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author | Wolfgang Draxinger <Wolfgang.Draxinger@draxit.de> | 2016-04-24 23:52:45 +0200 |
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committer | Wolfgang Draxinger <Wolfgang.Draxinger@draxit.de> | 2016-04-24 23:52:45 +0200 |
commit | 2ca04fbe7985ee944f3fa6302886a252a51add0c (patch) | |
tree | b373879928a1060e564d29d44f6e20b620b272e9 /linmath.h | |
download | pointoverdrawbench-2ca04fbe7985ee944f3fa6302886a252a51add0c.tar.gz pointoverdrawbench-2ca04fbe7985ee944f3fa6302886a252a51add0c.tar.bz2 |
initial commit
Diffstat (limited to 'linmath.h')
-rw-r--r-- | linmath.h/LICENCE | 13 | ||||
-rw-r--r-- | linmath.h/README | 12 | ||||
-rw-r--r-- | linmath.h/linmath.h | 474 |
3 files changed, 499 insertions, 0 deletions
diff --git a/linmath.h/LICENCE b/linmath.h/LICENCE new file mode 100644 index 0000000..bb3444d --- /dev/null +++ b/linmath.h/LICENCE @@ -0,0 +1,13 @@ + DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE + Version 2, December 2004 + + Copyright (C) 2013 Wolfgang 'datenwolf' Draxinger <code@datenwolf.net> + + Everyone is permitted to copy and distribute verbatim or modified + copies of this license document, and changing it is allowed as long + as the name is changed. + + DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE + TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION + + 0. You just DO WHAT THE FUCK YOU WANT TO. diff --git a/linmath.h/README b/linmath.h/README new file mode 100644 index 0000000..9c43c8e --- /dev/null +++ b/linmath.h/README @@ -0,0 +1,12 @@ +# linmath.h -- A small library for linear math as required for computer graphics + +linmath.h provides the most used types required programming computer graphice: + +vec3 -- 3 element vector of floats +vec4 -- 4 element vector of floats (4th component used for homogenous computations) +mat4x4 -- 4 by 4 elements matrix, computations are done in column major order +quat -- quaternion + +The types are deliberately named like the types in GLSL. In fact they are meant to +be used for the client side computations and passing to same typed GLSL uniforms. + diff --git a/linmath.h/linmath.h b/linmath.h/linmath.h new file mode 100644 index 0000000..d21fd7d --- /dev/null +++ b/linmath.h/linmath.h @@ -0,0 +1,474 @@ +#ifndef LINMATH_H +#define LINMATH_H + +#include <math.h> +#include <string.h> + +#define LINMATH_H_DEFINE_VEC(n) \ +typedef float vec##n[n]; \ +static inline void vec##n##_add(vec##n r, vec##n a, vec##n b) \ +{ \ + int i; \ + for(i=0; i<n; ++i) \ + r[i] = a[i] + b[i]; \ +} \ +static inline void vec##n##_sub(vec##n r, vec##n a, vec##n b) \ +{ \ + int i; \ + for(i=0; i<n; ++i) \ + r[i] = a[i] - b[i]; \ +} \ +static inline void vec##n##_scale(vec##n r, vec##n v, float s) \ +{ \ + int i; \ + for(i=0; i<n; ++i) \ + r[i] = v[i] * s; \ +} \ +static inline float vec##n##_mul_inner(vec##n a, vec##n b) \ +{ \ + float p = 0.; \ + int i; \ + for(i=0; i<n; ++i) \ + p += b[i]*a[i]; \ + return p; \ +} \ +static inline float vec##n##_len(vec##n v) \ +{ \ + return sqrtf(vec##n##_mul_inner(v,v)); \ +} \ +static inline void vec##n##_norm(vec##n r, vec##n v) \ +{ \ + float k = 1.0 / vec##n##_len(v); \ + vec##n##_scale(r, v, k); \ +} + +LINMATH_H_DEFINE_VEC(2); +LINMATH_H_DEFINE_VEC(3); +LINMATH_H_DEFINE_VEC(4); + +static inline void vec3_mul_cross(vec3 r, vec3 a, vec3 b) +{ + vec3 c; + c[0] = a[1]*b[2] - a[2]*b[1]; + c[1] = a[2]*b[0] - a[0]*b[2]; + c[2] = a[0]*b[1] - a[1]*b[0]; + memcpy(r, c, sizeof(c)); +} + +static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) +{ + vec4 c; + c[0] = a[1]*b[2] - a[2]*b[1]; + c[1] = a[2]*b[0] - a[0]*b[2]; + c[2] = a[0]*b[1] - a[1]*b[0]; + c[3] = 1.; + memcpy(r, c, sizeof(c)); +} + +typedef vec4 mat4x4[4]; +static inline void mat4x4_identity(mat4x4 M) +{ + int i, j; + for(j=0; j<4; ++j) for(i=0; i<4; ++i) { + M[i][j] = i==j ? 1 : 0; + } +} +static inline void mat4x4_dup(mat4x4 M, mat4x4 N) +{ + int i, j; + for(j=0; j<4; ++j) { + for(i=0; i<4; ++i) { + M[i][j] = N[i][j]; + } + } +} +static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) +{ + int i; + for(i=0; i<4; ++i) + vec4_add(M[i], a[i], b[i]); +} +static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) +{ + int i; + for(i=0; i<4; ++i) + vec4_sub(M[i], a[i], b[i]); +} +static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) +{ + int i; + for(i=0; i<4; ++i) + vec4_scale(M[i], a[i], k); +} +static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z) +{ + vec4_scale(M[0], a[0], x); + vec4_scale(M[1], a[1], y); + vec4_scale(M[2], a[2], z); +} +static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) +{ + int k, r, c; + mat4x4 R; + for(r=0; r<4; ++r) for(c=0; c<4; ++c) { + R[c][r] = 0; + for(k=0; k<4; ++k) { + R[c][r] += a[k][r] * b[c][k]; + } + } + memcpy(M, R, sizeof(R)); +} +static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) +{ + vec4 r_; + int i, j; + for(j=0; j<4; ++j) { + r_[j] = 0.; + for(i=0; i<4; ++i) { + r_[j] += M[i][j] * v[i]; + } + } + memcpy(r, r_, sizeof(r_)); +} +static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) +{ + mat4x4_identity(T); + T[3][0] = x; + T[3][1] = y; + T[3][2] = z; +} +static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) +{ + int i, j; + for(i=0; i<4; ++i) for(j=0; j<4; ++j) { + M[i][j] = i<3 && j<3 ? a[i] * b[j] : 0.; + } +} +static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle) +{ + float s = sinf(angle); + float c = cosf(angle); + vec3 u = {x, y, z}; + + if(vec3_len(u) > 1e-4) { + vec3_norm(u, u); + mat4x4 T; + mat4x4_from_vec3_mul_outer(T, u, u); + + mat4x4 S = { + { 0, u[2], -u[1], 0}, + {-u[2], 0, u[0], 0}, + { u[1], -u[0], 0, 0}, + { 0, 0, 0, 0} + }; + mat4x4_scale(S, S, s); + + mat4x4 C; + mat4x4_identity(C); + mat4x4_sub(C, C, T); + + mat4x4_scale(C, C, c); + + mat4x4_add(T, T, C); + mat4x4_add(T, T, S); + + T[3][3] = 1.; + mat4x4_mul(R, M, T); + } else { + mat4x4_dup(R, M); + } +} +static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) +{ + float s = sinf(angle); + float c = cosf(angle); + mat4x4 R = { + {1, 0, 0, 0}, + {0, c, s, 0}, + {0,-s, c, 0}, + {0, 0, 0, 1} + }; + mat4x4_mul(Q, M, R); +} +static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) +{ + float s = sinf(angle); + float c = cosf(angle); + mat4x4 R = { + { c, 0, s, 0}, + { 0, 1, 0, 0}, + {-s, 0, c, 0}, + { 0, 0, 0, 1} + }; + mat4x4_mul(Q, M, R); +} +static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) +{ + float s = sinf(angle); + float c = cosf(angle); + mat4x4 R = { + { c, s, 0, 0}, + {-s, c, 0, 0}, + { 0, 0, 1, 0}, + { 0, 0, 0, 1} + }; + mat4x4_mul(Q, M, R); +} +static inline void mat4x4_row(vec4 r, mat4x4 M, int i) +{ + int k; + for(k=0; k<4; ++k) + r[k] = M[k][i]; +} +static inline void mat4x4_col(vec4 r, mat4x4 M, int i) +{ + int k; + for(k=0; k<4; ++k) + r[k] = M[i][k]; +} +static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) +{ + int i, j; + mat4x4 R; + for(j=0; j<4; ++j) { + for(i=0; i<4; ++i) { + R[i][j] = N[j][i]; + } + } + memcpy(M, R, sizeof(R)); +} +static inline void mat4x4_invert(mat4x4 T, mat4x4 M) +{ + mat4x4 R; + R[0][0] = M[1][1]*(M[2][2]*M[3][3] - M[2][3]*M[3][2]) - M[2][1]*(M[1][2]*M[3][3] - M[1][3]*M[3][2]) - M[3][1]*(M[1][3]*M[2][2] - M[1][2]*M[2][3]); + R[0][1] = M[0][1]*(M[2][3]*M[3][2] - M[2][2]*M[3][3]) - M[2][1]*(M[0][3]*M[3][2] - M[0][2]*M[3][3]) - M[3][1]*(M[0][2]*M[2][3] - M[0][3]*M[2][2]); + R[0][2] = M[0][1]*(M[1][2]*M[3][3] - M[1][3]*M[3][2]) - M[1][1]*(M[0][2]*M[3][3] - M[0][3]*M[3][2]) - M[3][1]*(M[0][3]*M[1][2] - M[0][2]*M[1][3]); + R[0][3] = M[0][1]*(M[1][3]*M[2][2] - M[1][2]*M[2][3]) - M[1][1]*(M[0][3]*M[2][2] - M[0][2]*M[2][3]) - M[2][1]*(M[0][2]*M[1][3] - M[0][3]*M[1][2]); + + R[1][0] = M[1][0]*(M[2][3]*M[3][2] - M[2][2]*M[3][3]) - M[2][0]*(M[1][3]*M[3][2] - M[1][2]*M[3][3]) - M[3][0]*(M[1][2]*M[2][3] - M[1][3]*M[2][2]); + R[1][1] = M[0][0]*(M[2][2]*M[3][3] - M[2][3]*M[3][2]) - M[2][0]*(M[0][2]*M[3][3] - M[0][3]*M[3][2]) - M[3][0]*(M[0][3]*M[2][2] - M[0][2]*M[2][3]); + R[1][2] = M[0][0]*(M[1][3]*M[3][2] - M[1][2]*M[3][3]) - M[1][0]*(M[0][3]*M[3][2] - M[0][2]*M[3][3]) - M[3][0]*(M[0][2]*M[1][3] - M[0][3]*M[1][2]); + R[1][3] = M[0][0]*(M[1][2]*M[2][3] - M[1][3]*M[2][2]) - M[1][0]*(M[0][2]*M[2][3] - M[0][3]*M[2][2]) - M[2][0]*(M[0][3]*M[1][2] - M[0][2]*M[1][3]); + + R[2][0] = M[1][0]*(M[2][1]*M[3][3] - M[2][3]*M[3][1]) - M[2][0]*(M[1][1]*M[3][3] - M[1][3]*M[3][1]) - M[3][0]*(M[1][3]*M[2][1] - M[1][1]*M[2][3]); + R[2][1] = M[0][0]*(M[2][3]*M[3][1] - M[2][1]*M[3][3]) - M[2][0]*(M[0][3]*M[3][1] - M[0][1]*M[3][3]) - M[3][0]*(M[0][1]*M[2][3] - M[0][3]*M[2][1]); + R[2][2] = M[0][0]*(M[1][1]*M[3][3] - M[1][3]*M[3][1]) - M[1][0]*(M[0][1]*M[3][3] - M[0][3]*M[3][1]) - M[3][0]*(M[0][3]*M[1][1] - M[0][1]*M[1][3]); + R[2][3] = M[0][0]*(M[1][3]*M[2][1] - M[1][1]*M[2][3]) - M[1][0]*(M[0][3]*M[2][1] - M[0][1]*M[2][3]) - M[2][0]*(M[0][1]*M[1][3] - M[0][3]*M[1][1]); + + R[3][0] = M[1][0]*(M[2][2]*M[3][1] - M[2][1]*M[3][2]) - M[2][0]*(M[1][2]*M[3][1] - M[1][1]*M[3][2]) - M[3][0]*(M[1][1]*M[2][2] - M[1][2]*M[2][1]); + R[3][1] = M[0][0]*(M[2][1]*M[3][2] - M[2][2]*M[3][1]) - M[2][0]*(M[0][1]*M[3][2] - M[0][2]*M[3][1]) - M[3][0]*(M[0][2]*M[2][1] - M[0][1]*M[2][2]); + R[3][2] = M[0][0]*(M[1][2]*M[3][1] - M[1][1]*M[3][2]) - M[1][0]*(M[0][2]*M[3][1] - M[0][1]*M[3][2]) - M[3][0]*(M[0][1]*M[1][2] - M[0][2]*M[1][1]); + R[3][3] = M[0][0]*(M[1][1]*M[2][2] - M[1][2]*M[2][1]) - M[1][0]*(M[0][1]*M[2][2] - M[0][2]*M[2][1]) - M[2][0]*(M[0][2]*M[1][1] - M[0][1]*M[1][2]); + memcpy(T, R, 16*sizeof(float)); +} +static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) +{ + mat4x4_dup(R, M); + float s = 1.; + vec3 h; + + vec3_norm(R[2], R[2]); + + s = vec3_mul_inner(R[1], R[2]); + vec3_scale(h, R[2], s); + vec3_sub(R[1], R[1], h); + vec3_norm(R[2], R[2]); + + s = vec3_mul_inner(R[1], R[2]); + vec3_scale(h, R[2], s); + vec3_sub(R[1], R[1], h); + vec3_norm(R[1], R[1]); + + s = vec3_mul_inner(R[0], R[1]); + vec3_scale(h, R[1], s); + vec3_sub(R[0], R[0], h); + vec3_norm(R[0], R[0]); +} + +static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f) +{ + M[0][0] = 2.*n/(r-l); + M[0][1] = M[0][2] = M[0][3] = 0.; + + M[1][1] = 2.*n/(t-b); + M[1][0] = M[1][2] = M[1][3] = 0.; + + M[2][0] = (r+l)/(r-l); + M[2][1] = (t+b)/(t-b); + M[2][2] = -(f+n)/(f-n); + M[2][3] = -1; + + M[3][2] = -2.*(f*n)/(f-n); + M[3][0] = M[3][1] = M[3][3] = 0.; +} +static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f) +{ + M[0][0] = 2./(r-l); + M[0][1] = M[0][2] = M[0][3] = 0.; + + M[1][1] = 2./(t-b); + M[1][0] = M[1][2] = M[1][3] = 0.; + + M[2][2] = -2./(f-n); + M[2][0] = M[2][1] = M[2][3] = 0.; + + M[3][0] = (r+l)/(r-l); + M[3][1] = (t+b)/(t-b); + M[3][2] = (f+n)/(f-n); + M[3][3] = 1.; +} + +typedef float quat[4]; +static inline void quat_identity(quat q) +{ + q[0] = q[1] = q[2] = 0.; + q[3] = 1.; +} +static inline void quat_add(quat r, quat a, quat b) +{ + int i; + for(i=0; i<4; ++i) + r[i] = a[i] + b[i]; +} +static inline void quat_sub(quat r, quat a, quat b) +{ + int i; + for(i=0; i<4; ++i) + r[i] = a[i] - b[i]; +} +static inline void quat_mul(quat r, quat p, quat q) +{ + vec3 w; + vec3_mul_cross(r, p, q); + vec3_scale(w, p, q[3]); + vec3_add(r, r, w); + vec3_scale(w, q, p[3]); + vec3_add(r, r, w); + r[3] = p[3]*q[3] - vec3_mul_inner(p, q); +} +static inline void quat_scale(quat r, quat v, float s) +{ + int i; + for(i=0; i<4; ++i) + r[i] = v[i] * s; +} +static inline float quat_inner_product(quat a, quat b) +{ + float p = 0.; + int i; + for(i=0; i<4; ++i) + p += b[i]*a[i]; + return p; +} +static inline void quat_conj(quat r, quat q) +{ + int i; + for(i=0; i<3; ++i) + r[i] = -q[i]; + r[3] = q[3]; +} +static inline void quat_norm(quat r, quat v) { vec4_norm(r, v); } +static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) +{ + quat q_; + quat v_ = {v[0], v[1], v[2], 0.}; + + quat_conj(q_, q); + quat_norm(q_, q_); + quat_mul(q_, v_, q_); + quat_mul(q_, q, q_); + memcpy(r, q_, 3*sizeof(float)); +} +static inline void mat4x4_from_quat(mat4x4 M, quat q) +{ + float a = q[3]; + float b = q[0]; + float c = q[1]; + float d = q[2]; + float a2 = a*a; + float b2 = b*b; + float c2 = c*c; + float d2 = d*d; + + M[0][0] = a2 + b2 - c2 - d2; + M[0][1] = 2*(b*c + a*d); + M[0][2] = 2*(b*d - a*c); + M[0][3] = 0.; + + M[1][0] = 2*(b*c - a*d); + M[1][1] = a2 - b2 + c2 - d2; + M[1][2] = 2*(c*d + a*b); + M[1][3] = 0.; + + M[2][0] = 2*(b*d + a*c); + M[2][1] = 2*(c*d - a*b); + M[2][2] = a2 - b2 - c2 + d2; + M[2][3] = 0.; + + M[3][0] = M[3][1] = M[3][2] = 0.; + M[3][3] = 1.; +} +static inline void mat4x4_mul_quat(mat4x4 R, mat4x4 M, quat q) +{ + quat_mul_vec3(R[0], M[0], q); + quat_mul_vec3(R[1], M[1], q); + quat_mul_vec3(R[2], M[2], q); + + R[3][0] = R[3][1] = R[3][2] = 0.; + R[3][3] = 1.; +} +static inline void quat_from_mat4x4(quat q, mat4x4 M) +{ + float r=0.; + int i; + + int perm[] = { 0, 1, 2, 0, 1 }; + int *p = perm; + + for(i = 0; i<3; i++) { + float m = M[i][i]; + if( m < r ) + continue; + m = r; + p = &perm[i]; + } + + r = sqrtf(1. + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]] ); + + q[0] = r/2.; + q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]])/(2.*r); + q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]])/(2.*r); + q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.*r); +} + +static inline void mat4x4_arcball(mat4x4 R, mat4x4 M, vec2 _a, vec2 _b, float s) +{ + vec2 a; memcpy(a, _a, sizeof(a)); + vec2 b; memcpy(b, _b, sizeof(b)); + + float z_a = 0.; + float z_b = 0.; + + if(vec2_len(a) < 1.) { + z_a = sqrtf(1. - vec2_mul_inner(a, a)); + } else { + vec2_norm(a, a); + } + + if(vec2_len(b) < 1.) { + z_b = sqrtf(1. - vec2_mul_inner(b, b)); + } else { + vec2_norm(b, b); + } + + vec3 a_ = {a[0], a[1], z_a}; + vec3 b_ = {b[0], b[1], z_b}; + + vec3 c_; + vec3_mul_cross(c_, a_, b_); + + float const angle = acos(vec3_mul_inner(a_, b_)) * s; + mat4x4_rotate(R, M, c_[0], c_[1], c_[2], angle); +} + +#endif |