EP, NP > &iPolygon, const LineSegment3D< T, PP > &iSegment, T &oT, const T &iMinT=0)
template<typename T , class EP1 , class NP1 , class EP2 , class NP2 >
SimplePolygon3D< T, EP2, NP2 >	clip (const Plane3D< T, EP1, NP1 > &iPlane, const SimplePolygon3D< T, EP2, NP2 > &iPolygon)
template<typename T , class EP , class NP >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const SimplePolygon3D< T, EP, NP > &iPolygon)
template<typename T , class EP , class NP >
std::ostream &	operator<< (std::ostream &ioOStream, const SimplePolygon3D< T, EP, NP > &iPolygon)
template<typename T >
const T	squaredDistance (const Sphere3D< T > &sphere, const Point3D< T > &point)
template<typename T >
const T	distance (const Sphere3D< T > &sphere, const Point3D< T > &point)
template<typename T >
std::ostream &	operator<< (std::ostream &oOStream, const Sphere3D< T > &iB)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Sphere3D< T > &iB)
template<typename T >
Transformation2D< T >	concatenate (const Transformation2D< T > &first, const Transformation2D< T > &second)
template<typename T >
Vector2D< T >	transform (const Vector2D< T > &subject, const Transformation2D< T > &transformation)
template<typename T >
Point2D< T >	transform (const Point2D< T > &subject, const Transformation2D< T > &transformation)
template<typename T >
Vector2D< T >	normalTransform (const Vector2D< T > &subject, const Transformation2D< T > &transformation)
template<typename T >
std::pair< Vector2D< T >, T >	normalTransform (const std::pair< Vector2D< T >, T > &subject, const Transformation2D< T > &transformation)
template<typename T , typename Char , typename Traits >
std::basic_ostream< Char, Traits > &	operator<< (std::basic_ostream< Char, Traits > &stream, const Transformation2D< T > &transformation)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Transformation2D< T > &transformation)
template<typename T >
Transformation3D< T >	concatenate (const Transformation3D< T > &first, const Transformation3D< T > &second)
template<typename T >
Vector3D< T >	transform (const Vector3D< T > &subject, const Transformation3D< T > &transformation)
template<typename T >
Point3D< T >	transform (const Point3D< T > &subject, const Transformation3D< T > &transformation)
template<typename T >
Vector3D< T >	normalTransform (const Vector3D< T > &subject, const Transformation3D< T > &transformation)
template<typename T >
std::pair< Vector3D< T >, T >	normalTransform (const std::pair< Vector3D< T >, T > &subject, const Transformation3D< T > &transformation)
template<typename T , typename Char , typename Traits >
std::basic_ostream< Char, Traits > &	operator<< (std::basic_ostream< Char, Traits > &stream, const Transformation3D< T > &transformation)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Transformation3D< T > &transformation)
template<typename T >
const T	distance (const Triangle2D< T > &triangle, const Point2D< T > &point)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Triangle2D< T > &iTriangle)
template<typename T >
std::ostream &	operator<< (std::ostream &ioOStream, const Triangle2D< T > &iTriangle)
template<typename T >
lass::io::MatlabOStream &	operator<< (lass::io::MatlabOStream &oOStream, const Triangle2D< T > &iTriangle)
template<typename T >
T	partialVoronoiArea (const Triangle2D< T > iT, int iIndexOfVertex)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &ioOStream, const Triangle3D< T > &iTriangle)
template<typename T >
std::ostream &	operator<< (std::ostream &ioOStream, const Triangle3D< T > &iTriangle)
template<typename T >
Vector2D< T >::TValue	dot (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >::TValue	perpDot (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >::TValue	cos (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
bool	operator== (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
bool	operator!= (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator+ (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator- (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator* (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator/ (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator+ (const Vector2D< T > &a, typename Vector2D< T >::TParam b)
template<typename T >
Vector2D< T >	operator- (const Vector2D< T > &a, typename Vector2D< T >::TParam b)
template<typename T >
Vector2D< T >	operator* (const Vector2D< T > &a, typename Vector2D< T >::TParam b)
template<typename T >
Vector2D< T >	operator/ (const Vector2D< T > &a, typename Vector2D< T >::TParam b)
template<typename T >
Vector2D< T >	operator+ (typename Vector2D< T >::TParam a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator- (typename Vector2D< T >::TParam a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	operator* (typename Vector2D< T >::TParam a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	pointwiseMin (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	pointwiseMax (const Vector2D< T > &a, const Vector2D< T > &b)
template<typename T >
Vector2D< T >	lerp (typename Vector2D< T >::TParam a, const Vector2D< T > &b, typename Vector2D< T >::TParam t)
template<typename T , typename Char , typename Traits >
std::basic_ostream< Char, Traits > &	operator<< (std::basic_ostream< Char, Traits > &stream, const Vector2D< T > &b)
template<typename T , typename Char , typename Traits >
std::basic_istream< Char, Traits > &	operator>> (std::basic_istream< Char, Traits > &ioIStream, Vector2D< T > &b)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Vector2D< T > &b)
template<typename T >
Vector3D< T >::TValue	dot (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	cross (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
bool	operator== (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
bool	operator!= (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator+ (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator- (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator* (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator/ (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator+ (const Vector3D< T > &a, typename Vector3D< T >::TParam b)
template<typename T >
Vector3D< T >	operator- (const Vector3D< T > &a, typename Vector3D< T >::TParam b)
template<typename T >
Vector3D< T >	operator* (const Vector3D< T > &a, typename Vector3D< T >::TParam b)
template<typename T >
Vector3D< T >	operator/ (const Vector3D< T > &a, typename Vector3D< T >::TParam b)
template<typename T >
Vector3D< T >	operator+ (typename Vector3D< T >::TParam a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator- (typename Vector3D< T >::TParam a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	operator* (typename Vector3D< T >::TParam a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	pointwiseMin (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	pointwiseMax (const Vector3D< T > &a, const Vector3D< T > &b)
template<typename T >
Vector3D< T >	lerp (const Vector3D< T > &a, const Vector3D< T > &b, typename Vector3D< T >::TParam t)
template<typename T , typename Char , typename Traits >
std::basic_ostream< Char, Traits > &	operator<< (std::basic_ostream< Char, Traits > &stream, const Vector3D< T > &b)
template<typename T , typename Char , typename Traits >
std::basic_istream< Char, Traits > &	operator>> (std::basic_istream< Char, Traits > &stream, Vector3D< T > &b)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Vector3D< T > &b)
template<typename T >
Vector4D< T >::TValue	dot (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
bool	operator== (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
bool	operator!= (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	operator+ (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	operator- (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	operator* (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	operator/ (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	operator+ (const Vector4D< T > &a, typename Vector4D< T >::TParam b)
template<typename T >
Vector4D< T >	operator- (const Vector4D< T > &a, typename Vector4D< T >::TParam b)
template<typename T >
Vector4D< T >	operator* (const Vector4D< T > &a, typename Vector4D< T >::TParam b)
template<typename T >
Vector4D< T >	operator/ (const Vector4D< T > &a, typename Vector4D< T >::TParam b)
template<typename T >
Vector4D< T >	operator+ (typename Vector4D< T >::TParam a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	operator- (typename Vector4D< T >::TParam a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	operator* (typename Vector4D< T >::TParam a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	pointwiseMin (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	pointwiseMax (const Vector4D< T > &a, const Vector4D< T > &b)
template<typename T >
Vector4D< T >	lerp (const Vector4D< T > &a, const Vector4D< T > &b, typename Vector4D< T >::TParam t)
template<typename T , typename Char , typename Traits >
std::basic_ostream< Char, Traits > &	operator<< (std::basic_ostream< Char, Traits > &stream, const Vector4D< T > &b)
template<typename T , typename Char , typename Traits >
std::basic_istream< Char, Traits > &	operator>> (std::basic_istream< Char, Traits > &stream, Vector4D< T > &b)
template<typename T >
io::XmlOStream &	operator<< (io::XmlOStream &stream, const Vector4D< T > &b)
LASS_DLL bool LASS_CALL	operator== (const XY &iA, const XY &iB)
LASS_DLL bool LASS_CALL	operator== (const XY &iA, char iB)
LASS_DLL bool LASS_CALL	operator== (char iA, const XY &iB)
LASS_DLL bool LASS_CALL	operator== (const XY &iA, const std::string &iB)
LASS_DLL bool LASS_CALL	operator== (const std::string &iA, const XY &iB)
LASS_DLL bool LASS_CALL	operator!= (const XY &iA, const XY &iB)
LASS_DLL bool LASS_CALL	operator!= (const XY &iA, char iB)
LASS_DLL bool LASS_CALL	operator!= (char iA, const XY &iB)
LASS_DLL bool LASS_CALL	operator!= (const XY &iA, const std::string &iB)
LASS_DLL bool LASS_CALL	operator!= (const std::string &iA, const XY &iB)
LASS_DLL XY LASS_CALL	operator+ (const XY &iA, int iOffset)
LASS_DLL XY LASS_CALL	operator- (const XY &iA, int iOffset)
LASS_DLL bool LASS_CALL	operator== (const XYZ &iA, const XYZ &iB)
LASS_DLL bool LASS_CALL	operator== (const XYZ &iA, char iB)
LASS_DLL bool LASS_CALL	operator== (char iA, const XYZ &iB)
LASS_DLL bool LASS_CALL	operator== (const XYZ &iA, const std::string &iB)
LASS_DLL bool LASS_CALL	operator== (const std::string &iA, const XYZ &iB)
LASS_DLL bool LASS_CALL	operator!= (const XYZ &iA, const XYZ &iB)
LASS_DLL bool LASS_CALL	operator!= (const XYZ &iA, char iB)
LASS_DLL bool LASS_CALL	operator!= (char iA, const XYZ &iB)
LASS_DLL bool LASS_CALL	operator!= (const XYZ &iA, const std::string &iB)
LASS_DLL bool LASS_CALL	operator!= (const std::string &iA, const XYZ &iB)
LASS_DLL XYZ LASS_CALL	operator+ (const XYZ &iA, int iOffset)
LASS_DLL XYZ LASS_CALL	operator- (const XYZ &iA, int iOffset)
LASS_DLL bool LASS_CALL	operator== (const XYZW &iA, const XYZW &iB)
LASS_DLL bool LASS_CALL	operator== (const XYZW &iA, char iB)
LASS_DLL bool LASS_CALL	operator== (char iA, const XYZW &iB)
LASS_DLL bool LASS_CALL	operator== (const XYZW &iA, const std::string &iB)
LASS_DLL bool LASS_CALL	operator== (const std::string &iA, const XYZW &iB)
LASS_DLL bool LASS_CALL	operator!= (const XYZW &iA, const XYZW &iB)
LASS_DLL bool LASS_CALL	operator!= (const XYZW &iA, char iB)
LASS_DLL bool LASS_CALL	operator!= (char iA, const XYZW &iB)
LASS_DLL bool LASS_CALL	operator!= (const XYZW &iA, const std::string &iB)
LASS_DLL bool LASS_CALL	operator!= (const std::string &iA, const XYZW &iB)
LASS_DLL XYZW LASS_CALL	operator+ (const XYZW &iA, int iOffset)
LASS_DLL XYZW LASS_CALL	operator- (const XYZW &iA, int iOffset)

---

Detailed Description

set of geometrical primitives

Author:

Bram de Greve [BdG]

Date:

2003

lass::prim is the library for geometrical primitives and related constructions. It consists of structures and classes to represent primitives as vectors, points, lines, planes, polygons etc., some policy classes that can modify the implementation of some of these primitives, and a few related enumerations.

All primitives are templated with an underlying value type (think of floats, doubles, fixed point, ...). This value type can be set as by the template parameter T, and is typedef'ed in all primitives as TValue (convenient, isn't it? :). It's the subatomic unit (proton if you like) on which more complex types are built.

overview

I think the best way to explore this library, is to give an overview of its components. Here we go ...

primitives

If TValue is the proton, then vectors are the smallest atomic units in lass::prim you can build. Vectors represent a direction, a translation, and we have three of them in our library (with 2, 3 and 4 protons respective :):

• Vector2D: a two dimensional vector.
• Vector3D: a three dimensional vector.
• Vector4D: a four dimensional vector.

The above vectors are free vectors and have no position. To express the position of a location in space, we need points. we have two of these thingies. It's a little unusual to distinguish between vectors and points. Usually, only one is used for both concepts, whether they uses point or vector. Yet, these are totally different mathematical entities. You can add two vectors together, but you can't add two points (what would it mean?). Transforming a vector is different that a point (a vector will only be rotated, a point will also be translated). Points and vectors are clearly to be traited differently. This cries for different classes or structures. In C however, it has little use to do that, because of the lack of function overloading and strong type checking. However, here we are in C++ and the good news is: C++ does have overloading and strong type checking, so we can clearly distinguish between points and vectors in our code. And that's what we do here. For more info on this subject, I gladly refer to [1, 2, 3]. You can see the points as ions: vectors with some extra (or lacking) electrons: same number of protons (same dimension), but not completely the same thing.

• Point2D: a two dimensional point.
• Point3D: a three dimensional point.

One problem of not being able to add and scale points is not being able to use barycentric combinations. This is a linear combination of points in which the sum of all weight is equal to 1. The result of such a combination is a point and is mathematical sensefull. In [1], I didn't find a satisfying solution to this problem, because I wanted to limit myself to eucledian entities. To do barycentric combinations, I had to convert the points to vectors, do the combination, and the convert back to a point. Not only this is a bit clumsy, it didn't guarantee that the sum of the weights would be 1. In [2], I introduced homogenous points to solve this question. And they are also introduced in here. Homogenous points are with the sole capability to do barycentric combinations on points. You can see the homogenous points as points with some extra neutrons: pretty compatible.

• Point2DH: a homogenous representation of a two dimensional point.
• Point3DH: a homogenous representation of a three dimensional point.

So far for the essential building blocks of the more complex primitives. Until now we had the atoms, now we'll build moleculs. The simplest thing we can construct from it are axis-aligned-bounding-boxes.

• Aabb2D: a two dimensional axis aligned boundig box ... or a rectangle :)
• Aabb3D: a three dimensional axis aligned bounding box.

Objects of infinite size are lines and planes. We have them in parametric and cartesian versions.

• Line2D: a two dimensional line with different implementation policies, or a half plane.
• Line3D: a three dimensional parametric line.
• Plane3D: a three dimensional plane with different implementation policies, or a half space.

For the circular guys:

• Sphere3D: a sphere!

Objects of not so infinite size: line segments and rays.

• LineSegment2D: a two dimensional line segment
• LineSegment3D: a three dimensional line segment
• Ray2D: a two dimensional ray (or a half line)
• Ray3D: a three dimensional ray (or a half line in 3D)

Polygons and stuff:

• SimplePolygon2D: a two dimensional convex/concave polygon
• SimplePolygon3D: a three dimensional convex/concave polygon
• Triangle2D: a two dimensional polygon with three vertices
• Triangle3D: a three dimensional polygon with three vertices

policies

• NormalizingPolicy: Normalized, Unnormalized
• ParameterPolicy: Bounded, Unbounded
• MinMaxPolicy: StrictMinMax, AutoMinMax
• EquationPolicy: Cartesian, Parametric, Combined

enumerations

• Result
• Side
• Orientation

colors

• ColorRGBA: a four dimensional color with floating point channels red, green, blue and alpha.

iterators

These three classes are iterators over the different axes (components). You can use this instead of directly calling the .x or .y members of a vector. With these iterators, you can access those components through the operator[] .

• XY
• XYZ
• XYZW

---

Enumeration Type Documentation

enum lass::prim::Orientation

enumeration of clockwise versus counterclockwise

Author:

Bram de Greve [BdG]

Enumerator:

oInvalid	invalid state
oClockWise	clockwise orientation
oCounterClockWise	counterclockwise orientation

Definition at line 57 of file orientation.h.

enum lass::prim::Result

meta information on the result you have from an operation like an intersection .

..

Author:

[BdG]

Date:

2003

If you want to find the intersection of two lines 'a' and 'b', you expect a point as result. However, that's not always true. 'a' and 'b' can be coincident so that all points of 'a' and 'b' are intersection points, or they could be not intersecting at all so that you don't have an intersection point. 'Result' will tell you this. In this same example, it will return rNone if the lines are not intersectiong, rOne if there is exactly one intersection point, and rInfinite if the lines are coincident.

Unlike lass::util::Side, results can't be OR'ed. Afterall, what would 'rNone | rOne' mean?

rInvalid is the invalid state of Result, if you encounter this, something is wrong. Notice the difference with rNone that is a valid state (although it says there's no answer).

Note:

rOne does not mean there's only one point in the solution. No, it means there's exactly one solution possible, and the output parameter contains this solution. In the case of an AABB this one solution can contain infinite many points.

Enumerator:

rInvalid	0 is an invalid value, nothing is known.
rNone	operation has no answer, output arguments are meaningless
rOne	there's exactly one answer, 1 output argument contains the answer
rTwo	there are two solutions, 2 output argunemts contain the answers
rInfinite	there are infinite many solutions, output arguments are meaningless

Definition at line 73 of file result.h.

enum lass::prim::Side

Different sides of a surface.

Author:

[BdG]

Date:

2003

Not all possibilities make sense for all surfaces. e.g. in case of a plane, only sFront, sSurface, sBack mean something, and in case of a sphere or bounding box you have sInside, sSurface, sOutside.

Side can be OR'ed, like (sFront | sBack) means in the front or in the back of the surface. However, return values of Side Foo::classify(const Bar& iBar) normally won't use this, and the equality test of this enums doesn't understand this neither (which is btw, a good thing). So if you try to do 'if (foo.classify(bar) == sFront | sBack)', this will always evaluate to false, no matter what the return value of classify is.

This is a simple workaround though. In many cases (sFont | sBack) means exaclty the same as !sSurface (OK OK WHAT I JUST HAVE WRITTEN HERE IS NONSES, but you get the idea :) So, if you want the above test to work, you should test for 'if (foo.classify(bar) != sSurface)'

In the future there will be another work around with bit and mask operations that will be available in the util namespace, but I still have to code these :D

Enumerator:

sInvalid	0 is an invalid value
sFront	in front of the surface
sLeft	alias for sFront in 2D
sBack	in back of the surface
sRight	alias for sBack in 2D
sInside	inside the surface
sOutside	outside the surface
sSurface	right on the surface

Definition at line 78 of file side.h.

---

Function Documentation

template<typename T , class MMPa , class MMPb >

const Aabb2D<T, MMPa> lass::prim::operator+	(	const Aabb2D< T, MMPa > &	a,
		const Aabb2D< T, MMPb > &	b
	)			[related]

template<typename T , class MMP >

const Aabb2D<T, MMP> lass::prim::operator+	(	const Aabb2D< T, MMP > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T , class MMP >

const Aabb2D<T, MMP> lass::prim::operator+	(	const Point2D< T > &	a,
		const Aabb2D< T, MMP > &	b
	)			[related]

template<typename T >

const Aabb2D<T> lass::prim::aabb

(

const Point2D< T > &

point

)

[related]

Referenced by collides(), intersects(), lass::prim::Aabb3D< T, MinMaxPolicy >::operator<<(), and lass::prim::Aabb2D< T, MinMaxPolicy >::operator<<().

template<typename T , class MMP >

T lass::prim::distance	(	const Aabb2D< T, MMP > &	a,
		const Point2D< T > &	b
	)			[related]

Referenced by lass::prim::Triangle3D< T >::perimeter(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::perimeter(), and lass::prim::SimplePolygon2D< T, DegeneratePolicy >::perimeter().

template<typename T , class MMPa , class MMPb >

T lass::prim::distance	(	const Aabb2D< T, MMPa > &	a,
		const Aabb2D< T, MMPb > &	b
	)			[related]

template<typename T , class MMPa , class MMPb , class MMPr >

Result lass::prim::intersect	(	const Aabb2D< T, MMPa > &	a,
		const Aabb2D< T, MMPb > &	b,
		Aabb2D< T, MMPr > &	result
	)			[related]

Referenced by lass::spat::PlanarMesh::insertEdge(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::intersect(), lass::prim::Parallelogram3D< T >::intersect(), lass::prim::Line2D< T, EquationPolicy, NormalizingPolicy >::intersect(), and lass::prim::Triangle2D< T >::partialVoronoiArea().

template<typename T , class MMPa , class MMPb >

const bool lass::prim::intersects	(	const Aabb2D< T, MMPa > &	a,
		const Aabb2D< T, MMPb > &	b
	)			[related]

Referenced by lass::prim::Sphere3D< T >::intersects(), and intersects().

template<typename T , class MMP >

const bool lass::prim::intersects	(	const Aabb2D< T, MMP > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T , class MMP >

const bool lass::prim::intersects	(	const Point2D< T > &	a,
		const Aabb2D< T, MMP > &	b
	)			[related]

template<typename T , class MMPa , class MMPb >

const bool lass::prim::collides	(	const Aabb2D< T, MMPa > &	a,
		const Aabb2D< T, MMPb > &	b
	)			[related]

Referenced by lass::prim::Sphere3D< T >::collides(), collides(), and lass::prim::Aabb2D< T, MinMaxPolicy >::collides().

template<typename T , class MMP >

const bool lass::prim::collides	(	const Aabb2D< T, MMP > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T , class MMP >

const bool lass::prim::collides	(	const Point2D< T > &	a,
		const Aabb2D< T, MMP > &	b
	)			[related]

template<typename T , class MMP >

std::ostream& lass::prim::operator<<	(	std::ostream &	ioOStream,
		const Aabb2D< T, MMP > &	aabb
	)			[related]

template<typename T , class MMP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Aabb2D< T, MMP > &	aabb
	)			[related]

template<typename T , class MMP >

io::MatlabOStream& lass::prim::operator<<	(	io::MatlabOStream &	ioOStream,
		const Aabb2D< T, MMP > &	aabb
	)			[related]

template<typename T , typename MMP >

const bool lass::prim::intersects	(	const Triangle2D< T > &	triangle,
		const Aabb2D< T, MMP > &	box
	)			[inline]

Definition at line 73 of file aabb_2d_triangle_2d.h.

References aabb(), lass::prim::Aabb2D< T, MinMaxPolicy >::intersects(), LASS_ASSERT, lass::prim::Aabb2D< T, MinMaxPolicy >::max(), lass::prim::Aabb2D< T, MinMaxPolicy >::min(), and perpDot().

template<typename T , typename MMP >

const bool lass::prim::intersects	(	const Aabb2D< T, MMP > &	box,
		const Triangle2D< T > &	triangle
	)			[inline]

Definition at line 123 of file aabb_2d_triangle_2d.h.

References intersects().

template<typename T , typename MMP >

const bool lass::prim::collides	(	const Triangle2D< T > &	triangle,
		const Aabb2D< T, MMP > &	box
	)			[inline]

Definition at line 134 of file aabb_2d_triangle_2d.h.

References aabb(), lass::prim::Aabb2D< T, MinMaxPolicy >::collides(), LASS_ASSERT, lass::prim::Aabb2D< T, MinMaxPolicy >::max(), lass::prim::Aabb2D< T, MinMaxPolicy >::min(), and perpDot().

template<typename T , typename MMP >

const bool lass::prim::collides	(	const Aabb2D< T, MMP > &	box,
		const Triangle2D< T > &	triangle
	)			[inline]

Definition at line 184 of file aabb_2d_triangle_2d.h.

References collides().

template<typename T , class MMPa , class MMPb >

const Aabb3D<T, MMPa> lass::prim::operator+	(	const Aabb3D< T, MMPa > &	a,
		const Aabb3D< T, MMPb > &	b
	)			[related]

template<typename T , class MMP >

const Aabb3D<T, MMP> lass::prim::operator+	(	const Aabb3D< T, MMP > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T , class MMP >

const Aabb3D<T, MMP> lass::prim::operator+	(	const Point3D< T > &	a,
		const Aabb3D< T, MMP > &	b
	)			[related]

template<typename T >

const Aabb3D<T> lass::prim::aabb

(

const Point3D< T > &

point

)

[related]

Referenced by lass::spat::DefaultObjectTraits< ObjectType, AabbType, RayType, ObjectIterator >::objectAabb(), and lass::spat::DefaultSplitHeuristics< numObjectsPerLeaf >::split().

template<typename T , class MMP >

T lass::prim::distance	(	const Aabb3D< T, MMP > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T , class MMPa , class MMPb >

T lass::prim::distance	(	const Aabb3D< T, MMPa > &	a,
		const Aabb3D< T, MMPb > &	b
	)			[related]

template<typename T , class MMPa , class MMPb , class MMPr >

Result lass::prim::intersect	(	const Aabb3D< T, MMPa > &	a,
		const Aabb3D< T, MMPb > &	b,
		Aabb3D< T, MMPr > &	result
	)			[related]

template<typename T , class MMPa , class MMPb >

const bool lass::prim::intersects	(	const Aabb3D< T, MMPa > &	a,
		const Aabb3D< T, MMPb > &	b
	)			[inline]

Definition at line 650 of file aabb_3d.inl.

References lass::prim::Aabb3D< T, MinMaxPolicy >::intersects().

template<typename T , class MMP >

const bool lass::prim::intersects	(	const Aabb3D< T, MMP > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T , class MMP >

const bool lass::prim::intersects	(	const Point3D< T > &	a,
		const Aabb3D< T, MMP > &	b
	)			[related]

Referenced by lass::spat::DefaultObjectTraits< ObjectType, AabbType, RayType, ObjectIterator >::objectOverlaps().

template<typename T , class MMPa , class MMPb >

const bool lass::prim::collides	(	const Aabb3D< T, MMPa > &	a,
		const Aabb3D< T, MMPb > &	b
	)			[inline]

Definition at line 678 of file aabb_3d.inl.

References lass::prim::Aabb3D< T, MinMaxPolicy >::collides().

template<typename T , class MMP >

const bool lass::prim::collides	(	const Aabb3D< T, MMP > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T , class MMP >

const bool lass::prim::collides	(	const Point3D< T > &	a,
		const Aabb3D< T, MMP > &	b
	)			[related]

template<typename T , class MMP >

std::ostream& lass::prim::operator<<	(	std::ostream &	stream,
		const Aabb3D< T, MMP > &	aabb
	)			[related]

template<typename T , class MMP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Aabb3D< T, MMP > &	aabb
	)			[related]

template<typename T , class DegeneratePolicy >

bool lass::prim::triangulate	(	const SimplePolygon2D< T, DegenerationPolicy > &	iPolygon,
		std::vector< Triangle2D< T > > &	oTriangles
	)			[inline]

Deprecated:

Use triangulate from simple_polygon_2d_triangle_2d.h

Definition at line 59 of file algorithm.h.

LASS_DLL ColorRGBA LASS_CALL lass::prim::over	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)

placement of foreground iA in front of background iB.

iA is painted over iB and leaves only a that part of iB visible that isn't painted over: 1 - alphaA.

Precondition:

iA and iB are considered non-premultiplied

  alphaR = alphaA + (1 - alphaA) * alphaB.
  ColorR * alphaR = ColorA * alphaA + ColorB * alphaB * (1 - alphaA).

• T. Porter, T. Duff. Compositing Digital Images, Comp. Graphics, 18(3):253-259, July 1984.
• http://en.wikipedia.org/wiki/Alpha_channel

Definition at line 747 of file color_rgba.cpp.

References lass::prim::ColorRGBA::a, and lass::num::NumTraits< C >::one.

Referenced by lass::io::Image::over(), and lass::io::Image::rover().

LASS_DLL ColorRGBA LASS_CALL lass::prim::in	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)

part of iA inside iB.

iA is only painted where iB is present, and iB is not painted at all. This is the equivalent of only drawing clipped by the alpha channel of iB

Precondition:

iA and iB are considered non-premultiplied

  alphaR = alphaA * alphaB.
  ColorR = ColorA.

• T. Porter, T. Duff. Compositing Digital Images, Comp. Graphics, 18(3):253-259, July 1984.
• http://en.wikipedia.org/wiki/Alpha_channel

Definition at line 776 of file color_rgba.cpp.

References lass::prim::ColorRGBA::a.

Referenced by lass::io::Image::in(), and lass::io::Image::rin().

LASS_DLL ColorRGBA LASS_CALL lass::prim::out	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)

iA held out by iB, part of iA outside iB.

iA is only painted where iB is not present, and iB is not painted at all. This is the equivalent of only drawing clipped by the inverse alpha channel of iB.

Precondition:

iA and iB are considered non-premultiplied

  alphaR = alphaA * (1 - alphaB).
  ColorR = ColorA.

• T. Porter, T. Duff. Compositing Digital Images, Comp. Graphics, 18(3):253-259, July 1984.
• http://en.wikipedia.org/wiki/Alpha_channel

Definition at line 800 of file color_rgba.cpp.

References lass::prim::ColorRGBA::a, and lass::num::NumTraits< C >::one.

Referenced by lass::io::XmlOFile::open(), lass::io::Logger::openLog(), lass::io::Image::out(), lass::io::Image::rout(), and lass::util::stringCast().

LASS_DLL ColorRGBA LASS_CALL lass::prim::atop	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)

union of iA in iB and iB out iA.

iA atop iB includes iA where it's on top of iB, otherwise it's iB. But nothing outside iB is included.

Precondition:

iA and iB are considered non-premultiplied

  alphaR = alphaB.
  ColorR = ColorA * alphaA + ColorB * (1 - alphaA).

• T. Porter, T. Duff. Compositing Digital Images, Comp. Graphics, 18(3):253-259, July 1984.
• http://en.wikipedia.org/wiki/Alpha_channel

Definition at line 824 of file color_rgba.cpp.

References lass::prim::ColorRGBA::a, and lass::num::NumTraits< C >::one.

Referenced by lass::io::Image::atop(), and lass::io::Image::ratop().

LASS_DLL ColorRGBA LASS_CALL lass::prim::plus	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)

Precondition:

iA and iB are considered non-premultiplied

  alphaR = alphaA + alphaB
  colorR * alphaR = colorA * alphaA + colorB * alphaB.

• T. Porter, T. Duff. Compositing Digital Images, Comp. Graphics, 18(3):253-259, July 1984.
• http://en.wikipedia.org/wiki/Alpha_channel

Definition at line 845 of file color_rgba.cpp.

References lass::prim::ColorRGBA::a.

Referenced by lass::io::Image::plus().

LASS_DLL ColorRGBA LASS_CALL lass::prim::through	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)

iA seen through color filter iB.

Precondition:

iA and iB are considered non-premultiplied

  alphaR = alphaA.
  colorR = colorA * (1 - alphaB) + colorA * colorB * alphaB.

Definition at line 866 of file color_rgba.cpp.

References lass::prim::ColorRGBA::a, lass::prim::ColorRGBA::b, and lass::num::NumTraits< C >::one.

Referenced by lass::io::Image::rthrough(), and lass::io::Image::through().

LASS_DLL ColorRGBA::TValue LASS_CALL lass::prim::distance	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)

distance between non-non-premultiplied colours as 3D points (alpha channel is disregarded).

Returns:

num::sqrt(dR ** 2 + dG ** 2 + dB ** 2)

Definition at line 881 of file color_rgba.cpp.

References lass::prim::ColorRGBA::a, lass::prim::ColorRGBA::g, lass::prim::ColorRGBA::r, lass::num::sqr(), and sqrt().

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator+	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator-	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator*	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator/	(	const ColorRGBA &	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator+	(	ColorRGBA::TParam	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator-	(	ColorRGBA::TParam	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator*	(	ColorRGBA::TParam	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator/	(	ColorRGBA::TParam	iA,
		const ColorRGBA &	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator+	(	const ColorRGBA &	iA,
		ColorRGBA::TParam	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator-	(	const ColorRGBA &	iA,
		ColorRGBA::TParam	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator*	(	const ColorRGBA &	iA,
		ColorRGBA::TParam	iB
	)			[related]

LASS_DLL ColorRGBA LASS_CALL lass::prim::operator/	(	const ColorRGBA &	iA,
		ColorRGBA::TParam	iB
	)			[related]

template<typename T , class EP , class NP >

T lass::prim::signedDistance	(	const Point2D< T > &	iA,
		const Line2D< T, EP, NP > &	iB
	)			[inline]

template<typename T , class EPa , class NPa , class EPb , class NPb >

T lass::prim::signedDistance	(	const Line2D< T, EPa, NPa > &	iA,
		const Line2D< T, EPb, NPb > &	iB
	)			[inline]

template<typename T , class EPa , class NPa , class EPb , class NPb >

Result lass::prim::intersect	(	const Line2D< T, EPa, NPa > &	iA,
		const Line2D< T, EPb, NPb > &	iB,
		T &	oTa,
		T &	oTb
	)			[related]

template<typename T , class EPa , class NPa , class EPb , class NPb >

Result lass::prim::intersect	(	const Line2D< T, EPa, NPa > &	iA,
		const Line2D< T, EPb, NPb > &	iB,
		Point2D< T > &	oPoint
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Line2D< T, Cartesian > &	iLine
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Line2D< T, Parametric > &	iLine
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Line2D< T, Combined > &	iLine
	)			[related]

template<typename T , class NP >

std::ostream& lass::prim::operator<<	(	std::ostream &	oOStream,
		const Line3D< T, NP > &	iB
	)			[related]

template<typename T , class NP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	oOStream,
		const Line3D< T, NP > &	iB
	)			[related]

template<typename T , class PPa , class PPb >

bool lass::prim::operator==	(	const LineSegment2D< T, PPa > &	a,
		const LineSegment2D< T, PPb > &	b
	)			[related]

template<typename T , class PPa , class PPb >

bool lass::prim::operator!=	(	const LineSegment2D< T, PPa > &	a,
		const LineSegment2D< T, PPb > &	b
	)			[related]

template<typename T , class PP >

T lass::prim::squaredDistance	(	const LineSegment2D< T, PP > &	segment,
		const Point2D< T > &	point
	)			[inline]

Definition at line 164 of file line_segment_2d.inl.

References dot(), lass::prim::LineSegment2D< T, ParameterPolicy >::head(), lass::prim::LineSegment2D< T, ParameterPolicy >::tail(), and lass::prim::LineSegment2D< T, ParameterPolicy >::vector().

Referenced by closestsPoints(), lass::prim::Triangle2D< T >::distance(), distance(), and squaredDistance().

template<typename T , class PP >

T lass::prim::distance	(	const LineSegment2D< T, PP > &	segment,
		const Point2D< T > &	point
	)			[inline]

Definition at line 187 of file line_segment_2d.inl.

References sqrt(), and squaredDistance().

template<typename T , class PPa , class PPb >

Result lass::prim::intersect	(	const LineSegment2D< T, PPa > &	a,
		const LineSegment2D< T, PPb > &	b,
		T &	tA,
		T &	tB
	)			[related]

template<typename T , class PPa , class PPb >

Result lass::prim::intersect	(	const LineSegment2D< T, PPa > &	a,
		const LineSegment2D< T, PPb > &	b,
		Point2D< T > &	point
	)			[related]

template<typename T , class PP >

std::ostream& lass::prim::operator<<	(	std::ostream &	stream,
		const LineSegment2D< T, PP > &	segment
	)			[related]

template<typename T , class PP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const LineSegment2D< T, PP > &	segment
	)			[related]

template<typename T , class PP >

lass::io::MatlabOStream& lass::prim::operator<<	(	lass::io::MatlabOStream &	stream,
		const LineSegment2D< T, PP > &	segment
	)			[related]

template<typename T , class PPa , class PPb >

bool lass::prim::operator==	(	const LineSegment3D< T, PPa > &	iA,
		const LineSegment3D< T, PPb > &	iB
	)			[related]

template<typename T , class PPa , class PPb >

bool lass::prim::operator!=	(	const LineSegment3D< T, PPa > &	iA,
		const LineSegment3D< T, PPb > &	iB
	)			[related]

template<typename T , class PPa , class PPb >

Result lass::prim::intersect	(	const LineSegment3D< T, PPa > &	iA,
		const LineSegment3D< T, PPb > &	iB,
		T &	oTa,
		T &	oTb
	)			[inline]

template<typename T , class PPa , class PPb >

Result lass::prim::intersect	(	const LineSegment3D< T, PPa > &	iA,
		const LineSegment3D< T, PPb > &	iB,
		Point3D< T > &	oPoint
	)			[inline]

template<typename T , class PP >

std::ostream& lass::prim::operator<<	(	std::ostream &	oOStream,
		const LineSegment3D< T, PP > &	iB
	)			[related]

template<typename T , class PP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	oOStream,
		const LineSegment3D< T, PP > &	iB
	)			[related]

template<typename T , class PP >

lass::io::MatlabOStream& lass::prim::operator<<	(	lass::io::MatlabOStream &	oOStream,
		const LineSegment3D< T, PP > &	iLineSegment
	)			[inline]

template<typename T , class PP1 , class NP2 , class PP2 >

T lass::prim::distance	(	const LineSegment3D< T, PP1 > &	lineSegment,
		const Ray3D< T, NP2, PP2 > &	ray,
		const T &	tMin = T()
	)			[inline]

Definition at line 57 of file line_segment_3d_ray_3d.h.

References sqrt(), and squaredDistance().

template<typename T , class PP1 , class NP2 , class PP2 >

T lass::prim::squaredDistance	(	const LineSegment3D< T, PP1 > &	lineSegment,
		const Ray3D< T, NP2, PP2 > &	ray,
		const T &	tMin = T()
	)			[inline]

Definition at line 65 of file line_segment_3d_ray_3d.h.

References lass::num::abs(), cross(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::direction(), lass::prim::LineSegment3D< T, ParameterPolicy >::head(), lass::prim::LineSegment3D< T, ParameterPolicy >::point(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::point(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::project(), lass::prim::LineSegment3D< T, ParameterPolicy >::squaredDistance(), squaredDistance(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::support(), lass::prim::LineSegment3D< T, ParameterPolicy >::t(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::t(), lass::prim::LineSegment3D< T, ParameterPolicy >::tail(), and lass::prim::LineSegment3D< T, ParameterPolicy >::vector().

template<typename T , class PP1 , class NP2 , class PP2 >

T lass::prim::closestsPoints	(	const LineSegment3D< T, PP1 > &	lineSegment,
		const Ray3D< T, NP2, PP2 > &	ray,
		T &	tSeg,
		T &	tRay,
		const T &	tMin = T()
	)			[inline]

Definition at line 142 of file line_segment_3d_ray_3d.h.

References lass::num::abs(), lass::prim::LineSegment3D< T, ParameterPolicy >::closestsPoint(), cross(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::direction(), lass::prim::LineSegment3D< T, ParameterPolicy >::head(), lass::prim::LineSegment3D< T, ParameterPolicy >::point(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::point(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::project(), squaredDistance(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::support(), lass::prim::LineSegment3D< T, ParameterPolicy >::t(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::t(), lass::prim::LineSegment3D< T, ParameterPolicy >::tail(), and lass::prim::LineSegment3D< T, ParameterPolicy >::vector().

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Parallelogram3D< T > &	iParallelogram
	)			[related]

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	ioOStream,
		const Parallelogram3D< T > &	iParallelogram
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Plane3D< T, Cartesian > &	iPlane
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Plane3D< T, Parametric > &	iPlane
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Plane3D< T, Combined > &	iPlane
	)			[related]

template<typename T >

bool lass::prim::operator==	(	const Point2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T >

bool lass::prim::operator!=	(	const Point2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T >

Point2D<T> lass::prim::operator+	(	const Point2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Point2D<T> lass::prim::operator+	(	const Vector2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T >

Point2D<T> lass::prim::operator-	(	const Point2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::operator-	(	const Point2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T >

Point2D<T>::TValue lass::prim::distance	(	const Point2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T >

Point2D<T>::TValue lass::prim::squaredDistance	(	const Point2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

template<typename T >

Point2D<T> lass::prim::pointwiseMin	(	const Point2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

Referenced by lass::prim::AutoMinMax::checkMinMax(), lass::prim::StrictMinMax::checkMinMax(), lass::prim::Aabb3D< T, MinMaxPolicy >::intersect(), lass::prim::Aabb2D< T, MinMaxPolicy >::intersect(), lass::prim::Aabb3D< T, MinMaxPolicy >::operator+=(), lass::prim::Aabb2D< T, MinMaxPolicy >::operator+=(), lass::prim::AutoMinMax::setMax(), lass::prim::StrictMinMax::setMax(), and lass::prim::StrictMinMax::setMin().

template<typename T >

Point2D<T> lass::prim::pointwiseMax	(	const Point2D< T > &	a,
		const Point2D< T > &	b
	)			[related]

Referenced by lass::prim::AutoMinMax::checkMinMax(), lass::prim::Aabb3D< T, MinMaxPolicy >::collides(), lass::prim::Aabb3D< T, MinMaxPolicy >::distance(), lass::prim::Aabb2D< T, MinMaxPolicy >::distance(), lass::prim::Aabb3D< T, MinMaxPolicy >::intersect(), lass::prim::Aabb2D< T, MinMaxPolicy >::intersect(), lass::prim::Aabb3D< T, MinMaxPolicy >::intersects(), lass::prim::Aabb3D< T, MinMaxPolicy >::operator+=(), lass::prim::Aabb2D< T, MinMaxPolicy >::operator+=(), and lass::prim::AutoMinMax::setMin().

template<typename T >

Point2D<T> lass::prim::lerp	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		typename Point2D< T >::TParam	t
	)			[inline]

Referenced by lass::prim::Point3D< T >::lerp(), and lass::prim::Point2D< T >::lerp().

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	stream,
		const Point2D< T > &	b
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Point2D< T > &	b
	)			[related]

template<typename T >

std::istream& lass::prim::operator>>	(	std::istream &	stream,
		Point2D< T > &	b
	)			[related]

template<typename T >

lass::io::MatlabOStream& lass::prim::operator<<	(	lass::io::MatlabOStream &	stream,
		const Point2D< T > &	b
	)			[related]

template<typename T >

T lass::prim::doubleTriangleArea	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		const Point2D< T > &	c
	)			[related]

Referenced by lass::prim::Point2D< T >::ccw(), lass::prim::Ray2D< T, NormalizingPolicy, ParameterPolicy >::classify(), lass::prim::Point2D< T >::cw(), lass::spat::impl::BrutePointLocatorVerbose::findEdge(), lass::prim::Point2D< T >::inCircle(), lass::spat::PlanarMesh::insertEdge(), lass::spat::PlanarMesh::insertSite(), lass::prim::LineSegment2D< T, ParameterPolicy >::intersect(), lass::spat::impl::EdgeGatherer::makeConvexPolygon(), lass::spat::PlanarMesh::onEdge(), lass::spat::PlanarMesh::pointShoot(), lass::spat::PlanarMesh::pointWalk(), lass::spat::PlanarMesh::shoot(), lass::spat::PlanarMesh::snap(), lass::spat::PlanarMesh::walk(), lass::prim::Point2D< T >::weakCcw(), and lass::prim::Point2D< T >::weakCw().

template<typename T >

bool lass::prim::cw	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		const Point2D< T > &	c
	)			[related]

template<typename T >

bool lass::prim::ccw	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		const Point2D< T > &	c
	)			[related]

Referenced by lass::spat::PlanarMesh::fastLeftOf(), lass::spat::PlanarMesh::fastRightOf(), lass::spat::PlanarMesh::insertEdge(), lass::spat::PlanarMesh::leftOf(), lass::spat::impl::EdgeGatherer::makeRectangular(), and lass::spat::PlanarMesh::rightOf().

template<typename T >

bool lass::prim::weakCw	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		const Point2D< T > &	c
	)			[related]

template<typename T >

bool lass::prim::weakCcw	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		const Point2D< T > &	c
	)			[related]

Referenced by lass::spat::impl::EdgeGatherer::makeConvexPolygon(), lass::spat::PlanarMesh::pointWalk(), lass::spat::PlanarMesh::walk(), and lass::spat::PlanarMesh::walkTillConstrained().

template<typename T >

bool lass::prim::inCircle	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		const Point2D< T > &	c,
		const Point2D< T > &	d
	)			[related]

Referenced by lass::spat::PlanarMesh::fixEdge(), lass::spat::PlanarMesh::init4(), and lass::spat::PlanarMesh::insertSite().

template<typename T >

T lass::prim::preciseDoubleTriangleArea	(	const Point2D< T > &	a,
		const Point2D< T > &	b,
		const Point2D< T > &	c
	)			[inline]

Definition at line 389 of file point_2d.inl.

References perpDot().

template<typename T >

bool lass::prim::operator==	(	const Point2DH< T > &	iA,
		const Point2DH< T > &	iB
	)			[related]

template<typename T >

bool lass::prim::operator!=	(	const Point2DH< T > &	iA,
		const Point2DH< T > &	iB
	)			[related]

template<typename T >

Point2DH<T> lass::prim::operator+	(	const Point2DH< T > &	iA,
		const Point2DH< T > &	iB
	)			[related]

template<typename T >

Point2DH<T> lass::prim::operator+	(	const Point2DH< T > &	iA,
		const Point2D< T > &	iB
	)			[related]

template<typename T >

Point2DH<T> lass::prim::operator+	(	const Point2D< T > &	iA,
		const Point2DH< T > &	iB
	)			[related]

template<typename T >

Point2DH<T> lass::prim::operator+	(	const Point2D< T > &	iA,
		const Point2D< T > &	iB
	)			[related]

template<typename T >

Point2DH<T> lass::prim::operator-	(	const Point2DH< T > &	iA,
		const Point2DH< T > &	iB
	)			[related]

template<typename T >

Point2DH<T> lass::prim::operator*	(	const Point2DH< T > &	iA,
		typename Point2DH< T >::TParam	iB
	)			[inline]

template<typename T >

Point2DH<T> lass::prim::operator/	(	const Point2DH< T > &	iA,
		typename Point2DH< T >::TParam	iB
	)			[inline]

template<typename T >

Point2DH<T> lass::prim::operator*	(	typename Point2DH< T >::TParam	iA,
		const Point2DH< T > &	iB
	)			[inline]

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	oOStream,
		const Point2DH< T > &	iB
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	oOStream,
		const Point2DH< T > &	iB
	)			[related]

template<typename T >

std::istream& lass::prim::operator>>	(	std::istream &	ioIStream,
		Point2DH< T > &	oB
	)			[related]

template<typename T >

bool lass::prim::operator==	(	const Point3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

bool lass::prim::operator!=	(	const Point3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

Point3D<T> lass::prim::operator+	(	const Point3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Point3D<T> lass::prim::operator+	(	const Vector3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

Point3D<T> lass::prim::operator-	(	const Point3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::operator-	(	const Point3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

Point3D<T>::TValue lass::prim::distance	(	const Point3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

Point3D<T>::TValue lass::prim::squaredDistance	(	const Point3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

Point3D<T> lass::prim::pointwiseMin	(	const Point3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

Point3D<T> lass::prim::pointwiseMax	(	const Point3D< T > &	a,
		const Point3D< T > &	b
	)			[related]

template<typename T >

Point3D<T> lass::prim::lerp	(	const Point3D< T > &	a,
		const Point3D< T > &	b,
		typename Point3D< T >::TParam	t
	)			[inline]

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	stream,
		const Point3D< T > &	b
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Point3D< T > &	b
	)			[related]

template<typename T >

std::istream& lass::prim::operator>>	(	std::istream &	stream,
		Point3D< T > &	b
	)			[related]

template<typename T >

bool lass::prim::operator==	(	const Point3DH< T > &	iA,
		const Point3DH< T > &	iB
	)			[related]

template<typename T >

bool lass::prim::operator!=	(	const Point3DH< T > &	iA,
		const Point3DH< T > &	iB
	)			[related]

template<typename T >

Point3DH<T> lass::prim::operator+	(	const Point3DH< T > &	iA,
		const Point3DH< T > &	iB
	)			[related]

template<typename T >

Point3DH<T> lass::prim::operator-	(	const Point3DH< T > &	iA,
		Point3DH< T > &	iB
	)			[inline]

template<typename T >

Point3DH<T> lass::prim::operator*	(	const Point3DH< T > &	iA,
		typename Point3DH< T >::TParam	iB
	)			[inline]

template<typename T >

Point3DH<T> lass::prim::operator/	(	const Point3DH< T > &	iA,
		typename Point3DH< T >::TParam	iB
	)			[inline]

template<typename T >

Point3DH<T> lass::prim::operator*	(	typename Point3DH< T >::TParam	iA,
		const Point3DH< T > &	iB
	)			[inline]

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	oOStream,
		const Point3DH< T > &	iB
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	oOStream,
		const Point3DH< T > &	iB
	)			[related]

template<typename T >

std::istream& lass::prim::operator>>	(	std::istream &	ioIStream,
		Point3DH< T > &	oB
	)			[related]

template<typename T >

Point3DH<T> lass::prim::operator+	(	const Point3D< T > &	iA,
		const Point3D< T > &	iB
	)			[inline]

Definition at line 144 of file point_3dh.h.

template<typename T >

Point3DH<T> lass::prim::operator*	(	typename Point3D< T >::TParam	iA,
		const Point3D< T > &	iB
	)			[inline]

Definition at line 148 of file point_3dh.h.

template<typename T >

Point3DH<T> lass::prim::operator*	(	const Point3D< T > &	iA,
		typename Point3D< T >::TParam	iB
	)			[inline]

Definition at line 152 of file point_3dh.h.

template<typename T , class NP , class PP >

std::ostream& lass::prim::operator<<	(	std::ostream &	oOStream,
		const Ray2D< T, NP, PP > &	iB
	)			[inline]

template<typename T , class NP , class PP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	oOStream,
		const Ray2D< T, NP, PP > &	iB
	)			[inline]

template<typename T , class NP , class PP >

std::ostream& lass::prim::operator<<	(	std::ostream &	oOStream,
		const Ray3D< T, NP, PP > &	iB
	)			[inline]

template<typename T , class NP , class PP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	oOStream,
		const Ray3D< T, NP, PP > &	iB
	)			[inline]

template<typename T , class DP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const SimplePolygon2D< T, DP > &	iPolygon
	)			[related]

template<typename T , class DP >

std::ostream& lass::prim::operator<<	(	std::ostream &	ioOStream,
		const SimplePolygon2D< T, DP > &	iPolygon
	)			[related]

template<typename T , class DP >

lass::io::MatlabOStream& lass::prim::operator<<	(	lass::io::MatlabOStream &	oOStream,
		const SimplePolygon2D< T, DP > &	iPolygon
	)			[related]

template<typename T , class DP >

bool lass::prim::set_difference	(	const SimplePolygon2D< T, DP > &	iPolygonA,
		const SimplePolygon2D< T, DP > &	iPolygonB,
		std::vector< SimplePolygon2D< T, DP > > &	oPolygonsC
	)			[inline]

C = A \ B.

template<typename T , class DP >

bool lass::prim::set_union	(	const SimplePolygon2D< T, DP > &	iPolygonA,
		const SimplePolygon2D< T, DP > &	iPolygonB,
		std::vector< SimplePolygon2D< T, DP > > &	oPolygonsC
	)			[inline]

C = A U B.

template<typename T , class DP >

bool lass::prim::set_intersect	(	const SimplePolygon2D< T, DP > &	iPolygonA,
		const SimplePolygon2D< T, DP > &	iPolygonB,
		std::vector< SimplePolygon2D< T, DP > > &	oPolygonsC
	)			[inline]

C = (A U B) \ (A \ B) \ (B \ A).

template<typename T , class DegeneratePolicy , typename OutputIterator >

OutputIterator lass::prim::triangulate	(	const SimplePolygon2D< T, DegenerationPolicy > &	polygon,
		OutputIterator	triangles
	)			[inline]

Definition at line 56 of file simple_polygon_2d_triangle_2d.h.

References lass::prim::SimplePolygon2D< T, DegeneratePolicy >::isConvex(), LASS_THROW, and lass::prim::SimplePolygon2D< T, DegeneratePolicy >::size().

template<typename T , class EP , class NP , class PP >

Result lass::prim::intersect	(	const SimplePolygon3D< T, EP, NP > &	iPolygon,
		const LineSegment3D< T, PP > &	iSegment,
		T &	oT,
		const T &	iMinT = 0
	)			[related]

Referenced by lass::spat::DefaultAabbRayTraits< lass::prim::Aabb3D, lass::prim::Ray3D >::aabbIntersect(), lass::spat::DefaultObjectTraits< ObjectType, AabbType, RayType, ObjectIterator >::objectIntersect(), and lass::spat::DefaultObjectTraits< ObjectType, AabbType, RayType, ObjectIterator >::objectIntersects().

template<typename T , class EP1 , class NP1 , class EP2 , class NP2 >

SimplePolygon3D<T, EP2, NP2> lass::prim::clip	(	const Plane3D< T, EP1, NP1 > &	iPlane,
		const SimplePolygon3D< T, EP2, NP2 > &	iPolygon
	)			[related]

Referenced by lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::clip().

template<typename T , class EP , class NP >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const SimplePolygon3D< T, EP, NP > &	iPolygon
	)			[related]

template<typename T , class EP , class NP >

std::ostream& lass::prim::operator<<	(	std::ostream &	ioOStream,
		const SimplePolygon3D< T, EP, NP > &	iPolygon
	)			[related]

template<typename T >

const T lass::prim::squaredDistance	(	const Sphere3D< T > &	sphere,
		const Point3D< T > &	point
	)			[related]

Referenced by lass::spat::QuadTree< ObjectType, ObjectTraits >::doNearestNeighbour(), lass::spat::AabpTree< ObjectType, ObjectTraits, SplitHeuristics >::doNearestNeighbour(), lass::spat::AabbTree< ObjectType, ObjectTraits, SplitHeuristics >::doNearestNeighbour(), lass::spat::impl::BrutePointLocatorVerbose::findEdge(), lass::spat::impl::BrutePointLocator::findEdge(), lass::spat::PlanarMesh::insertSite(), lass::spat::PlanarMesh::locate(), lass::spat::DefaultObjectTraits< ObjectType, AabbType, RayType, ObjectIterator >::objectSquaredDistance(), and lass::spat::PlanarMesh::walkIntersections().

template<typename T >

const T lass::prim::distance	(	const Sphere3D< T > &	sphere,
		const Point3D< T > &	point
	)			[related]

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	oOStream,
		const Sphere3D< T > &	iB
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Sphere3D< T > &	iB
	)			[related]

template<typename T >

Transformation2D<T> lass::prim::concatenate	(	const Transformation2D< T > &	first,
		const Transformation2D< T > &	second
	)			[related]

template<typename T >

Vector2D<T> lass::prim::transform	(	const Vector2D< T > &	subject,
		const Transformation2D< T > &	transformation
	)			[related]

Referenced by lass::prim::Transformation3D< T >::transform().

template<typename T >

Point2D<T> lass::prim::transform	(	const Point2D< T > &	subject,
		const Transformation2D< T > &	transformation
	)			[related]

template<typename T >

Vector2D<T> lass::prim::normalTransform	(	const Vector2D< T > &	subject,
		const Transformation2D< T > &	transformation
	)			[related]

template<typename T >

std::pair<Vector2D<T>, T> lass::prim::normalTransform	(	const std::pair< Vector2D< T >, T > &	subject,
		const Transformation2D< T > &	transformation
	)			[related]

template<typename T , typename Char , typename Traits >

std::basic_ostream<Char, Traits>& lass::prim::operator<<	(	std::basic_ostream< Char, Traits > &	stream,
		const Transformation2D< T > &	transformation
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Transformation2D< T > &	transformation
	)			[related]

template<typename T >

Transformation3D<T> lass::prim::concatenate	(	const Transformation3D< T > &	first,
		const Transformation3D< T > &	second
	)			[related]

Referenced by lass::io::Image::transformColors().

template<typename T >

Vector3D<T> lass::prim::transform	(	const Vector3D< T > &	subject,
		const Transformation3D< T > &	transformation
	)			[related]

template<typename T >

Point3D<T> lass::prim::transform	(	const Point3D< T > &	subject,
		const Transformation3D< T > &	transformation
	)			[related]

Referenced by lass::io::Image::atop(), lass::io::Image::in(), lass::num::DataTraitsSequence< SequenceType >::multiplyAccumulate(), lass::io::Image::out(), lass::io::Image::over(), lass::io::Image::plus(), lass::io::Image::ratop(), lass::io::Image::rin(), lass::io::Image::rout(), lass::io::Image::rover(), lass::io::Image::rthrough(), lass::num::DataTraitsSequence< SequenceType >::scale(), lass::io::Image::through(), lass::stde::transform_r(), and lass::io::Image::transformColors().

template<typename T >

Vector3D<T> lass::prim::normalTransform	(	const Vector3D< T > &	subject,
		const Transformation3D< T > &	transformation
	)			[related]

template<typename T >

std::pair<Vector3D<T>, T> lass::prim::normalTransform	(	const std::pair< Vector3D< T >, T > &	subject,
		const Transformation3D< T > &	transformation
	)			[related]

template<typename T , typename Char , typename Traits >

std::basic_ostream<Char, Traits>& lass::prim::operator<<	(	std::basic_ostream< Char, Traits > &	stream,
		const Transformation3D< T > &	transformation
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Transformation3D< T > &	transformation
	)			[related]

template<typename T >

const T lass::prim::distance	(	const Triangle2D< T > &	triangle,
		const Point2D< T > &	point
	)			[related]

Referenced by lass::stde::static_vector< T, maxsize >::assign(), lass::num::DataTraitsSequence< SequenceType >::dimension(), lass::io::Image::filterMedian(), lass::num::SplineLinear< ScalarType, DataType, DataTraits >::findNode(), lass::num::SplineCubic< ScalarType, DataType, DataTraits >::findNode(), lass::num::SplineBezierPath< ScalarType, DataType, DataTraits >::findNode(), lass::spat::KdTree< ObjectType, ObjectTraits >::findSplitAxis(), lass::stde::static_vector< T, maxsize >::insert(), lass::spat::PlanarMesh::insertEdge(), lass::spat::KdTree< ObjectType, ObjectTraits >::KdTree(), lass::num::impl::laplaceToZHelper(), lass::python::impl::pyBuildList(), lass::python::impl::pyBuildTuple(), lass::python::impl::PyIteratorRangeImpl< M >::PyIteratorRange_Length(), lass::num::RandomMT19937::seed(), lass::stde::iterator_range< iterator_type >::size(), lass::spat::DefaultSplitHeuristics< numObjectsPerLeaf >::split(), lass::prim::Transformation2D< T >::Transformation2D(), and lass::prim::Transformation3D< T >::Transformation3D().

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Triangle2D< T > &	iTriangle
	)			[related]

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	ioOStream,
		const Triangle2D< T > &	iTriangle
	)			[related]

template<typename T >

lass::io::MatlabOStream& lass::prim::operator<<	(	lass::io::MatlabOStream &	oOStream,
		const Triangle2D< T > &	iTriangle
	)			[related]

template<typename T >

T lass::prim::partialVoronoiArea	(	const Triangle2D< T >	iT,
		int	iIndexOfVertex
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	ioOStream,
		const Triangle3D< T > &	iTriangle
	)			[related]

template<typename T >

std::ostream& lass::prim::operator<<	(	std::ostream &	ioOStream,
		const Triangle3D< T > &	iTriangle
	)			[related]

template<typename T >

Vector2D<T>::TValue lass::prim::dot	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

Referenced by lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::clip(), lass::prim::Vector2D< T >::cos(), lass::prim::impl::Plane3DParametric< T, NormalizingPolicy >::equation(), lass::prim::impl::Plane3DCombined< T, NormalizingPolicy >::equation(), lass::prim::impl::Plane3DCartesian< T, NormalizingPolicy >::equation(), lass::prim::impl::Line2DParametric< T, NormalizingPolicy >::equation(), lass::prim::impl::Line2DCombined< T, NormalizingPolicy >::equation(), lass::prim::impl::Line2DCartesian< T, NormalizingPolicy >::equation(), lass::prim::impl::Plane3DImplDetail::generateCartesian(), lass::prim::impl::Plane3DImplDetail::generateReciprocal(), lass::prim::impl::Line2DParametric< T, NormalizingPolicy >::getCartesian(), lass::spat::PlanarMesh::insertEdge(), lass::prim::impl::RaySphere< Normalized >::intersect(), lass::prim::impl::RaySphere< NormalizingPolicy >::intersect(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::intersect(), lass::prim::Parallelogram3D< T >::intersect(), lass::prim::impl::intersectTriangle3D(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::isReflex(), lass::prim::impl::Line2DCartesian< T, NormalizingPolicy >::Line2DCartesian(), lass::prim::impl::Line2DCombined< T, NormalizingPolicy >::Line2DCombined(), lass::spat::impl::EdgeGatherer::makeRectangular(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::project(), lass::prim::Ray2D< T, NormalizingPolicy, ParameterPolicy >::project(), lass::prim::Line3D< T, NormalizingPolicy >::project(), lass::prim::impl::Line2DParametric< T, NormalizingPolicy >::project(), lass::prim::impl::Plane3DParametric< T, NormalizingPolicy >::reject(), lass::prim::impl::Plane3DCombined< T, NormalizingPolicy >::reject(), lass::prim::impl::Plane3DCartesian< T, NormalizingPolicy >::reject(), lass::prim::impl::Line2DCombined< T, NormalizingPolicy >::reject(), lass::prim::impl::Line2DCartesian< T, NormalizingPolicy >::reject(), lass::spat::PlanarMesh::setOrientedEdgeHandle(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::signedArea(), lass::prim::TriangleMesh3D< T, BoundingVolumeHierarchy, SplitHeuristics >::smoothNormals(), lass::prim::Triangle2D< T >::squaredDistance(), squaredDistance(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::surfaceCentroid(), lass::prim::Ray3D< T, NormalizingPolicy, ParameterPolicy >::t(), lass::prim::Ray2D< T, NormalizingPolicy, ParameterPolicy >::t(), lass::prim::LineSegment3D< T, ParameterPolicy >::t(), lass::prim::LineSegment2D< T, ParameterPolicy >::t(), lass::prim::Line3D< T, NormalizingPolicy >::t(), lass::prim::impl::Line2DParametric< T, NormalizingPolicy >::t(), lass::prim::impl::Line2DCombined< T, NormalizingPolicy >::t(), lass::prim::impl::Line2DCartesian< T, NormalizingPolicy >::t(), lass::prim::impl::Plane3DParametric< T, NormalizingPolicy >::uv(), lass::prim::impl::Plane3DCombined< T, NormalizingPolicy >::uv(), lass::prim::impl::Plane3DCartesian< T, NormalizingPolicy >::uv(), and lass::prim::Parallelogram3D< T >::uv().

template<typename T >

Vector2D<T>::TValue lass::prim::perpDot	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

Referenced by collides(), lass::prim::Triangle2D< T >::contains(), lass::prim::Line2D< T, EquationPolicy, NormalizingPolicy >::distance(), lass::prim::Point2D< T >::doubleTriangleArea(), lass::spat::impl::fastIntersect(), lass::prim::SimplePolygon2D< T, DegeneratePolicy >::fixDegenerate(), lass::prim::LineSegment2D< T, ParameterPolicy >::intersect(), lass::prim::Ray2D< T, NormalizingPolicy, ParameterPolicy >::intersect(), lass::prim::Line2D< T, EquationPolicy, NormalizingPolicy >::intersect(), lass::prim::impl::intersectEdge2D(), intersects(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::isConvex(), lass::prim::SimplePolygon2D< T, DegeneratePolicy >::isConvex(), lass::prim::SimplePolygon2D< T, DegeneratePolicy >::isReflex(), preciseDoubleTriangleArea(), lass::prim::Triangle2D< T >::signedArea(), lass::prim::SimplePolygon2D< T, DegeneratePolicy >::signedArea(), and lass::prim::SimplePolygon2D< T, DegeneratePolicy >::surfaceCentroid().

template<typename T >

Vector2D<T>::TValue lass::prim::cos	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

Referenced by lass::prim::Vector3D< T >::random(), lass::prim::Transformation3D< T >::rotation(), lass::prim::Transformation2D< T >::rotation(), and lass::prim::TriangleMesh3D< T, BoundingVolumeHierarchy, SplitHeuristics >::smoothNormals().

template<typename T >

bool lass::prim::operator==	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

bool lass::prim::operator!=	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::operator+	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::operator-	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::operator*	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::operator/	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::operator+	(	const Vector2D< T > &	a,
		typename Vector2D< T >::TParam	b
	)			[inline]

template<typename T >

Vector2D<T> lass::prim::operator-	(	const Vector2D< T > &	a,
		typename Vector2D< T >::TParam	b
	)			[inline]

template<typename T >

Vector2D<T> lass::prim::operator*	(	const Vector2D< T > &	a,
		typename Vector2D< T >::TParam	b
	)			[inline]

template<typename T >

Vector2D<T> lass::prim::operator/	(	const Vector2D< T > &	a,
		typename Vector2D< T >::TParam	b
	)			[inline]

template<typename T >

Vector2D<T> lass::prim::operator+	(	typename Vector2D< T >::TParam	a,
		const Vector2D< T > &	b
	)			[inline]

template<typename T >

Vector2D<T> lass::prim::operator-	(	typename Vector2D< T >::TParam	a,
		const Vector2D< T > &	b
	)			[inline]

template<typename T >

Vector2D<T> lass::prim::operator*	(	typename Vector2D< T >::TParam	a,
		const Vector2D< T > &	b
	)			[inline]

template<typename T >

Vector2D<T> lass::prim::pointwiseMin	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::pointwiseMax	(	const Vector2D< T > &	a,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector2D<T> lass::prim::lerp	(	typename Vector2D< T >::TParam	a,
		const Vector2D< T > &	b,
		typename Vector2D< T >::TParam	t
	)			[inline]

template<typename T , typename Char , typename Traits >

std::basic_ostream<Char, Traits>& lass::prim::operator<<	(	std::basic_ostream< Char, Traits > &	stream,
		const Vector2D< T > &	b
	)			[related]

template<typename T , typename Char , typename Traits >

std::basic_istream<Char, Traits>& lass::prim::operator>>	(	std::basic_istream< Char, Traits > &	ioIStream,
		Vector2D< T > &	b
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Vector2D< T > &	b
	)			[related]

template<typename T >

Vector3D<T>::TValue lass::prim::dot	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::cross	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

Referenced by lass::prim::TriangleMesh3D< T, BoundingVolumeHierarchy, SplitHeuristics >::area(), closestsPoints(), lass::prim::impl::Plane3DImplDetail::generateCartesian(), lass::prim::impl::Plane3DImplDetail::generateDirections(), lass::prim::TriangleMesh3D< T, BoundingVolumeHierarchy, SplitHeuristics >::Triangle::intersect(), lass::prim::Parallelogram3D< T >::intersect(), lass::prim::impl::intersectTriangle3D(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::isReflex(), lass::prim::impl::Plane3DParametric< T, NormalizingPolicy >::isValid(), lass::prim::impl::Plane3DCombined< T, NormalizingPolicy >::isValid(), lass::prim::Parallelogram3D< T >::plane(), lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::signedArea(), lass::prim::TriangleMesh3D< T, BoundingVolumeHierarchy, SplitHeuristics >::smoothNormals(), lass::prim::Triangle3D< T >::squaredArea(), lass::prim::Parallelogram3D< T >::squaredArea(), squaredDistance(), and lass::prim::SimplePolygon3D< T, PlaneEquationPolicy, PlaneNormalizingPolicy >::surfaceCentroid().

template<typename T >

bool lass::prim::operator==	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

bool lass::prim::operator!=	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::operator+	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::operator-	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::operator*	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::operator/	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::operator+	(	const Vector3D< T > &	a,
		typename Vector3D< T >::TParam	b
	)			[inline]

template<typename T >

Vector3D<T> lass::prim::operator-	(	const Vector3D< T > &	a,
		typename Vector3D< T >::TParam	b
	)			[inline]

template<typename T >

Vector3D<T> lass::prim::operator*	(	const Vector3D< T > &	a,
		typename Vector3D< T >::TParam	b
	)			[inline]

template<typename T >

Vector3D<T> lass::prim::operator/	(	const Vector3D< T > &	a,
		typename Vector3D< T >::TParam	b
	)			[inline]

template<typename T >

Vector3D<T> lass::prim::operator+	(	typename Vector3D< T >::TParam	a,
		const Vector3D< T > &	b
	)			[inline]

template<typename T >

Vector3D<T> lass::prim::operator-	(	typename Vector3D< T >::TParam	a,
		const Vector3D< T > &	b
	)			[inline]

template<typename T >

Vector3D<T> lass::prim::operator*	(	typename Vector3D< T >::TParam	a,
		const Vector3D< T > &	b
	)			[inline]

template<typename T >

Vector3D<T> lass::prim::pointwiseMin	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::pointwiseMax	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector3D<T> lass::prim::lerp	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b,
		typename Vector3D< T >::TParam	t
	)			[inline]

template<typename T , typename Char , typename Traits >

std::basic_ostream<Char, Traits>& lass::prim::operator<<	(	std::basic_ostream< Char, Traits > &	stream,
		const Vector3D< T > &	b
	)			[related]

template<typename T , typename Char , typename Traits >

std::basic_istream<Char, Traits>& lass::prim::operator>>	(	std::basic_istream< Char, Traits > &	stream,
		Vector3D< T > &	b
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Vector3D< T > &	b
	)			[related]

template<typename T >

Vector4D<T>::TValue lass::prim::dot	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

Referenced by lass::spat::barycenters(), and lass::spat::PlanarMesh::snap().

template<typename T >

bool lass::prim::operator==	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

bool lass::prim::operator!=	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

Vector4D<T> lass::prim::operator+	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

Vector4D<T> lass::prim::operator-	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

Vector4D<T> lass::prim::operator*	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

Vector4D<T> lass::prim::operator/	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

Vector4D<T> lass::prim::operator+	(	const Vector4D< T > &	a,
		typename Vector4D< T >::TParam	b
	)			[inline]

template<typename T >

Vector4D<T> lass::prim::operator-	(	const Vector4D< T > &	a,
		typename Vector4D< T >::TParam	b
	)			[inline]

template<typename T >

Vector4D<T> lass::prim::operator*	(	const Vector4D< T > &	a,
		typename Vector4D< T >::TParam	b
	)			[inline]

template<typename T >

Vector4D<T> lass::prim::operator/	(	const Vector4D< T > &	a,
		typename Vector4D< T >::TParam	b
	)			[inline]

template<typename T >

Vector4D<T> lass::prim::operator+	(	typename Vector4D< T >::TParam	a,
		const Vector4D< T > &	b
	)			[inline]

template<typename T >

Vector4D<T> lass::prim::operator-	(	typename Vector4D< T >::TParam	a,
		const Vector4D< T > &	b
	)			[inline]

template<typename T >

Vector4D<T> lass::prim::operator*	(	typename Vector4D< T >::TParam	a,
		const Vector4D< T > &	b
	)			[inline]

template<typename T >

Vector4D<T> lass::prim::pointwiseMin	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

Vector4D<T> lass::prim::pointwiseMax	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b
	)			[related]

template<typename T >

Vector4D<T> lass::prim::lerp	(	const Vector4D< T > &	a,
		const Vector4D< T > &	b,
		typename Vector4D< T >::TParam	t
	)			[inline]

template<typename T , typename Char , typename Traits >

std::basic_ostream<Char, Traits>& lass::prim::operator<<	(	std::basic_ostream< Char, Traits > &	stream,
		const Vector4D< T > &	b
	)			[related]

template<typename T , typename Char , typename Traits >

std::basic_istream<Char, Traits>& lass::prim::operator>>	(	std::basic_istream< Char, Traits > &	stream,
		Vector4D< T > &	b
	)			[related]

template<typename T >

io::XmlOStream& lass::prim::operator<<	(	io::XmlOStream &	stream,
		const Vector4D< T > &	b
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XY &	iA,
		const XY &	iB
	)

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XY &	iA,
		char	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	char	iA,
		const XY &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XY &	iA,
		const std::string &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const std::string &	iA,
		const XY &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XY &	iA,
		const XY &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XY &	iA,
		char	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	char	iA,
		const XY &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XY &	iA,
		const std::string &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const std::string &	iA,
		const XY &	iB
	)			[related]

LASS_DLL XY LASS_CALL lass::prim::operator+	(	const XY &	iA,
		int	iOffset
	)			[related]

LASS_DLL XY LASS_CALL lass::prim::operator-	(	const XY &	iA,
		int	iOffset
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XYZ &	iA,
		const XYZ &	iB
	)

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XYZ &	iA,
		char	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	char	iA,
		const XYZ &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XYZ &	iA,
		const std::string &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const std::string &	iA,
		const XYZ &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XYZ &	iA,
		const XYZ &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XYZ &	iA,
		char	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	char	iA,
		const XYZ &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XYZ &	iA,
		const std::string &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const std::string &	iA,
		const XYZ &	iB
	)			[related]

LASS_DLL XYZ LASS_CALL lass::prim::operator+	(	const XYZ &	iA,
		int	iOffset
	)			[related]

LASS_DLL XYZ LASS_CALL lass::prim::operator-	(	const XYZ &	iA,
		int	iOffset
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XYZW &	iA,
		const XYZW &	iB
	)

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XYZW &	iA,
		char	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	char	iA,
		const XYZW &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const XYZW &	iA,
		const std::string &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator==	(	const std::string &	iA,
		const XYZW &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XYZW &	iA,
		const XYZW &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XYZW &	iA,
		char	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	char	iA,
		const XYZW &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const XYZW &	iA,
		const std::string &	iB
	)			[related]

LASS_DLL bool LASS_CALL lass::prim::operator!=	(	const std::string &	iA,
		const XYZW &	iB
	)			[related]

LASS_DLL XYZW LASS_CALL lass::prim::operator+	(	const XYZW &	iA,
		int	iOffset
	)			[related]

LASS_DLL XYZW LASS_CALL lass::prim::operator-	(	const XYZW &	iA,
		int	iOffset
	)			[related]