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Diffstat (limited to 'kscreensaver/kdesavers/vec3.h')
| -rw-r--r-- | kscreensaver/kdesavers/vec3.h | 214 |
1 files changed, 214 insertions, 0 deletions
diff --git a/kscreensaver/kdesavers/vec3.h b/kscreensaver/kdesavers/vec3.h new file mode 100644 index 00000000..62aeb8ed --- /dev/null +++ b/kscreensaver/kdesavers/vec3.h @@ -0,0 +1,214 @@ +//============================================================================ +// +// 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 |