vector_2d.inl

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/** @file
 *  @author Bram de Greve (bramz@users.sourceforge.net)
 *  @author Tom De Muer (tomdemuer@users.sourceforge.net)
 *
 *  *** BEGIN LICENSE INFORMATION ***
 *  
 *  The contents of this file are subject to the Common Public Attribution License 
 *  Version 1.0 (the "License"); you may not use this file except in compliance with 
 *  the License. You may obtain a copy of the License at 
 *  http://lass.sourceforge.net/cpal-license. The License is based on the 
 *  Mozilla Public License Version 1.1 but Sections 14 and 15 have been added to cover 
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 *  the Original Developer. In addition, Exhibit A has been modified to be consistent 
 *  with Exhibit B.
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 *  Software distributed under the License is distributed on an "AS IS" basis, WITHOUT 
 *  WARRANTY OF ANY KIND, either express or implied. See the License for the specific 
 *  language governing rights and limitations under the License.
 *  
 *  The Original Code is LASS - Library of Assembled Shared Sources.
 *  
 *  The Initial Developer of the Original Code is Bram de Greve and Tom De Muer.
 *  The Original Developer is the Initial Developer.
 *  
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 *  Copyright (C) 2004-2007 the Initial Developer.
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 *  *** END LICENSE INFORMATION ***
 */



#ifndef LASS_GUARDIAN_OF_INCLUSION_PRIM_VECTOR_2D_INL
#define LASS_GUARDIAN_OF_INCLUSION_PRIM_VECTOR_2D_INL




#include "vector_2d.h"
#include "../num/basic_ops.h"
#include "../num/distribution.h"

namespace lass
{

namespace prim
{

template<typename T> inline
Vector2D<T>::Vector2D():
    x(T()),
    y(T())
{
}



template<typename T> inline
Vector2D<T>::Vector2D(TParam x, TParam y):
    x(x),
    y(y)
{
}



template <typename T>
template <typename U>
Vector2D<T>::Vector2D(const Vector2D<U>& other):
    x(static_cast<TValue>(other.x)),
    y(static_cast<TValue>(other.y))
{
}



template <typename T>
template <typename U>
Vector2D<T>::Vector2D(const U& x, const U& y):
    x(static_cast<TValue>(x)),
    y(static_cast<TValue>(y))
{
}



template<typename T> inline
typename Vector2D<T>::TConstReference Vector2D<T>::operator[](size_t index) const
{
    LASS_ASSERT(index < dimension);
    return *(&x + index);
}



template<typename T> inline
typename Vector2D<T>::TReference Vector2D<T>::operator[](size_t index)
{
    LASS_ASSERT(index < dimension);
    return *(&x + index);
}



/** Wrap index around range.
 */
template<typename T> inline
typename Vector2D<T>::TConstReference Vector2D<T>::at(signed index) const
{
    return *(&x + num::mod(index, dimension));
}



/** Wrap index around range.
 */
template<typename T> inline
typename Vector2D<T>::TReference Vector2D<T>::at(signed index)
{
    return *(&x + num::mod(index, dimension));
}



/** A weird way to get back the same object
 */
template<typename T> inline
const Vector2D<T>& Vector2D<T>::operator+() const
{
    return *this;
}



template<typename T> inline
const Vector2D<T> Vector2D<T>::operator-() const
{
    return Vector2D(-x, -y);
}



/** componentwise addition
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator+=(const Vector2D<T>& other)
{
    x += other.x;
    y += other.y;
    return *this;
}



/** componentwise subtraction
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator-=(const Vector2D<T>& other)
{
    x -= other.x;
    y -= other.y;
    return *this;
}



/** Componentwise multiplication.
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator*=(const Vector2D<T>& other)
{
    x *= other.x;
    y *= other.y;
    return *this;
}



/** Componentwise division.
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator/=(const Vector2D<T>& other)
{
    x /= other.x;
    y /= other.y;
    return *this;
}



/** add other to each component of this.
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator+=(TParam other)
{
    x += other;
    y += other;
    return *this;
}



/** subtract other of each component of this.
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator-=(TParam other)
{
    x -= other;
    y -= other;
    return *this;
}



/** multiply each component of this with other.
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator*=(TParam other)
{
    x *= other;
    y *= other;
    return *this;
}



/** divide each component of this by other.
 */
template<typename T> inline
Vector2D<T>& Vector2D<T>::operator/=(TParam other)
{
    x /= other;
    y /= other;
    return *this;
}



/** Return true if all the components are (exactly!) zero
 */
template<typename T> inline
const bool Vector2D<T>::isZero() const
{
    return x == TNumTraits::zero && y == TNumTraits::zero;
}



/** Return true if at least one of the components is NaN
 */
template<typename T> inline
const bool Vector2D<T>::isNaN() const
{
    return num::isNaN(x) || num::isNaN(y);
}



/** Return squared norm of vector.
 */
template<typename T> inline
const typename Vector2D<T>::TValue Vector2D<T>::squaredNorm() const
{
    return dot(*this, *this);
}



/** Return norm of vector.
 */
template<typename T> inline
const typename Vector2D<T>::TValue Vector2D<T>::norm() const
{
    return ::lass::num::sqrt(squaredNorm());
}



/** return a unit vector with same direction/sense as this vector.
 *
 * <i>The normalized vector of <b>X</b> is a vector in the same direction but with norm (length) 1.
 * It is denoted <b>X^</b> and given by <b>X^</b> = <b>X</b> / |<b>X</b>|</i>,
 * http://mathworld.wolfram.com/NormalizedVector.html.
 */
template<typename T>
const Vector2D<T> Vector2D<T>::normal() const
{
    Vector2D<T> result(*this);
    result.normalize();
    return result;
}



/** return the reciprocal version of this vector
 */
template<typename T>
const Vector2D<T> Vector2D<T>::reciprocal() const
{
    Vector2D<T> result(TNumTraits::one, TNumTraits::one);
    result /= *this;
    return result;
}



/** return the vector perpendicular to this one, 90° to the left.
 */
template<typename T> inline
const Vector2D<T> Vector2D<T>::perp() const
{
    return Vector2D<T>(-y, x);
}



/** Project vector on this one
 */
template <typename T>
const Vector2D<T> Vector2D<T>::project(const Vector2D<T>& other) const
{
    Vector2D<T> result(*this);
    result *= dot(other, *this);
    result /= squaredNorm();
    return result;
}



/** Project vector on this one
 */
template<typename T> inline
const Vector2D<T> Vector2D<T>::reject(const Vector2D<T>& other) const
{
    return other - project(other);
}



template<typename T> inline
const Vector2D<T> Vector2D<T>::reflect(const Vector2D<T>& other) const
{
    return 2 * project(other) - other;
}



/** apply a function to every component
 */
template <typename T>
const Vector2D<T> Vector2D<T>::transform(T (*op)(T)) const
{
    return Vector2D<T>(op(x), op(y));
}



/** Normalize vector.
 */
template<typename T> inline
void Vector2D<T>::normalize()
{
    *this /= norm();
}



/** Random unit vector
 */
template <typename T>
template <class RandomGenerator>
Vector2D<T> Vector2D<T>::random(RandomGenerator& generator)
{
    num::DistributionUniform<T, RandomGenerator, num::rtRightOpen> distribution(
        generator, TNumTraits::zero, 2 * TNumTraits::pi);
    const TValue theta = distribution();
    return Vector2D<T>(num::cos(theta), num::sin(theta));
}



/** dot product.
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
typename Vector2D<T>::TValue dot(const Vector2D<T>& a, const Vector2D<T>& b)
{
    return a.x * b.x + a.y * b.y;
}



/** returns cosine of angle between both vectors.
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
typename Vector2D<T>::TValue cos(const Vector2D<T>& a, const Vector2D<T>& b)
{
    return dot(a, b) / num::sqrt(a.squaredNorm() * b.squaredNorm());
}



/** perp dot product (cross product for 2D vectors).
 *  @relates lass::prim::Vector2D
 *
 *  <i>The "perp dot product" for <b>a</b> and <b>b</b> vectors in the plane is a modification of
 *  the two-dimensional dot product in which a is replaced by the perpendicular vector rotated 90°
 *  to the left defined by Hill (1994)</i>, http://mathworld.wolfram.com/PerpDotProduct.html.
 *
 *  It reminds a lot to the 3D cross product, as its result is equal to the z-value of the
 *  cross product of a and b extended to 3D space by setting their z-value to 0:
 *  Vector3D<T> c = cross(Vector3D<T>(a.x, a.y, 0), Vector3D<T>(b.x, b.y, 0)).  We know of this
 *  that c.x and c.y are both zero, and that c.z equals the perp dot product between a and b.
 */
template<typename T> inline
typename Vector2D<T>::TValue perpDot(const Vector2D<T>& a, const Vector2D<T>& b)
{
    return a.x * b.y - a.y * b.x;
}



/** @relates lass::prim::Vector2D
 */
template<typename T> inline
bool operator==(const Vector2D<T>& a, const Vector2D<T>& b)
{
    return a.x == b.x && a.y == b.y;
}



/** @relates lass::prim::Vector2D
 */
template<typename T> inline
bool operator!=(const Vector2D<T>& a, const Vector2D<T>& b)
{
    return !(a == b);
}



/** componentwise addition
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator+(const Vector2D<T>& a, const Vector2D<T>& b)
{
    Vector2D<T> result(a);
    result += b;
    return result;
}



/** componentwise subtraction
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator-(const Vector2D<T>& a, const Vector2D<T>& b)
{
    Vector2D<T> result(a);
    result -= b;
    return result;
}



/** Componentwise multiplication
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator*(const Vector2D<T>& a, const Vector2D<T>& b)
{
    Vector2D<T> result(a);
    result *= b;
    return result;
}



/** Componentwise division
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator/(const Vector2D<T>& a, const Vector2D<T>& b)
{
    Vector2D<T> result(a);
    result /= b;
    return result;
}



/** add b to all components of a.
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator+(const Vector2D<T>& a, typename Vector2D<T>::TParam b)
{
    Vector2D<T> result(a);
    result += b;
    return result;
}



/** subtract b of all components of a.
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator-(const Vector2D<T>& a, typename Vector2D<T>::TParam b)
{
    Vector2D<T> result(a);
    result -= b;
    return result;
}



/** muliply all components of a by b
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator*(const Vector2D<T>& a, typename Vector2D<T>::TParam b)
{
    Vector2D<T> result(a);
    result *= b;
    return result;
}



/** divide all components of a by b
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator/(const Vector2D<T>& a, typename Vector2D<T>::TParam b)
{
    Vector2D<T> result(a);
    result /= b;
    return result;
}



/** add a to all components of b
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator+(typename Vector2D<T>::TParam a, const Vector2D<T>& b)
{
    Vector2D<T> result(b);
    result += a;
    return result;
}



/** subtract a of all components of b
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator-(typename Vector2D<T>::TParam a, const Vector2D<T>& b)
{
    Vector2D<T> result(-b);
    result += a;
    return result;
}



/** multiply all components of b with a
 *  @relates lass::prim::Vector2D
 */
template<typename T> inline
Vector2D<T> operator*(typename Vector2D<T>::TParam a, const Vector2D<T>& b)
{
    Vector2D<T> result(b);
    result *= a;
    return result;
}



/** return a vector with, for each coordinate, the minimum value of @a a and @a b
 *  @relates lass::prim::Vector2D
 */
template<typename T>
inline Vector2D<T> pointwiseMin(const Vector2D<T>& a, const Vector2D<T>& b)
{
    return Vector2D<T>(std::min(a.x, b.x), std::min(a.y, b.y));
}



/** return a vector with, for each coordinate, the maximum value of @a a and @a b
 *  @relates lass::prim::Vector2D
 */
template<typename T>
inline Vector2D<T> pointwiseMax(const Vector2D<T>& a, const Vector2D<T>& b)
{
    return Vector2D<T>(std::max(a.x, b.x), std::max(a.y, b.y));
}



/** interpolate linearly between two vectors: a + t * (b - a)
 *  @relates lass::prim::Vector2D
 */
template<typename T>
inline Vector2D<T> lerp(const Vector2D<T>& a, const Vector2D<T>& b, typename Vector2D<T>::TParam t)
{
    Vector2D<T> result = b;
    result -= a;
    result *= t;
    result += a;
    return result;
}



/** @relates lass::prim::Vector2D
 */
template<typename T, typename Char, typename Traits>
std::basic_ostream<Char, Traits>& operator<<(
        std::basic_ostream<Char, Traits>& stream, const Vector2D<T>& b)
{
    LASS_ENFORCE_STREAM(stream) << "(" << b.x << ", " << b.y  << ")";

    return stream;
}



/** @relates lass::prim::Vector2D
 */
template<typename T, typename Char, typename Traits>
std::basic_istream<Char, Traits>& operator>>(
        std::basic_istream<Char, Traits>& stream, Vector2D<T>& b)
{
    Vector2D<T> result;

    Char c = 0;
    stream >> c;
    if (c != '(')
    {
        stream.clear(std::ios::failbit);
        return stream;
    }

    c = 0;
    stream >> result.x >> c;

    if (c != ',')
    {
        stream.clear(std::ios::failbit);
        return stream;
    }

    c = 0;
    stream >> result.y >> c;
    if (c != ')')
    {
        stream.clear(std::ios::failbit);
        return stream;
    }

    b = result;
    return stream;
}



/** @relates lass::prim::Vector2D
 */
template<typename T>
io::XmlOStream& operator<<(io::XmlOStream& stream, const Vector2D<T>& b)
{
    LASS_ENFORCE_STREAM(stream)
        << "<Vector2D>" << b.x << " " << b.y << "</Vector2D>\n";
    return stream;
}



}

}

#endif