diff options
Diffstat (limited to 'graphics/asymptote/algebra3.cc')
-rw-r--r-- | graphics/asymptote/algebra3.cc | 1610 |
1 files changed, 1610 insertions, 0 deletions
diff --git a/graphics/asymptote/algebra3.cc b/graphics/asymptote/algebra3.cc new file mode 100644 index 0000000000..4b76942815 --- /dev/null +++ b/graphics/asymptote/algebra3.cc @@ -0,0 +1,1610 @@ +/* + + algebra3.cpp, algebra3.h - C++ Vector and Matrix Algebra routines + + GLUI User Interface Toolkit (LGPL) + Copyright (c) 1998 Paul Rademacher + + WWW: http://sourceforge.net/projects/glui/ + Forums: http://sourceforge.net/forum/?group_id=92496 + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, write to the Free Software + Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + +*/ + +/************************************************************************** + + There are three vector classes and two matrix classes: vec2, vec3, + vec4, mat3, and mat4. + + All the standard arithmetic operations are defined, with '*' + for dot product of two vectors and multiplication of two matrices, + and '^' for cross product of two vectors. + + Additional functions include length(), normalize(), homogenize for + vectors, and print(), set(), apply() for all classes. + + There is a function transpose() for matrices, but note that it + does not actually change the matrix, + + When multiplied with a matrix, a vector is treated as a row vector + if it precedes the matrix (v*M), and as a column vector if it + follows the matrix (M*v). + + Matrices are stored in row-major form. + + A vector of one dimension (2d, 3d, or 4d) can be cast to a vector + of a higher or lower dimension. If casting to a higher dimension, + the new component is set by default to 1.0, unless a value is + specified: + vec3 a(1.0, 2.0, 3.0 ); + vec4 b( a, 4.0 ); // now b == {1.0, 2.0, 3.0, 4.0}; + When casting to a lower dimension, the vector is homogenized in + the lower dimension. E.g., if a 4d {X,Y,Z,W} is cast to 3d, the + resulting vector is {X/W, Y/W, Z/W}. It is up to the user to + insure the fourth component is not zero before casting. + + There are also the following function for building matrices: + identity2D(), translation2D(), rotation2D(), + scaling2D(), identity3D(), translation3D(), + rotation3D(), rotation3Drad(), scaling3D(), + perspective3D() + + + --------------------------------------------------------------------- + + Author: Jean-Francois DOUEg + Revised: Paul Rademacher + Version 3.2 - Feb 1998 + Revised: Nigel Stewart (GLUI Code Cleaning) + +**************************************************************************/ + +#include "algebra3.h" +#include <cmath> + +static const double radians=std::acos(-1)/180.0; + +#ifdef VEC_ERROR_FATAL +#ifndef VEC_ERROR +#define VEC_ERROR(E) { printf( "VERROR %s\n", E ); exit(1); } +#endif +#else +#ifndef VEC_ERROR +#define VEC_ERROR(E) { printf( "VERROR %s\n", E ); } +#endif +#endif + +/**************************************************************** + * * + * vec2 Member functions * + * * + ****************************************************************/ + +/******************** vec2 CONSTRUCTORS ********************/ + +vec2::vec2() +{ + n[VX] = n[VY] = 0.0; +} + +vec2::vec2(float x, float y) +{ + n[VX] = x; + n[VY] = y; +} + +vec2::vec2(const vec2 &v) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; +} + +vec2::vec2(const vec3 &v) // it is up to caller to avoid divide-by-zero +{ + n[VX] = v.n[VX]/v.n[VZ]; + n[VY] = v.n[VY]/v.n[VZ]; +} + +vec2::vec2(const vec3 &v, int dropAxis) +{ + switch (dropAxis) + { + case VX: n[VX] = v.n[VY]; n[VY] = v.n[VZ]; break; + case VY: n[VX] = v.n[VX]; n[VY] = v.n[VZ]; break; + default: n[VX] = v.n[VX]; n[VY] = v.n[VY]; break; + } +} + +/******************** vec2 ASSIGNMENT OPERATORS ******************/ + +vec2 & vec2::operator=(const vec2 &v) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + return *this; +} + +vec2 & vec2::operator+=(const vec2 &v) +{ + n[VX] += v.n[VX]; + n[VY] += v.n[VY]; + return *this; +} + +vec2 & vec2::operator-=(const vec2 &v) +{ + n[VX] -= v.n[VX]; + n[VY] -= v.n[VY]; + return *this; +} + +vec2 &vec2::operator*=(float d) +{ + n[VX] *= d; + n[VY] *= d; + return *this; +} + +vec2 &vec2::operator/=(float d) +{ + float d_inv = 1.0f/d; + n[VX] *= d_inv; + n[VY] *= d_inv; + return *this; +} + +float &vec2::operator[](int i) +{ + if (i < VX || i > VY) + //VEC_ERROR("vec2 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("vec2 [] operator: illegal access" ); + return n[i]; +} + +const float &vec2::operator[](int i) const +{ + if (i < VX || i > VY) + //VEC_ERROR("vec2 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("vec2 [] operator: illegal access" ); + + return n[i]; +} + +/******************** vec2 SPECIAL FUNCTIONS ********************/ + +float vec2::length() const +{ + return (float) sqrt(length2()); +} + +float vec2::length2() const +{ + return n[VX]*n[VX] + n[VY]*n[VY]; +} + +vec2 &vec2::normalize() // it is up to caller to avoid divide-by-zero +{ + *this /= length(); + return *this; +} + +vec2 &vec2::apply(V_FCT_PTR fct) +{ + n[VX] = (*fct)(n[VX]); + n[VY] = (*fct)(n[VY]); + return *this; +} + +void vec2::set( float x, float y ) +{ + n[VX] = x; n[VY] = y; +} + +/******************** vec2 FRIENDS *****************************/ + +vec2 operator-(const vec2 &a) +{ + return vec2(-a.n[VX],-a.n[VY]); +} + +vec2 operator+(const vec2 &a, const vec2& b) +{ + return vec2(a.n[VX]+b.n[VX], a.n[VY]+b.n[VY]); +} + +vec2 operator-(const vec2 &a, const vec2& b) +{ + return vec2(a.n[VX]-b.n[VX], a.n[VY]-b.n[VY]); +} + +vec2 operator*(const vec2 &a, float d) +{ + return vec2(d*a.n[VX], d*a.n[VY]); +} + +vec2 operator*(float d, const vec2 &a) +{ + return a*d; +} + +vec2 operator*(const mat3 &a, const vec2 &v) +{ + vec3 av; + + av.n[VX] = a.v[0].n[VX]*v.n[VX] + a.v[0].n[VY]*v.n[VY] + a.v[0].n[VZ]; + av.n[VY] = a.v[1].n[VX]*v.n[VX] + a.v[1].n[VY]*v.n[VY] + a.v[1].n[VZ]; + av.n[VZ] = a.v[2].n[VX]*v.n[VX] + a.v[2].n[VY]*v.n[VY] + a.v[2].n[VZ]; + + return av; +} + +vec2 operator*(const vec2 &v, const mat3 &a) +{ + return a.transpose() * v; +} + +vec3 operator*(const mat3 &a, const vec3 &v) +{ + vec3 av; + + av.n[VX] = a.v[0].n[VX]*v.n[VX] + a.v[0].n[VY]*v.n[VY] + a.v[0].n[VZ]*v.n[VZ]; + av.n[VY] = a.v[1].n[VX]*v.n[VX] + a.v[1].n[VY]*v.n[VY] + a.v[1].n[VZ]*v.n[VZ]; + av.n[VZ] = a.v[2].n[VX]*v.n[VX] + a.v[2].n[VY]*v.n[VY] + a.v[2].n[VZ]*v.n[VZ]; + + return av; +} + +vec3 operator*(const vec3 &v, const mat3 &a) +{ + return a.transpose() * v; +} + +float operator*(const vec2 &a, const vec2 &b) +{ + return a.n[VX]*b.n[VX] + a.n[VY]*b.n[VY]; +} + +vec2 operator/(const vec2 &a, float d) +{ + float d_inv = 1.0f/d; + return vec2(a.n[VX]*d_inv, a.n[VY]*d_inv); +} + +vec3 operator^(const vec2 &a, const vec2 &b) +{ + return vec3(0.0, 0.0, a.n[VX] * b.n[VY] - b.n[VX] * a.n[VY]); +} + +int operator==(const vec2 &a, const vec2 &b) +{ + return (a.n[VX] == b.n[VX]) && (a.n[VY] == b.n[VY]); +} + +int operator!=(const vec2 &a, const vec2 &b) +{ + return !(a == b); +} + +/*ostream& operator << (ostream& s, vec2& v) +{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << " |"; } +*/ + +/*istream& operator >> (istream& s, vec2& v) { + vec2 v_tmp; + char c = ' '; + + while (isspace(c)) + s >> c; + // The vectors can be formatted either as x y or | x y | + if (c == '|') { + s >> v_tmp[VX] >> v_tmp[VY]; + while (s >> c && isspace(c)) ; + if (c != '|') + ;//s.set(_bad); + } + else { + s.putback(c); + s >> v_tmp[VX] >> v_tmp[VY]; + } + if (s) + v = v_tmp; + return s; +} +*/ + +void swap(vec2 &a, vec2 &b) +{ + vec2 tmp(a); + a = b; + b = tmp; +} + +vec2 min_vec(const vec2 &a, const vec2 &b) +{ + return vec2(MIN(a.n[VX], b.n[VX]), MIN(a.n[VY], b.n[VY])); +} + +vec2 max_vec(const vec2 &a, const vec2 &b) +{ + return vec2(MAX(a.n[VX], b.n[VX]), MAX(a.n[VY], b.n[VY])); +} + +vec2 prod(const vec2 &a, const vec2 &b) +{ + return vec2(a.n[VX] * b.n[VX], a.n[VY] * b.n[VY]); +} + +/**************************************************************** + * * + * vec3 Member functions * + * * + ****************************************************************/ + +// CONSTRUCTORS + +vec3::vec3() +{ + n[VX] = n[VY] = n[VZ] = 0.0; +} + +vec3::vec3(float x, float y, float z) +{ + n[VX] = x; + n[VY] = y; + n[VZ] = z; +} + +vec3::vec3(const vec3 &v) +{ + n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ]; +} + +vec3::vec3(const vec2 &v) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + n[VZ] = 1.0; +} + +vec3::vec3(const vec2 &v, float d) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + n[VZ] = d; +} + +vec3::vec3(const vec4 &v) // it is up to caller to avoid divide-by-zero +{ + n[VX] = v.n[VX] / v.n[VW]; + n[VY] = v.n[VY] / v.n[VW]; + n[VZ] = v.n[VZ] / v.n[VW]; +} + +vec3::vec3(const vec4 &v, int dropAxis) +{ + switch (dropAxis) + { + case VX: n[VX] = v.n[VY]; n[VY] = v.n[VZ]; n[VZ] = v.n[VW]; break; + case VY: n[VX] = v.n[VX]; n[VY] = v.n[VZ]; n[VZ] = v.n[VW]; break; + case VZ: n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VW]; break; + default: n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ]; break; + } +} + + +// ASSIGNMENT OPERATORS + +vec3 &vec3::operator=(const vec3 &v) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + n[VZ] = v.n[VZ]; + return *this; +} + +vec3 &vec3::operator+=(const vec3 &v) +{ + n[VX] += v.n[VX]; + n[VY] += v.n[VY]; + n[VZ] += v.n[VZ]; + return *this; +} + +vec3 &vec3::operator-=(const vec3& v) +{ + n[VX] -= v.n[VX]; + n[VY] -= v.n[VY]; + n[VZ] -= v.n[VZ]; + return *this; +} + +vec3 &vec3::operator*=(float d) +{ + n[VX] *= d; + n[VY] *= d; + n[VZ] *= d; + return *this; +} + +vec3 &vec3::operator/=(float d) +{ + float d_inv = 1.0f/d; + n[VX] *= d_inv; + n[VY] *= d_inv; + n[VZ] *= d_inv; + return *this; +} + +float &vec3::operator[](int i) +{ + if (i < VX || i > VZ) + //VEC_ERROR("vec3 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("vec3 [] operator: illegal access" ); + + return n[i]; +} + +const float &vec3::operator[](int i) const +{ + if (i < VX || i > VZ) + //VEC_ERROR("vec3 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("vec3 [] operator: illegal access" ); + + return n[i]; +} + +// SPECIAL FUNCTIONS + +float vec3::length() const +{ + return (float) sqrt(length2()); +} + +float vec3::length2() const +{ + return n[VX]*n[VX] + n[VY]*n[VY] + n[VZ]*n[VZ]; +} + +vec3 &vec3::normalize() // it is up to caller to avoid divide-by-zero +{ + *this /= length(); + return *this; +} + +vec3 &vec3::homogenize(void) // it is up to caller to avoid divide-by-zero +{ + n[VX] /= n[VZ]; + n[VY] /= n[VZ]; + n[VZ] = 1.0; + return *this; +} + +vec3 &vec3::apply(V_FCT_PTR fct) +{ + n[VX] = (*fct)(n[VX]); + n[VY] = (*fct)(n[VY]); + n[VZ] = (*fct)(n[VZ]); + return *this; +} + +void vec3::set(float x, float y, float z) // set vector +{ + n[VX] = x; + n[VY] = y; + n[VZ] = z; +} + +void vec3::print(FILE *file, const char *name) const // print vector to a file +{ + fprintf( file, "%s: <%f, %f, %f>\n", name, n[VX], n[VY], n[VZ] ); +} + +// FRIENDS + +vec3 operator-(const vec3 &a) +{ + return vec3(-a.n[VX],-a.n[VY],-a.n[VZ]); +} + +vec3 operator+(const vec3 &a, const vec3 &b) +{ + return vec3(a.n[VX]+ b.n[VX], a.n[VY] + b.n[VY], a.n[VZ] + b.n[VZ]); +} + +vec3 operator-(const vec3 &a, const vec3 &b) +{ + return vec3(a.n[VX]-b.n[VX], a.n[VY]-b.n[VY], a.n[VZ]-b.n[VZ]); +} + +vec3 operator*(const vec3 &a, float d) +{ + return vec3(d*a.n[VX], d*a.n[VY], d*a.n[VZ]); +} + +vec3 operator*(float d, const vec3 &a) +{ + return a*d; +} + +vec3 operator*(const mat4 &a, const vec3 &v) +{ + return a*vec4(v); +} + +vec3 operator*(const vec3 &v, mat4 &a) +{ + return a.transpose()*v; +} + +float operator*(const vec3 &a, const vec3 &b) +{ + return a.n[VX]*b.n[VX] + a.n[VY]*b.n[VY] + a.n[VZ]*b.n[VZ]; +} + +vec3 operator/(const vec3 &a, float d) +{ + float d_inv = 1.0f/d; + return vec3(a.n[VX]*d_inv, a.n[VY]*d_inv, a.n[VZ]*d_inv); +} + +vec3 operator^(const vec3 &a, const vec3 &b) +{ + return + vec3(a.n[VY]*b.n[VZ] - a.n[VZ]*b.n[VY], + a.n[VZ]*b.n[VX] - a.n[VX]*b.n[VZ], + a.n[VX]*b.n[VY] - a.n[VY]*b.n[VX]); +} + +int operator==(const vec3 &a, const vec3 &b) +{ + return (a.n[VX] == b.n[VX]) && (a.n[VY] == b.n[VY]) && (a.n[VZ] == b.n[VZ]); +} + +int operator!=(const vec3 &a, const vec3 &b) +{ + return !(a == b); +} + +/*ostream& operator << (ostream& s, vec3& v) +{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << ' ' << v.n[VZ] << " |"; } + +istream& operator >> (istream& s, vec3& v) { + vec3 v_tmp; + char c = ' '; + + while (isspace(c)) + s >> c; + // The vectors can be formatted either as x y z or | x y z | + if (c == '|') { + s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ]; + while (s >> c && isspace(c)) ; + if (c != '|') + ;//s.set(_bad); + } + else { + s.putback(c); + s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ]; + } + if (s) + v = v_tmp; + return s; +} +*/ + +void swap(vec3 &a, vec3 &b) +{ + vec3 tmp(a); + a = b; + b = tmp; +} + +vec3 min_vec(const vec3 &a, const vec3 &b) +{ + return vec3( + MIN(a.n[VX], b.n[VX]), + MIN(a.n[VY], b.n[VY]), + MIN(a.n[VZ], b.n[VZ])); +} + +vec3 max_vec(const vec3 &a, const vec3 &b) +{ + return vec3( + MAX(a.n[VX], b.n[VX]), + MAX(a.n[VY], b.n[VY]), + MAX(a.n[VZ], b.n[VZ])); +} + +vec3 prod(const vec3 &a, const vec3 &b) +{ + return vec3(a.n[VX]*b.n[VX], a.n[VY]*b.n[VY], a.n[VZ]*b.n[VZ]); +} + +/**************************************************************** + * * + * vec4 Member functions * + * * + ****************************************************************/ + +// CONSTRUCTORS + +vec4::vec4() +{ + n[VX] = n[VY] = n[VZ] = 0.0; + n[VW] = 1.0; +} + +vec4::vec4(float x, float y, float z, float w) +{ + n[VX] = x; + n[VY] = y; + n[VZ] = z; + n[VW] = w; +} + +vec4::vec4(const vec4 &v) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + n[VZ] = v.n[VZ]; + n[VW] = v.n[VW]; +} + +vec4::vec4(const vec3 &v) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + n[VZ] = v.n[VZ]; + n[VW] = 1.0; +} + +vec4::vec4(const vec3 &v, float d) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + n[VZ] = v.n[VZ]; + n[VW] = d; +} + +// ASSIGNMENT OPERATORS + +vec4 &vec4::operator=(const vec4 &v) +{ + n[VX] = v.n[VX]; + n[VY] = v.n[VY]; + n[VZ] = v.n[VZ]; + n[VW] = v.n[VW]; + return *this; +} + +vec4 &vec4::operator+=(const vec4 &v) +{ + n[VX] += v.n[VX]; + n[VY] += v.n[VY]; + n[VZ] += v.n[VZ]; + n[VW] += v.n[VW]; + return *this; +} + +vec4 &vec4::operator-=(const vec4 &v) +{ + n[VX] -= v.n[VX]; + n[VY] -= v.n[VY]; + n[VZ] -= v.n[VZ]; + n[VW] -= v.n[VW]; + return *this; +} + +vec4 &vec4::operator*=(float d) +{ + n[VX] *= d; + n[VY] *= d; + n[VZ] *= d; + n[VW] *= d; + return *this; +} + +vec4 &vec4::operator/=(float d) +{ + float d_inv = 1.0f/d; + n[VX] *= d_inv; + n[VY] *= d_inv; + n[VZ] *= d_inv; + n[VW] *= d_inv; + return *this; +} + +float &vec4::operator[](int i) +{ + if (i < VX || i > VW) + //VEC_ERROR("vec4 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("vec4 [] operator: illegal access" ); + + return n[i]; +} + +const float &vec4::operator[](int i) const +{ + if (i < VX || i > VW) + //VEC_ERROR("vec4 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("vec4 [] operator: illegal access" ); + + return n[i]; +} + +// SPECIAL FUNCTIONS + +float vec4::length() const +{ + return (float) sqrt(length2()); +} + +float vec4::length2() const +{ + return n[VX]*n[VX] + n[VY]*n[VY] + n[VZ]*n[VZ] + n[VW]*n[VW]; +} + +vec4 &vec4::normalize() // it is up to caller to avoid divide-by-zero +{ + *this /= length(); + return *this; +} + +vec4 &vec4::homogenize() // it is up to caller to avoid divide-by-zero +{ + n[VX] /= n[VW]; + n[VY] /= n[VW]; + n[VZ] /= n[VW]; + n[VW] = 1.0; + return *this; +} + +vec4 &vec4::apply(V_FCT_PTR fct) +{ + n[VX] = (*fct)(n[VX]); + n[VY] = (*fct)(n[VY]); + n[VZ] = (*fct)(n[VZ]); + n[VW] = (*fct)(n[VW]); + return *this; +} + +void vec4::print(FILE *file, const char *name) const // print vector to a file +{ + fprintf( file, "%s: <%f, %f, %f, %f>\n", name, n[VX], n[VY], n[VZ], n[VW]); +} + +void vec4::set(float x, float y, float z, float a) +{ + n[0] = x; + n[1] = y; + n[2] = z; + n[3] = a; +} + + +// FRIENDS + +vec4 operator-(const vec4 &a) +{ + return vec4(-a.n[VX],-a.n[VY],-a.n[VZ],-a.n[VW]); +} + +vec4 operator+(const vec4 &a, const vec4 &b) +{ + return vec4( + a.n[VX] + b.n[VX], + a.n[VY] + b.n[VY], + a.n[VZ] + b.n[VZ], + a.n[VW] + b.n[VW]); +} + +vec4 operator-(const vec4 &a, const vec4 &b) +{ + return vec4( + a.n[VX] - b.n[VX], + a.n[VY] - b.n[VY], + a.n[VZ] - b.n[VZ], + a.n[VW] - b.n[VW]); +} + +vec4 operator*(const vec4 &a, float d) +{ + return vec4(d*a.n[VX], d*a.n[VY], d*a.n[VZ], d*a.n[VW]); +} + +vec4 operator*(float d, const vec4 &a) +{ + return a*d; +} + +vec4 operator*(const mat4 &a, const vec4 &v) +{ + #define ROWCOL(i) \ + a.v[i].n[0]*v.n[VX] + \ + a.v[i].n[1]*v.n[VY] + \ + a.v[i].n[2]*v.n[VZ] + \ + a.v[i].n[3]*v.n[VW] + + return vec4(ROWCOL(0), ROWCOL(1), ROWCOL(2), ROWCOL(3)); + + #undef ROWCOL +} + +vec4 operator*(const vec4 &v, const mat4 &a) +{ + return a.transpose()*v; +} + +float operator*(const vec4 &a, const vec4 &b) +{ + return + a.n[VX]*b.n[VX] + + a.n[VY]*b.n[VY] + + a.n[VZ]*b.n[VZ] + + a.n[VW]*b.n[VW]; +} + +vec4 operator/(const vec4 &a, float d) +{ + float d_inv = 1.0f/d; + return vec4( + a.n[VX]*d_inv, + a.n[VY]*d_inv, + a.n[VZ]*d_inv, + a.n[VW]*d_inv); +} + +int operator==(const vec4 &a, const vec4 &b) +{ + return + (a.n[VX] == b.n[VX]) && + (a.n[VY] == b.n[VY]) && + (a.n[VZ] == b.n[VZ]) && + (a.n[VW] == b.n[VW]); +} + +int operator!=(const vec4 &a, const vec4 &b) +{ + return !(a == b); +} + +/*ostream& operator << (ostream& s, vec4& v) +{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << ' ' << v.n[VZ] << ' ' + << v.n[VW] << " |"; } + +istream& operator >> (istream& s, vec4& v) { + vec4 v_tmp; + char c = ' '; + + while (isspace(c)) + s >> c; + // The vectors can be formatted either as x y z w or | x y z w | + if (c == '|') { + s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ] >> v_tmp[VW]; + while (s >> c && isspace(c)) ; + if (c != '|') + ;//s.set(_bad); + } + else { + s.putback(c); + s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ] >> v_tmp[VW]; + } + if (s) + v = v_tmp; + return s; +} +*/ + +void swap(vec4 &a, vec4 &b) +{ + vec4 tmp(a); + a = b; + b = tmp; +} + +vec4 min_vec(const vec4 &a, const vec4 &b) +{ + return vec4( + MIN(a.n[VX], b.n[VX]), + MIN(a.n[VY], b.n[VY]), + MIN(a.n[VZ], b.n[VZ]), + MIN(a.n[VW], b.n[VW])); +} + +vec4 max_vec(const vec4 &a, const vec4 &b) +{ + return vec4( + MAX(a.n[VX], b.n[VX]), + MAX(a.n[VY], b.n[VY]), + MAX(a.n[VZ], b.n[VZ]), + MAX(a.n[VW], b.n[VW])); +} + +vec4 prod(const vec4 &a, const vec4 &b) +{ + return vec4( + a.n[VX] * b.n[VX], + a.n[VY] * b.n[VY], + a.n[VZ] * b.n[VZ], + a.n[VW] * b.n[VW]); +} + +/**************************************************************** + * * + * mat3 member functions * + * * + ****************************************************************/ + +// CONSTRUCTORS + +mat3::mat3() +{ + *this = identity2D(); +} + +mat3::mat3(const vec3 &v0, const vec3 &v1, const vec3 &v2) +{ + set(v0, v1, v2); +} + +mat3::mat3(const mat3 &m) +{ + v[0] = m.v[0]; + v[1] = m.v[1]; + v[2] = m.v[2]; +} + +// ASSIGNMENT OPERATORS + +mat3 &mat3::operator=(const mat3 &m) +{ + v[0] = m.v[0]; + v[1] = m.v[1]; + v[2] = m.v[2]; + return *this; +} + +mat3 &mat3::operator+=(const mat3& m) +{ + v[0] += m.v[0]; + v[1] += m.v[1]; + v[2] += m.v[2]; + return *this; +} + +mat3 &mat3::operator-=(const mat3& m) +{ + v[0] -= m.v[0]; + v[1] -= m.v[1]; + v[2] -= m.v[2]; + return *this; +} + +mat3 &mat3::operator*=(float d) +{ + v[0] *= d; + v[1] *= d; + v[2] *= d; + return *this; +} + +mat3 &mat3::operator/=(float d) +{ + v[0] /= d; + v[1] /= d; + v[2] /= d; + return *this; +} + +vec3 &mat3::operator[](int i) +{ + if (i < VX || i > VZ) + //VEC_ERROR("mat3 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("mat3 [] operator: illegal access" ); + + return v[i]; +} + +const vec3 &mat3::operator[](int i) const +{ + if (i < VX || i > VZ) + //VEC_ERROR("mat3 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("mat3 [] operator: illegal access" ); + + return v[i]; +} + +void mat3::set(const vec3 &v0, const vec3 &v1, const vec3 &v2) +{ + v[0] = v0; + v[1] = v1; + v[2] = v2; +} + +// SPECIAL FUNCTIONS + +mat3 mat3::transpose() const +{ + return mat3( + vec3(v[0][0], v[1][0], v[2][0]), + vec3(v[0][1], v[1][1], v[2][1]), + vec3(v[0][2], v[1][2], v[2][2])); +} + +mat3 mat3::inverse() const // Gauss-Jordan elimination with partial pivoting +{ + mat3 a(*this); // As a evolves from original mat into identity + mat3 b(identity2D()); // b evolves from identity into inverse(a) + int i, j, i1; + + // Loop over cols of a from left to right, eliminating above and below diag + for (j=0; j<3; j++) // Find largest pivot in column j among rows j..2 + { + i1 = j; // Row with largest pivot candidate + for (i=j+1; i<3; i++) + if (fabs(a.v[i].n[j]) > fabs(a.v[i1].n[j])) + i1 = i; + + // Swap rows i1 and j in a and b to put pivot on diagonal + swap(a.v[i1], a.v[j]); + swap(b.v[i1], b.v[j]); + + // Scale row j to have a unit diagonal + if (a.v[j].n[j]==0.) + VEC_ERROR("mat3::inverse: singular matrix; can't invert\n"); + + b.v[j] /= a.v[j].n[j]; + a.v[j] /= a.v[j].n[j]; + + // Eliminate off-diagonal elems in col j of a, doing identical ops to b + for (i=0; i<3; i++) + if (i!=j) + { + b.v[i] -= a.v[i].n[j]*b.v[j]; + a.v[i] -= a.v[i].n[j]*a.v[j]; + } + } + + return b; +} + +mat3 &mat3::apply(V_FCT_PTR fct) +{ + v[VX].apply(fct); + v[VY].apply(fct); + v[VZ].apply(fct); + return *this; +} + + +// FRIENDS + +mat3 operator-(const mat3 &a) +{ + return mat3(-a.v[0], -a.v[1], -a.v[2]); +} + +mat3 operator+(const mat3 &a, const mat3 &b) +{ + return mat3(a.v[0]+b.v[0], a.v[1]+b.v[1], a.v[2]+b.v[2]); +} + +mat3 operator-(const mat3 &a, const mat3 &b) +{ + return mat3(a.v[0]-b.v[0], a.v[1]-b.v[1], a.v[2]-b.v[2]); +} + +mat3 operator*(const mat3 &a, const mat3 &b) +{ + #define ROWCOL(i, j) \ + a.v[i].n[0]*b.v[0][j] + a.v[i].n[1]*b.v[1][j] + a.v[i].n[2]*b.v[2][j] + + return mat3( + vec3(ROWCOL(0,0), ROWCOL(0,1), ROWCOL(0,2)), + vec3(ROWCOL(1,0), ROWCOL(1,1), ROWCOL(1,2)), + vec3(ROWCOL(2,0), ROWCOL(2,1), ROWCOL(2,2))); + + #undef ROWCOL +} + +mat3 operator*(const mat3 &a, float d) +{ + return mat3(a.v[0]*d, a.v[1]*d, a.v[2]*d); +} + +mat3 operator*(float d, const mat3 &a) +{ + return a*d; +} + +mat3 operator/(const mat3 &a, float d) +{ + return mat3(a.v[0]/d, a.v[1]/d, a.v[2]/d); +} + +int operator==(const mat3 &a, const mat3 &b) +{ + return + (a.v[0] == b.v[0]) && + (a.v[1] == b.v[1]) && + (a.v[2] == b.v[2]); +} + +int operator!=(const mat3 &a, const mat3 &b) +{ + return !(a == b); +} + +/*ostream& operator << (ostream& s, mat3& m) +{ return s << m.v[VX] << '\n' << m.v[VY] << '\n' << m.v[VZ]; } + +istream& operator >> (istream& s, mat3& m) { + mat3 m_tmp; + + s >> m_tmp[VX] >> m_tmp[VY] >> m_tmp[VZ]; + if (s) + m = m_tmp; + return s; +} +*/ + +void swap(mat3 &a, mat3 &b) +{ + mat3 tmp(a); + a = b; + b = tmp; +} + +void mat3::print(FILE *file, const char *name) const +{ + int i, j; + + fprintf( stderr, "%s:\n", name ); + + for( i = 0; i < 3; i++ ) + { + fprintf( stderr, " " ); + for( j = 0; j < 3; j++ ) + { + fprintf( stderr, "%f ", v[i][j] ); + } + fprintf( stderr, "\n" ); + } +} + + + +/**************************************************************** + * * + * mat4 member functions * + * * + ****************************************************************/ + +// CONSTRUCTORS + +mat4::mat4() +{ + *this = identity3D(); +} + +mat4::mat4(const vec4& v0, const vec4& v1, const vec4& v2, const vec4& v3) +{ + v[0] = v0; + v[1] = v1; + v[2] = v2; + v[3] = v3; +} + +mat4::mat4(const mat4 &m) +{ + v[0] = m.v[0]; + v[1] = m.v[1]; + v[2] = m.v[2]; + v[3] = m.v[3]; +} + +mat4::mat4( + float a00, float a01, float a02, float a03, + float a10, float a11, float a12, float a13, + float a20, float a21, float a22, float a23, + float a30, float a31, float a32, float a33 ) +{ + v[0][0] = a00; v[0][1] = a01; v[0][2] = a02; v[0][3] = a03; + v[1][0] = a10; v[1][1] = a11; v[1][2] = a12; v[1][3] = a13; + v[2][0] = a20; v[2][1] = a21; v[2][2] = a22; v[2][3] = a23; + v[3][0] = a30; v[3][1] = a31; v[3][2] = a32; v[3][3] = a33; +} + +// ASSIGNMENT OPERATORS + +mat4 &mat4::operator=(const mat4 &m) +{ + v[0] = m.v[0]; + v[1] = m.v[1]; + v[2] = m.v[2]; + v[3] = m.v[3]; + return *this; +} + +mat4 &mat4::operator+=(const mat4 &m) +{ + v[0] += m.v[0]; + v[1] += m.v[1]; + v[2] += m.v[2]; + v[3] += m.v[3]; + return *this; +} + +mat4 &mat4::operator-=(const mat4 &m) +{ + v[0] -= m.v[0]; + v[1] -= m.v[1]; + v[2] -= m.v[2]; + v[3] -= m.v[3]; + return *this; +} + +mat4 &mat4::operator*=(float d) +{ + v[0] *= d; + v[1] *= d; + v[2] *= d; + v[3] *= d; + return *this; +} + +mat4 &mat4::operator/=(float d) +{ + v[0] /= d; + v[1] /= d; + v[2] /= d; + v[3] /= d; + return *this; +} + +vec4 &mat4::operator[](int i) +{ + if (i < VX || i > VW) + //VEC_ERROR("mat4 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("mat4 [] operator: illegal access" ); + return v[i]; +} + +const vec4 &mat4::operator[](int i) const +{ + if (i < VX || i > VW) + //VEC_ERROR("mat4 [] operator: illegal access; index = " << i << '\n') + VEC_ERROR("mat4 [] operator: illegal access" ); + return v[i]; +} + +// SPECIAL FUNCTIONS; + +mat4 mat4::transpose() const +{ + return mat4( + vec4(v[0][0], v[1][0], v[2][0], v[3][0]), + vec4(v[0][1], v[1][1], v[2][1], v[3][1]), + vec4(v[0][2], v[1][2], v[2][2], v[3][2]), + vec4(v[0][3], v[1][3], v[2][3], v[3][3])); +} + +mat4 mat4::inverse() const // Gauss-Jordan elimination with partial pivoting +{ + mat4 a(*this); // As a evolves from original mat into identity + mat4 b(identity3D()); // b evolves from identity into inverse(a) + int i, j, i1; + + // Loop over cols of a from left to right, eliminating above and below diag + for (j=0; j<4; j++) // Find largest pivot in column j among rows j..3 + { + i1 = j; // Row with largest pivot candidate + for (i=j+1; i<4; i++) + if (fabs(a.v[i].n[j]) > fabs(a.v[i1].n[j])) + i1 = i; + + // Swap rows i1 and j in a and b to put pivot on diagonal + swap(a.v[i1], a.v[j]); + swap(b.v[i1], b.v[j]); + + // Scale row j to have a unit diagonal + if (a.v[j].n[j]==0.) + VEC_ERROR("mat4::inverse: singular matrix; can't invert\n"); + + b.v[j] /= a.v[j].n[j]; + a.v[j] /= a.v[j].n[j]; + + // Eliminate off-diagonal elems in col j of a, doing identical ops to b + for (i=0; i<4; i++) + if (i!=j) + { + b.v[i] -= a.v[i].n[j]*b.v[j]; + a.v[i] -= a.v[i].n[j]*a.v[j]; + } + } + + return b; +} + +mat4 &mat4::apply(V_FCT_PTR fct) +{ + v[VX].apply(fct); + v[VY].apply(fct); + v[VZ].apply(fct); + v[VW].apply(fct); + return *this; +} + +void mat4::print(FILE *file, const char *name) const +{ + int i, j; + + fprintf( stderr, "%s:\n", name ); + + for( i = 0; i < 4; i++ ) + { + fprintf( stderr, " " ); + for( j = 0; j < 4; j++ ) + { + fprintf( stderr, "%f ", v[i][j] ); + } + fprintf( stderr, "\n" ); + } +} + +void mat4::swap_rows(int i, int j) +{ + vec4 t; + + t = v[i]; + v[i] = v[j]; + v[j] = t; +} + +void mat4::swap_cols(int i, int j) +{ + float t; + int k; + + for (k=0; k<4; k++) + { + t = v[k][i]; + v[k][i] = v[k][j]; + v[k][j] = t; + } +} + + +// FRIENDS + +mat4 operator-(const mat4 &a) +{ + return mat4(-a.v[0],-a.v[1],-a.v[2],-a.v[3]); +} + +mat4 operator+(const mat4 &a, const mat4 &b) +{ + return mat4( + a.v[0] + b.v[0], + a.v[1] + b.v[1], + a.v[2] + b.v[2], + a.v[3] + b.v[3]); +} + +mat4 operator-(const mat4 &a, const mat4 &b) +{ + return mat4( + a.v[0] - b.v[0], + a.v[1] - b.v[1], + a.v[2] - b.v[2], + a.v[3] - b.v[3]); +} + +mat4 operator*(const mat4 &a, const mat4 &b) +{ + #define ROWCOL(i, j) \ + a.v[i].n[0]*b.v[0][j] + \ + a.v[i].n[1]*b.v[1][j] + \ + a.v[i].n[2]*b.v[2][j] + \ + a.v[i].n[3]*b.v[3][j] + + return mat4( + vec4(ROWCOL(0,0), ROWCOL(0,1), ROWCOL(0,2), ROWCOL(0,3)), + vec4(ROWCOL(1,0), ROWCOL(1,1), ROWCOL(1,2), ROWCOL(1,3)), + vec4(ROWCOL(2,0), ROWCOL(2,1), ROWCOL(2,2), ROWCOL(2,3)), + vec4(ROWCOL(3,0), ROWCOL(3,1), ROWCOL(3,2), ROWCOL(3,3)) + ); + + #undef ROWCOL +} + +mat4 operator*(const mat4 &a, float d) +{ + return mat4(a.v[0]*d, a.v[1]*d, a.v[2]*d, a.v[3]*d); +} + +mat4 operator*(float d, const mat4 &a) +{ + return a*d; +} + +mat4 operator/(const mat4 &a, float d) +{ + return mat4(a.v[0]/d, a.v[1]/d, a.v[2]/d, a.v[3]/d); +} + +int operator==(const mat4 &a, const mat4 &b) +{ + return + (a.v[0] == b.v[0]) && + (a.v[1] == b.v[1]) && + (a.v[2] == b.v[2]) && + (a.v[3] == b.v[3]); +} + +int operator!=(const mat4 &a, const mat4 &b) +{ + return !(a == b); +} + +/*ostream& operator << (ostream& s, mat4& m) +{ return s << m.v[VX] << '\n' << m.v[VY] << '\n' << m.v[VZ] << '\n' << m.v[VW]; } + +istream& operator >> (istream& s, mat4& m) +{ + mat4 m_tmp; + + s >> m_tmp[VX] >> m_tmp[VY] >> m_tmp[VZ] >> m_tmp[VW]; + if (s) + m = m_tmp; + return s; +} +*/ + +void swap(mat4 &a, mat4 &b) +{ + mat4 tmp(a); + a = b; + b = tmp; +} + +/**************************************************************** + * * + * 2D functions and 3D functions * + * * + ****************************************************************/ + +mat3 identity2D() +{ + return mat3( + vec3(1.0, 0.0, 0.0), + vec3(0.0, 1.0, 0.0), + vec3(0.0, 0.0, 1.0)); +} + +mat3 translation2D(const vec2 &v) +{ + return mat3( + vec3(1.0, 0.0, v[VX]), + vec3(0.0, 1.0, v[VY]), + vec3(0.0, 0.0, 1.0)); +} + +mat3 rotation2D(const vec2 &Center, float angleDeg) +{ + float angleRad = (float) (angleDeg * radians); + float c = (float) cos(angleRad); + float s = (float) sin(angleRad); + + return mat3( + vec3(c, -s, Center[VX] * (1.0f-c) + Center[VY] * s), + vec3(s, c, Center[VY] * (1.0f-c) - Center[VX] * s), + vec3(0.0, 0.0, 1.0)); +} + +mat3 scaling2D(const vec2 &scaleVector) +{ + return mat3( + vec3(scaleVector[VX], 0.0, 0.0), + vec3(0.0, scaleVector[VY], 0.0), + vec3(0.0, 0.0, 1.0)); +} + +mat4 identity3D() +{ + return mat4( + vec4(1.0, 0.0, 0.0, 0.0), + vec4(0.0, 1.0, 0.0, 0.0), + vec4(0.0, 0.0, 1.0, 0.0), + vec4(0.0, 0.0, 0.0, 1.0)); +} + +mat4 translation3D(const vec3 &v) +{ + return mat4( + vec4(1.0, 0.0, 0.0, v[VX]), + vec4(0.0, 1.0, 0.0, v[VY]), + vec4(0.0, 0.0, 1.0, v[VZ]), + vec4(0.0, 0.0, 0.0, 1.0)); +} + +mat4 rotation3D(const vec3 &Axis, float angleDeg) +{ + float angleRad = (float) (angleDeg * radians); + float c = (float) cos(angleRad); + float s = (float) sin(angleRad); + float t = 1.0f - c; + + vec3 axis(Axis); + axis.normalize(); + + return mat4( + vec4(t * axis[VX] * axis[VX] + c, + t * axis[VX] * axis[VY] - s * axis[VZ], + t * axis[VX] * axis[VZ] + s * axis[VY], + 0.0), + vec4(t * axis[VX] * axis[VY] + s * axis[VZ], + t * axis[VY] * axis[VY] + c, + t * axis[VY] * axis[VZ] - s * axis[VX], + 0.0), + vec4(t * axis[VX] * axis[VZ] - s * axis[VY], + t * axis[VY] * axis[VZ] + s * axis[VX], + t * axis[VZ] * axis[VZ] + c, + 0.0), + vec4(0.0, 0.0, 0.0, 1.0)); +} + +mat4 rotation3Drad(const vec3 &Axis, float angleRad) +{ + float c = (float) cos(angleRad); + float s = (float) sin(angleRad); + float t = 1.0f - c; + + vec3 axis(Axis); + axis.normalize(); + + return mat4( + vec4(t * axis[VX] * axis[VX] + c, + t * axis[VX] * axis[VY] - s * axis[VZ], + t * axis[VX] * axis[VZ] + s * axis[VY], + 0.0), + vec4(t * axis[VX] * axis[VY] + s * axis[VZ], + t * axis[VY] * axis[VY] + c, + t * axis[VY] * axis[VZ] - s * axis[VX], + 0.0), + vec4(t * axis[VX] * axis[VZ] - s * axis[VY], + t * axis[VY] * axis[VZ] + s * axis[VX], + t * axis[VZ] * axis[VZ] + c, + 0.0), + vec4(0.0, 0.0, 0.0, 1.0)); +} + +mat4 scaling3D(const vec3 &scaleVector) +{ + return mat4( + vec4(scaleVector[VX], 0.0, 0.0, 0.0), + vec4(0.0, scaleVector[VY], 0.0, 0.0), + vec4(0.0, 0.0, scaleVector[VZ], 0.0), + vec4(0.0, 0.0, 0.0, 1.0)); +} + +mat4 perspective3D(float d) +{ + return mat4( + vec4(1.0f, 0.0f, 0.0f, 0.0f), + vec4(0.0f, 1.0f, 0.0f, 0.0f), + vec4(0.0f, 0.0f, 1.0f, 0.0f), + vec4(0.0f, 0.0f, 1.0f/d, 0.0f)); +} |