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//============================================================================
//
// 3-dim real vector class
// $Id$
// Copyright (C) 2004 Georg Drenkhahn
//
// This file is free software; you can redistribute it and/or modify it under
// the terms of the GNU General Public License version 2 as published by the
// Free Software Foundation.
//
//============================================================================
#ifndef VEC3_H
#define VEC3_H
#include <valarray>
/** @brief 3-dimensional real vector
*
* Implements regular 3 dimensional (space) vectors including the common inner
* scalar product (2 norm) and the cross product. @a T may be any integer or
* float data type which is an acceptable template argument of std::valarray. */
template<typename T>
class vec3 : public std::valarray<T>
{
public:
/** Default constructor */
vec3();
/** Constructor with initial element values */
vec3(const T&, const T&, const T&);
/** Copy constructor */
vec3(const std::valarray<T>&);
/** Copy constructor */
vec3(const std::slice_array<T>&);
/** Normalize the vector to have a norm of 1. @return Normalized vector if
* length is non-zero and otherwise the zero vector. */
vec3& normalize();
/** Rotate the vector (*this) in positive mathematical direction around the
* direction given by @a r. The norm of @a r specifies the rotation angle in
* radians.
* @param r Rotation vector.
* @return Rotated vector. */
vec3& rotate(const vec3& r);
/*--- static funcions ---*/
/** @param a first vector
* @param b second vector
* @return Cosine of the angle between @a a and @a b. If norm(@a a)==0 or
* norm(@a b)==0 the global variable errno is set to EDOM and NAN (or
* std::numeric_limits<T>::quiet_NaN()) is returned. */
static T cos_angle(const vec3& a, const vec3& b);
/** @brief Returns the angle between vectors @c a and @a b but with respect
* to a preferred rotation direction @a c.
*
* @param a First vector for angle. Must be | @a a |>0 otherwises NAN is
* returned.
* @param b Second vector for angle. Must be | @a b |>0 otherwises NAN is
* returned.
* @param c Indicates the rotation direction. @a c can be any vector which is
* not part of the plane spanned by @a a and @a b. If | @a c | = 0 the
* smalest possible angle angle is returned.
* @return Angle in radians between 0 and 2*Pi or NAN if | @a a |=0 or | @a b
* |=0.
*
* For @a a not parallel to @a b and @a a not antiparallel to @a b the 2
* vectors @a a,@a b span a unique plane in the 3-dimensional space. Let @b
* n<sub>1</sub> and @b n<sub>2</sub> be the two possible normal vectors for
* this plane with |@b n<sub>i</sub> |=1, i={1,2} and @b n<sub>1</sub> = -@b
* n<sub>2</sub> .
*
* Let further @a a and @a b enclose an angle alpha in [0,Pi], then there is
* one i in {1,2} so that (alpha*@b n<sub>i</sub> x @a a) * @a b = 0. This
* means @a a rotated by the rotation vector alpha*@b n<sub>i</sub> is
* parallel to @a b. One could also rotate @a a by (2*Pi-alpha)*(-@b
* n<sub>i</sub>) to acomplish the same transformation with
* ((2*Pi-alpha)*(-@b n<sub>i</sub>) x @a a) * @a b = 0
*
* The vector @a c defines the direction of the normal vector to take as
* reference. If @a c * @b n<sub>i</sub> > 0 alpha is returned and otherwise
* 2*Pi-alpha. If @a a parallel to @a b or @a a parallel to @a b the choice
* of @a c does not matter. */
static T angle(const vec3& a, const vec3& b, const vec3& c);
/*--- static inline funcions ---*/
/** Norm of argument vector.
* @param a vector.
* @return | @a a | */
static T norm(const vec3& a);
/** Angle between @a a and @a b.
* @param a fist vector. Must be | @a a | > 0 otherwises NAN is returned.
* @param b second vector. Must be | @a b | > 0 otherwises NAN is returned.
* @return Angle in radians between 0 and Pi or NAN if | @a a | = 0 or | @a b
* | = 0. */
static T angle(const vec3& a, const vec3& b);
/** Cross product of @a a and @a b.
* @param a fist vector.
* @param b second vector.
* @return Cross product of argument vectors @a a x @a b. */
static vec3 crossprod(const vec3& a, const vec3& b);
/** Normalized version of argument vector.
* @param a vector.
* @return @a a / | @a a | for | @a a | > 0 and otherwise the zero vector
* (=@a a). In the latter case the global variable errno is set to EDOM. */
static vec3 normalized(vec3 a);
};
/*--- inline member functions ---*/
template<typename T>
inline vec3<T>::vec3()
: std::valarray<T>(3)
{}
template<typename T>
inline vec3<T>::vec3(const T& a, const T& b, const T& c)
: std::valarray<T>(3)
{
(*this)[0] = a;
(*this)[1] = b;
(*this)[2] = c;
}
template<typename T>
inline vec3<T>::vec3(const std::valarray<T>& a)
: std::valarray<T>(a)
{
}
template<typename T>
inline vec3<T>::vec3(const std::slice_array<T>& a)
: std::valarray<T>(a)
{
}
/*--- inline non-member operators ---*/
/** @param a first vector summand
* @param b second vector summand
* @return Sum vector of vectors @a a and @a b. */
template<typename T>
inline vec3<T> operator+(vec3<T> a, const vec3<T>& b)
{
a += b; /* valarray<T>::operator+=(const valarray<T>&) */
return a;
}
/** @param a first vector multiplicant
* @param b second vector multiplicant
* @return Scalar product of vectors @a a and @a b. */
template<typename T>
inline T operator*(vec3<T> a, const vec3<T>& b)
{
a *= b; /* valarray<T>::operator*=(const T&) */
return a.sum();
}
/** @param a scalar multiplicant
* @param b vector operand
* @return Product vector of scalar @a a and vector @a b. */
template<typename T>
inline vec3<T> operator*(const T& a, vec3<T> b)
{
b *= a; /* valarray<T>::operator*=(const T&) */
return b;
}
/** @param a vector operand
* @param b scalar multiplicant
* @return Product vector of scalar @a b and vector @a a. */
template<typename T>
inline vec3<T> operator*(vec3<T> a, const T& b)
{
return b*a; /* vec3<T>::operator*(const T&, vec3<T>) */
}
/*--- static inline funcions ---*/
template<typename T>
inline T vec3<T>::norm(const vec3<T>& a)
{
return sqrt(a*a);
}
template<typename T>
inline T vec3<T>::angle(const vec3<T>& a, const vec3<T>& b)
{
// returns NAN if cos_angle() returns NAN (TODO: test this case)
return acos(cos_angle(a,b));
}
template<typename T>
inline vec3<T> vec3<T>::crossprod(const vec3<T>& a, const vec3<T>& b)
{
return vec3<T>(
a[1]*b[2] - a[2]*b[1],
a[2]*b[0] - a[0]*b[2],
a[0]*b[1] - a[1]*b[0]);
}
template<typename T>
inline vec3<T> vec3<T>::normalized(vec3<T> a)
{
return a.normalize();
}
#endif
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