From ecab47672040d34a1c17f940daa37c570a14c560 Mon Sep 17 00:00:00 2001 From: hgn Date: Sun, 23 Jun 2024 14:48:33 +0100 Subject: [PATCH] ? --- vg_m.hc | 2611 ------------------------------------------------------- 1 file changed, 2611 deletions(-) delete mode 100644 vg_m.hc diff --git a/vg_m.hc b/vg_m.hc deleted file mode 100644 index bdf5343..0000000 --- a/vg_m.hc +++ /dev/null @@ -1,2611 +0,0 @@ -/* Copyright (C) 2021-2024 Harry Godden (hgn) - All Rights Reserved - * - * 0. Misc - * 1. Scalar operations - * 2. Vectors - * 2.a 2D Vectors - * 2.b 3D Vectors - * 2.c 4D Vectors - * 3. Quaternions - * 4. Matrices - * 4.a 2x2 matrices - * 4.b 3x3 matrices - * 4.c 4x3 matrices - * 4.d 4x4 matrices - * 5. Geometry - * 5.a Boxes - * 5.b Planes - * 5.c Closest points - * 5.d Raycast & Spherecasts - * 5.e Curves - * 5.f Volumes - * 5.g Inertia tensors - * 6. Statistics - * 6.a Random numbers - */ - -#pragma once - -#include "vg_stdint.h" -#include -#include - -#define VG_PIf 3.14159265358979323846264338327950288f -#define VG_TAUf 6.28318530717958647692528676655900576f - -/* - * ----------------------------------------------------------------------------- - * Section 0. Misc Operations - * ----------------------------------------------------------------------------- - */ - -/* get the f32 as the raw bits in a u32 without converting */ -static u32 vg_ftu32( f32 a ) -{ - u32 *ptr = (u32 *)(&a); - return *ptr; -} - -/* check if f32 is infinite */ -static int vg_isinff( f32 a ) -{ - return ((vg_ftu32(a)) & 0x7FFFFFFFU) == 0x7F800000U; -} - -/* check if f32 is not a number */ -static int vg_isnanf( f32 a ) -{ - return !vg_isinff(a) && ((vg_ftu32(a)) & 0x7F800000U) == 0x7F800000U; -} - -/* check if f32 is a number and is not infinite */ -static int vg_validf( f32 a ) -{ - return ((vg_ftu32(a)) & 0x7F800000U) != 0x7F800000U; -} - -static int v3_valid( v3f a ){ - for( u32 i=0; i<3; i++ ) - if( !vg_validf(a[i]) ) return 0; - return 1; -} - -/* - * ----------------------------------------------------------------------------- - * Section 1. Scalar Operations - * ----------------------------------------------------------------------------- - */ - -static inline f32 vg_minf( f32 a, f32 b ){ return a < b? a: b; } -static inline f32 vg_maxf( f32 a, f32 b ){ return a > b? a: b; } - -static inline int vg_min( int a, int b ){ return a < b? a: b; } -static inline int vg_max( int a, int b ){ return a > b? a: b; } - -static inline f32 vg_clampf( f32 a, f32 min, f32 max ) -{ - return vg_minf( max, vg_maxf( a, min ) ); -} - -static inline f32 vg_signf( f32 a ) -{ - return a < 0.0f? -1.0f: 1.0f; -} - -static inline f32 vg_fractf( f32 a ) -{ - return a - floorf( a ); -} - -static inline f64 vg_fractf64( f64 a ){ - return a - floor( a ); -} - -static f32 vg_cfrictf( f32 velocity, f32 F ) -{ - return -vg_signf(velocity) * vg_minf( F, fabsf(velocity) ); -} - -static inline f32 vg_rad( f32 deg ) -{ - return deg * VG_PIf / 180.0f; -} - -/* angle to reach b from a */ -static f32 vg_angle_diff( f32 a, f32 b ){ - f32 d = fmod(b,VG_TAUf)-fmodf(a,VG_TAUf); - if( fabsf(d) > VG_PIf ) - d = -vg_signf(d) * (VG_TAUf - fabsf(d)); - - return d; -} - -/* - * quantize float to bit count - */ -static u32 vg_quantf( f32 a, u32 bits, f32 min, f32 max ){ - u32 mask = (0x1 << bits) - 1; - return vg_clampf((a - min) * ((f32)mask/(max-min)), 0.0f, mask ); -} - -/* - * un-quantize discreet to float - */ -static f32 vg_dequantf( u32 q, u32 bits, f32 min, f32 max ){ - u32 mask = (0x1 << bits) - 1; - return min + (f32)q * ((max-min) / (f32)mask); -} - -/* https://iquilezles.org/articles/functions/ - * - * Use k to control the stretching of the function. Its maximum, which is 1, - * happens at exactly x = 1/k. - */ -static f32 vg_exp_impulse( f32 x, f32 k ){ - f32 h = k*x; - return h*expf(1.0f-h); -} - -/* - * ----------------------------------------------------------------------------- - * Section 2.a 2D Vectors - * ----------------------------------------------------------------------------- - */ - -static inline void v2_copy( v2f a, v2f d ) -{ - d[0] = a[0]; d[1] = a[1]; -} - -static inline void v2_zero( v2f a ) -{ - a[0] = 0.f; a[1] = 0.f; -} - -static inline void v2_add( v2f a, v2f b, v2f d ) -{ - d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; -} - -static inline void v2_sub( v2f a, v2f b, v2f d ) -{ - d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; -} - -static inline void v2_minv( v2f a, v2f b, v2f dest ) -{ - dest[0] = vg_minf(a[0], b[0]); - dest[1] = vg_minf(a[1], b[1]); -} - -static inline void v2_maxv( v2f a, v2f b, v2f dest ) -{ - dest[0] = vg_maxf(a[0], b[0]); - dest[1] = vg_maxf(a[1], b[1]); -} - -static inline f32 v2_dot( v2f a, v2f b ) -{ - return a[0] * b[0] + a[1] * b[1]; -} - -static inline f32 v2_cross( v2f a, v2f b ) -{ - return a[0]*b[1] - a[1]*b[0]; -} - -static inline void v2_abs( v2f a, v2f d ) -{ - d[0] = fabsf( a[0] ); - d[1] = fabsf( a[1] ); -} - -static inline void v2_muls( v2f a, f32 s, v2f d ) -{ - d[0] = a[0]*s; d[1] = a[1]*s; -} - -static inline void v2_divs( v2f a, f32 s, v2f d ) -{ - d[0] = a[0]/s; d[1] = a[1]/s; -} - -static inline void v2_mul( v2f a, v2f b, v2f d ) -{ - d[0] = a[0]*b[0]; - d[1] = a[1]*b[1]; -} - -static inline void v2_div( v2f a, v2f b, v2f d ) -{ - d[0] = a[0]/b[0]; d[1] = a[1]/b[1]; -} - -static inline void v2_muladd( v2f a, v2f b, v2f s, v2f d ) -{ - d[0] = a[0]+b[0]*s[0]; - d[1] = a[1]+b[1]*s[1]; -} - -static inline void v2_muladds( v2f a, v2f b, f32 s, v2f d ) -{ - d[0] = a[0]+b[0]*s; - d[1] = a[1]+b[1]*s; -} - -static inline f32 v2_length2( v2f a ) -{ - return a[0]*a[0] + a[1]*a[1]; -} - -static inline f32 v2_length( v2f a ) -{ - return sqrtf( v2_length2( a ) ); -} - -static inline f32 v2_dist2( v2f a, v2f b ) -{ - v2f delta; - v2_sub( a, b, delta ); - return v2_length2( delta ); -} - -static inline f32 v2_dist( v2f a, v2f b ) -{ - return sqrtf( v2_dist2( a, b ) ); -} - -static inline void v2_lerp( v2f a, v2f b, f32 t, v2f d ) -{ - d[0] = a[0] + t*(b[0]-a[0]); - d[1] = a[1] + t*(b[1]-a[1]); -} - -static inline void v2_normalize( v2f a ) -{ - v2_muls( a, 1.0f / v2_length( a ), a ); -} - -static void v2_normalize_clamp( v2f a ) -{ - f32 l2 = v2_length2( a ); - if( l2 > 1.0f ) - v2_muls( a, 1.0f/sqrtf(l2), a ); -} - -static inline void v2_floor( v2f a, v2f b ) -{ - b[0] = floorf( a[0] ); - b[1] = floorf( a[1] ); -} - -static inline void v2_fill( v2f a, f32 v ) -{ - a[0] = v; - a[1] = v; -} - -static inline void v2_copysign( v2f a, v2f b ) -{ - a[0] = copysignf( a[0], b[0] ); - a[1] = copysignf( a[1], b[1] ); -} - -/* integer variants - * ---------------- */ - -static inline void v2i_copy( v2i a, v2i b ) -{ - b[0] = a[0]; b[1] = a[1]; -} - -static inline int v2i_eq( v2i a, v2i b ) -{ - return ((a[0] == b[0]) && (a[1] == b[1])); -} - -static inline void v2i_add( v2i a, v2i b, v2i d ) -{ - d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; -} - -static inline void v2i_sub( v2i a, v2i b, v2i d ) -{ - d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; -} - -/* - * ----------------------------------------------------------------------------- - * Section 2.b 3D Vectors - * ----------------------------------------------------------------------------- - */ - -static inline void v3_copy( v3f a, v3f b ) -{ - b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; -} - -static inline void v3_zero( v3f a ) -{ - a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; -} - -static inline void v3_add( v3f a, v3f b, v3f d ) -{ - d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2]; -} - -static inline void v3i_add( v3i a, v3i b, v3i d ) -{ - d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2]; -} - -static inline void v3_sub( v3f a, v3f b, v3f d ) -{ - d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2]; -} - -static inline void v3i_sub( v3i a, v3i b, v3i d ) -{ - d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2]; -} - -static inline void v3_mul( v3f a, v3f b, v3f d ) -{ - d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2]; -} - -static inline void v3_div( v3f a, v3f b, v3f d ) -{ - d[0] = b[0]!=0.0f? a[0]/b[0]: INFINITY; - d[1] = b[1]!=0.0f? a[1]/b[1]: INFINITY; - d[2] = b[2]!=0.0f? a[2]/b[2]: INFINITY; -} - -static inline void v3_muls( v3f a, f32 s, v3f d ) -{ - d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s; -} - -static inline void v3_fill( v3f a, f32 v ) -{ - a[0] = v; - a[1] = v; - a[2] = v; -} - -static inline void v3_divs( v3f a, f32 s, v3f d ) -{ - if( s == 0.0f ) - v3_fill( d, INFINITY ); - else - { - d[0] = a[0]/s; - d[1] = a[1]/s; - d[2] = a[2]/s; - } -} - -static inline void v3_muladds( v3f a, v3f b, f32 s, v3f d ) -{ - d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s; -} - -static inline void v3_muladd( v2f a, v2f b, v2f s, v2f d ) -{ - d[0] = a[0]+b[0]*s[0]; - d[1] = a[1]+b[1]*s[1]; - d[2] = a[2]+b[2]*s[2]; -} - -static inline f32 v3_dot( v3f a, v3f b ) -{ - return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; -} - -static inline void v3_cross( v3f a, v3f b, v3f dest ) -{ - v3f d; - d[0] = a[1]*b[2] - a[2]*b[1]; - d[1] = a[2]*b[0] - a[0]*b[2]; - d[2] = a[0]*b[1] - a[1]*b[0]; - v3_copy( d, dest ); -} - -static inline f32 v3_length2( v3f a ) -{ - return v3_dot( a, a ); -} - -static inline f32 v3_length( v3f a ) -{ - return sqrtf( v3_length2( a ) ); -} - -static inline f32 v3_dist2( v3f a, v3f b ) -{ - v3f delta; - v3_sub( a, b, delta ); - return v3_length2( delta ); -} - -static inline f32 v3_dist( v3f a, v3f b ) -{ - return sqrtf( v3_dist2( a, b ) ); -} - -static inline void v3_normalize( v3f a ) -{ - v3_muls( a, 1.f / v3_length( a ), a ); -} - -static inline f32 vg_lerpf( f32 a, f32 b, f32 t ){ - return a + t*(b-a); -} - -static inline f64 vg_lerp( f64 a, f64 b, f64 t ) -{ - return a + t*(b-a); -} - -static inline void vg_slewf( f32 *a, f32 b, f32 speed ){ - f32 d = vg_signf( b-*a ), - c = *a + d*speed; - *a = vg_minf( b*d, c*d ) * d; -} - -static inline f32 vg_smoothstepf( f32 x ){ - return x*x*(3.0f - 2.0f*x); -} - - -/* correctly lerp around circular period -pi -> pi */ -static f32 vg_alerpf( f32 a, f32 b, f32 t ) -{ - f32 d = fmodf( b-a, VG_TAUf ), - s = fmodf( 2.0f*d, VG_TAUf ) - d; - return a + s*t; -} - -static inline void v3_lerp( v3f a, v3f b, f32 t, v3f d ) -{ - d[0] = a[0] + t*(b[0]-a[0]); - d[1] = a[1] + t*(b[1]-a[1]); - d[2] = a[2] + t*(b[2]-a[2]); -} - -static inline void v3_minv( v3f a, v3f b, v3f dest ) -{ - dest[0] = vg_minf(a[0], b[0]); - dest[1] = vg_minf(a[1], b[1]); - dest[2] = vg_minf(a[2], b[2]); -} - -static inline void v3_maxv( v3f a, v3f b, v3f dest ) -{ - dest[0] = vg_maxf(a[0], b[0]); - dest[1] = vg_maxf(a[1], b[1]); - dest[2] = vg_maxf(a[2], b[2]); -} - -static inline f32 v3_minf( v3f a ) -{ - return vg_minf( vg_minf( a[0], a[1] ), a[2] ); -} - -static inline f32 v3_maxf( v3f a ) -{ - return vg_maxf( vg_maxf( a[0], a[1] ), a[2] ); -} - -static inline void v3_floor( v3f a, v3f b ) -{ - b[0] = floorf( a[0] ); - b[1] = floorf( a[1] ); - b[2] = floorf( a[2] ); -} - -static inline void v3_ceil( v3f a, v3f b ) -{ - b[0] = ceilf( a[0] ); - b[1] = ceilf( a[1] ); - b[2] = ceilf( a[2] ); -} - -static inline void v3_negate( v3f a, v3f b ) -{ - b[0] = -a[0]; - b[1] = -a[1]; - b[2] = -a[2]; -} - -static inline void v3_rotate( v3f v, f32 angle, v3f axis, v3f d ) -{ - v3f v1, v2, k; - f32 c, s; - - c = cosf( angle ); - s = sinf( angle ); - - v3_copy( axis, k ); - v3_normalize( k ); - v3_muls( v, c, v1 ); - v3_cross( k, v, v2 ); - v3_muls( v2, s, v2 ); - v3_add( v1, v2, v1 ); - v3_muls( k, v3_dot(k, v) * (1.0f - c), v2); - v3_add( v1, v2, d ); -} - -static void v3_tangent_basis( v3f n, v3f tx, v3f ty ){ - /* Compute tangent basis (box2d) */ - if( fabsf( n[0] ) >= 0.57735027f ){ - tx[0] = n[1]; - tx[1] = -n[0]; - tx[2] = 0.0f; - } - else{ - tx[0] = 0.0f; - tx[1] = n[2]; - tx[2] = -n[1]; - } - - v3_normalize( tx ); - v3_cross( n, tx, ty ); -} - -/* - * Compute yaw and pitch based of a normalized vector representing forward - * forward: -z - * result -> (YAW,PITCH,0.0) - */ -static void v3_angles( v3f v, v3f out_angles ){ - float yaw = atan2f( v[0], -v[2] ), - pitch = atan2f( - -v[1], - sqrtf( - v[0]*v[0] + v[2]*v[2] - ) - ); - - out_angles[0] = yaw; - out_angles[1] = pitch; - out_angles[2] = 0.0f; -} - -/* - * Compute the forward vector from (YAW,PITCH,ROLL) - * forward: -z - */ -static void v3_angles_vector( v3f angles, v3f out_v ){ - out_v[0] = sinf( angles[0] ) * cosf( angles[1] ); - out_v[1] = -sinf( angles[1] ); - out_v[2] = -cosf( angles[0] ) * cosf( angles[1] ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 2.c 4D Vectors - * ----------------------------------------------------------------------------- - */ - -static inline void v4_copy( v4f a, v4f b ) -{ - b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3]; -} - -static inline void v4_add( v4f a, v4f b, v4f d ) -{ - d[0] = a[0]+b[0]; - d[1] = a[1]+b[1]; - d[2] = a[2]+b[2]; - d[3] = a[3]+b[3]; -} - -static inline void v4_zero( v4f a ) -{ - a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f; -} - -static inline void v4_muls( v4f a, f32 s, v4f d ) -{ - d[0] = a[0]*s; - d[1] = a[1]*s; - d[2] = a[2]*s; - d[3] = a[3]*s; -} - -static inline void v4_muladds( v4f a, v4f b, f32 s, v4f d ) -{ - d[0] = a[0]+b[0]*s; - d[1] = a[1]+b[1]*s; - d[2] = a[2]+b[2]*s; - d[3] = a[3]+b[3]*s; -} - -static inline void v4_lerp( v4f a, v4f b, f32 t, v4f d ) -{ - d[0] = a[0] + t*(b[0]-a[0]); - d[1] = a[1] + t*(b[1]-a[1]); - d[2] = a[2] + t*(b[2]-a[2]); - d[3] = a[3] + t*(b[3]-a[3]); -} - -static inline f32 v4_dot( v4f a, v4f b ) -{ - return a[0]*b[0] + a[1]*b[1] + a[2]*b[2] + a[3]*b[3]; -} - -static inline f32 v4_length( v4f a ) -{ - return sqrtf( v4_dot(a,a) ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 3 Quaternions - * ----------------------------------------------------------------------------- - */ - -static inline void q_identity( v4f q ) -{ - q[0] = 0.0f; q[1] = 0.0f; q[2] = 0.0f; q[3] = 1.0f; -} - -static inline void q_axis_angle( v4f q, v3f axis, f32 angle ) -{ - f32 a = angle*0.5f, - c = cosf(a), - s = sinf(a); - - q[0] = s*axis[0]; - q[1] = s*axis[1]; - q[2] = s*axis[2]; - q[3] = c; -} - -static inline void q_mul( v4f q, v4f q1, v4f d ) -{ - v4f t; - t[0] = q[3]*q1[0] + q[0]*q1[3] + q[1]*q1[2] - q[2]*q1[1]; - t[1] = q[3]*q1[1] - q[0]*q1[2] + q[1]*q1[3] + q[2]*q1[0]; - t[2] = q[3]*q1[2] + q[0]*q1[1] - q[1]*q1[0] + q[2]*q1[3]; - t[3] = q[3]*q1[3] - q[0]*q1[0] - q[1]*q1[1] - q[2]*q1[2]; - v4_copy( t, d ); -} - -static inline void q_normalize( v4f q ) -{ - f32 l2 = v4_dot(q,q); - if( l2 < 0.00001f ) q_identity( q ); - else { - f32 s = 1.0f/sqrtf(l2); - q[0] *= s; - q[1] *= s; - q[2] *= s; - q[3] *= s; - } -} - -static inline void q_inv( v4f q, v4f d ) -{ - f32 s = 1.0f / v4_dot(q,q); - d[0] = -q[0]*s; - d[1] = -q[1]*s; - d[2] = -q[2]*s; - d[3] = q[3]*s; -} - -static inline void q_nlerp( v4f a, v4f b, f32 t, v4f d ){ - if( v4_dot(a,b) < 0.0f ){ - v4f c; - v4_muls( b, -1.0f, c ); - v4_lerp( a, c, t, d ); - } - else - v4_lerp( a, b, t, d ); - - q_normalize( d ); -} - -static inline void q_m3x3( v4f q, m3x3f d ) -{ - f32 - l = v4_length(q), - s = l > 0.0f? 2.0f/l: 0.0f, - - xx = s*q[0]*q[0], xy = s*q[0]*q[1], wx = s*q[3]*q[0], - yy = s*q[1]*q[1], yz = s*q[1]*q[2], wy = s*q[3]*q[1], - zz = s*q[2]*q[2], xz = s*q[0]*q[2], wz = s*q[3]*q[2]; - - d[0][0] = 1.0f - yy - zz; - d[1][1] = 1.0f - xx - zz; - d[2][2] = 1.0f - xx - yy; - d[0][1] = xy + wz; - d[1][2] = yz + wx; - d[2][0] = xz + wy; - d[1][0] = xy - wz; - d[2][1] = yz - wx; - d[0][2] = xz - wy; -} - -static void q_mulv( v4f q, v3f v, v3f d ) -{ - v3f v1, v2; - - v3_muls( q, 2.0f*v3_dot(q,v), v1 ); - v3_muls( v, q[3]*q[3] - v3_dot(q,q), v2 ); - v3_add( v1, v2, v1 ); - v3_cross( q, v, v2 ); - v3_muls( v2, 2.0f*q[3], v2 ); - v3_add( v1, v2, d ); -} - -static f32 q_dist( v4f q0, v4f q1 ){ - return acosf( 2.0f * v4_dot(q0,q1) -1.0f ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 4.a 2x2 matrices - * ----------------------------------------------------------------------------- - */ - -#define M2X2_INDENTIY {{1.0f, 0.0f, }, \ - {0.0f, 1.0f, }} - -#define M2X2_ZERO {{0.0f, 0.0f, }, \ - {0.0f, 0.0f, }} - -static inline void m2x2_copy( m2x2f a, m2x2f b ) -{ - v2_copy( a[0], b[0] ); - v2_copy( a[1], b[1] ); -} - -static inline void m2x2_identity( m2x2f a ) -{ - m2x2f id = M2X2_INDENTIY; - m2x2_copy( id, a ); -} - -static inline void m2x2_create_rotation( m2x2f a, f32 theta ) -{ - f32 s, c; - - s = sinf( theta ); - c = cosf( theta ); - - a[0][0] = c; - a[0][1] = -s; - a[1][0] = s; - a[1][1] = c; -} - -static inline void m2x2_mulv( m2x2f m, v2f v, v2f d ) -{ - v2f res; - - res[0] = m[0][0]*v[0] + m[1][0]*v[1]; - res[1] = m[0][1]*v[0] + m[1][1]*v[1]; - - v2_copy( res, d ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 4.b 3x3 matrices - * ----------------------------------------------------------------------------- - */ - -#define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\ - { 0.0f, 1.0f, 0.0f, },\ - { 0.0f, 0.0f, 1.0f, }} - -#define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\ - { 0.0f, 0.0f, 0.0f, },\ - { 0.0f, 0.0f, 0.0f, }} - - -static void euler_m3x3( v3f angles, m3x3f d ) -{ - f32 cosY = cosf( angles[0] ), - sinY = sinf( angles[0] ), - cosP = cosf( angles[1] ), - sinP = sinf( angles[1] ), - cosR = cosf( angles[2] ), - sinR = sinf( angles[2] ); - - d[2][0] = -sinY * cosP; - d[2][1] = sinP; - d[2][2] = cosY * cosP; - - d[0][0] = cosY * cosR; - d[0][1] = sinR; - d[0][2] = sinY * cosR; - - v3_cross( d[0], d[2], d[1] ); -} - -static void m3x3_q( m3x3f m, v4f q ) -{ - f32 diag, r, rinv; - - diag = m[0][0] + m[1][1] + m[2][2]; - if( diag >= 0.0f ) - { - r = sqrtf( 1.0f + diag ); - rinv = 0.5f / r; - q[0] = rinv * (m[1][2] - m[2][1]); - q[1] = rinv * (m[2][0] - m[0][2]); - q[2] = rinv * (m[0][1] - m[1][0]); - q[3] = r * 0.5f; - } - else if( m[0][0] >= m[1][1] && m[0][0] >= m[2][2] ) - { - r = sqrtf( 1.0f - m[1][1] - m[2][2] + m[0][0] ); - rinv = 0.5f / r; - q[0] = r * 0.5f; - q[1] = rinv * (m[0][1] + m[1][0]); - q[2] = rinv * (m[0][2] + m[2][0]); - q[3] = rinv * (m[1][2] - m[2][1]); - } - else if( m[1][1] >= m[2][2] ) - { - r = sqrtf( 1.0f - m[0][0] - m[2][2] + m[1][1] ); - rinv = 0.5f / r; - q[0] = rinv * (m[0][1] + m[1][0]); - q[1] = r * 0.5f; - q[2] = rinv * (m[1][2] + m[2][1]); - q[3] = rinv * (m[2][0] - m[0][2]); - } - else - { - r = sqrtf( 1.0f - m[0][0] - m[1][1] + m[2][2] ); - rinv = 0.5f / r; - q[0] = rinv * (m[0][2] + m[2][0]); - q[1] = rinv * (m[1][2] + m[2][1]); - q[2] = r * 0.5f; - q[3] = rinv * (m[0][1] - m[1][0]); - } -} - -/* a X b == [b]T a == ...*/ -static void m3x3_skew_symetric( m3x3f a, v3f v ) -{ - a[0][0] = 0.0f; - a[0][1] = v[2]; - a[0][2] = -v[1]; - a[1][0] = -v[2]; - a[1][1] = 0.0f; - a[1][2] = v[0]; - a[2][0] = v[1]; - a[2][1] = -v[0]; - a[2][2] = 0.0f; -} - -/* aka kronecker product */ -static void m3x3_outer_product( m3x3f out_m, v3f a, v3f b ) -{ - out_m[0][0] = a[0]*b[0]; - out_m[0][1] = a[0]*b[1]; - out_m[0][2] = a[0]*b[2]; - out_m[1][0] = a[1]*b[0]; - out_m[1][1] = a[1]*b[1]; - out_m[1][2] = a[1]*b[2]; - out_m[2][0] = a[2]*b[0]; - out_m[2][1] = a[2]*b[1]; - out_m[2][2] = a[2]*b[2]; -} - -static void m3x3_add( m3x3f a, m3x3f b, m3x3f d ) -{ - v3_add( a[0], b[0], d[0] ); - v3_add( a[1], b[1], d[1] ); - v3_add( a[2], b[2], d[2] ); -} - -static void m3x3_sub( m3x3f a, m3x3f b, m3x3f d ) -{ - v3_sub( a[0], b[0], d[0] ); - v3_sub( a[1], b[1], d[1] ); - v3_sub( a[2], b[2], d[2] ); -} - -static inline void m3x3_copy( m3x3f a, m3x3f b ) -{ - v3_copy( a[0], b[0] ); - v3_copy( a[1], b[1] ); - v3_copy( a[2], b[2] ); -} - -static inline void m3x3_identity( m3x3f a ) -{ - m3x3f id = M3X3_IDENTITY; - m3x3_copy( id, a ); -} - -static void m3x3_diagonal( m3x3f out_a, f32 v ) -{ - m3x3_identity( out_a ); - out_a[0][0] = v; - out_a[1][1] = v; - out_a[2][2] = v; -} - -static void m3x3_setdiagonalv3( m3x3f a, v3f v ) -{ - a[0][0] = v[0]; - a[1][1] = v[1]; - a[2][2] = v[2]; -} - -static inline void m3x3_zero( m3x3f a ) -{ - m3x3f z = M3X3_ZERO; - m3x3_copy( z, a ); -} - -static inline void m3x3_inv( m3x3f src, m3x3f dest ) -{ - f32 a = src[0][0], b = src[0][1], c = src[0][2], - d = src[1][0], e = src[1][1], f = src[1][2], - g = src[2][0], h = src[2][1], i = src[2][2]; - - f32 det = 1.f / - (+a*(e*i-h*f) - -b*(d*i-f*g) - +c*(d*h-e*g)); - - dest[0][0] = (e*i-h*f)*det; - dest[0][1] = -(b*i-c*h)*det; - dest[0][2] = (b*f-c*e)*det; - dest[1][0] = -(d*i-f*g)*det; - dest[1][1] = (a*i-c*g)*det; - dest[1][2] = -(a*f-d*c)*det; - dest[2][0] = (d*h-g*e)*det; - dest[2][1] = -(a*h-g*b)*det; - dest[2][2] = (a*e-d*b)*det; -} - -static f32 m3x3_det( m3x3f m ) -{ - return m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2]) - - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0]) - + m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]); -} - -static inline void m3x3_transpose( m3x3f src, m3x3f dest ) -{ - f32 a = src[0][0], b = src[0][1], c = src[0][2], - d = src[1][0], e = src[1][1], f = src[1][2], - g = src[2][0], h = src[2][1], i = src[2][2]; - - dest[0][0] = a; - dest[0][1] = d; - dest[0][2] = g; - dest[1][0] = b; - dest[1][1] = e; - dest[1][2] = h; - dest[2][0] = c; - dest[2][1] = f; - dest[2][2] = i; -} - -static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d ) -{ - f32 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], - a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], - a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], - - b00 = b[0][0], b01 = b[0][1], b02 = b[0][2], - b10 = b[1][0], b11 = b[1][1], b12 = b[1][2], - b20 = b[2][0], b21 = b[2][1], b22 = b[2][2]; - - d[0][0] = a00*b00 + a10*b01 + a20*b02; - d[0][1] = a01*b00 + a11*b01 + a21*b02; - d[0][2] = a02*b00 + a12*b01 + a22*b02; - d[1][0] = a00*b10 + a10*b11 + a20*b12; - d[1][1] = a01*b10 + a11*b11 + a21*b12; - d[1][2] = a02*b10 + a12*b11 + a22*b12; - d[2][0] = a00*b20 + a10*b21 + a20*b22; - d[2][1] = a01*b20 + a11*b21 + a21*b22; - d[2][2] = a02*b20 + a12*b21 + a22*b22; -} - -static inline void m3x3_mulv( m3x3f m, v3f v, v3f d ) -{ - v3f res; - - res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2]; - res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2]; - res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2]; - - v3_copy( res, d ); -} - -static inline void m3x3_projection( m3x3f dst, - f32 const left, f32 const right, f32 const bottom, f32 const top ) -{ - f32 rl, tb; - - m3x3_zero( dst ); - - rl = 1.0f / (right - left); - tb = 1.0f / (top - bottom); - - dst[0][0] = 2.0f * rl; - dst[1][1] = 2.0f * tb; - dst[2][2] = 1.0f; -} - -static inline void m3x3_translate( m3x3f m, v3f v ) -{ - m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0]; - m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1]; - m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2]; -} - -static inline void m3x3_scale( m3x3f m, v3f v ) -{ - v3_muls( m[0], v[0], m[0] ); - v3_muls( m[1], v[1], m[1] ); - v3_muls( m[2], v[2], m[2] ); -} - -static inline void m3x3_scalef( m3x3f m, f32 f ) -{ - v3f v; - v3_fill( v, f ); - m3x3_scale( m, v ); -} - -static inline void m3x3_rotate( m3x3f m, f32 angle ) -{ - f32 m00 = m[0][0], m10 = m[1][0], - m01 = m[0][1], m11 = m[1][1], - m02 = m[0][2], m12 = m[1][2]; - f32 c, s; - - s = sinf( angle ); - c = cosf( angle ); - - m[0][0] = m00 * c + m10 * s; - m[0][1] = m01 * c + m11 * s; - m[0][2] = m02 * c + m12 * s; - - m[1][0] = m00 * -s + m10 * c; - m[1][1] = m01 * -s + m11 * c; - m[1][2] = m02 * -s + m12 * c; -} - -/* - * ----------------------------------------------------------------------------- - * Section 4.c 4x3 matrices - * ----------------------------------------------------------------------------- - */ - -#define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\ - { 0.0f, 1.0f, 0.0f, },\ - { 0.0f, 0.0f, 1.0f, },\ - { 0.0f, 0.0f, 0.0f }} - -static inline void m4x3_to_3x3( m4x3f a, m3x3f b ) -{ - v3_copy( a[0], b[0] ); - v3_copy( a[1], b[1] ); - v3_copy( a[2], b[2] ); -} - -static inline void m4x3_invert_affine( m4x3f a, m4x3f b ) -{ - m3x3_transpose( a, b ); - m3x3_mulv( b, a[3], b[3] ); - v3_negate( b[3], b[3] ); -} - -static void m4x3_invert_full( m4x3f src, m4x3f dst ) -{ - f32 t2, t4, t5, - det, - a = src[0][0], b = src[0][1], c = src[0][2], - e = src[1][0], f = src[1][1], g = src[1][2], - i = src[2][0], j = src[2][1], k = src[2][2], - m = src[3][0], n = src[3][1], o = src[3][2]; - - t2 = j*o - n*k; - t4 = i*o - m*k; - t5 = i*n - m*j; - - dst[0][0] = f*k - g*j; - dst[1][0] =-(e*k - g*i); - dst[2][0] = e*j - f*i; - dst[3][0] =-(e*t2 - f*t4 + g*t5); - - dst[0][1] =-(b*k - c*j); - dst[1][1] = a*k - c*i; - dst[2][1] =-(a*j - b*i); - dst[3][1] = a*t2 - b*t4 + c*t5; - - t2 = f*o - n*g; - t4 = e*o - m*g; - t5 = e*n - m*f; - - dst[0][2] = b*g - c*f ; - dst[1][2] =-(a*g - c*e ); - dst[2][2] = a*f - b*e ; - dst[3][2] =-(a*t2 - b*t4 + c * t5); - - det = 1.0f / (a * dst[0][0] + b * dst[1][0] + c * dst[2][0]); - v3_muls( dst[0], det, dst[0] ); - v3_muls( dst[1], det, dst[1] ); - v3_muls( dst[2], det, dst[2] ); - v3_muls( dst[3], det, dst[3] ); -} - -static inline void m4x3_copy( m4x3f a, m4x3f b ) -{ - v3_copy( a[0], b[0] ); - v3_copy( a[1], b[1] ); - v3_copy( a[2], b[2] ); - v3_copy( a[3], b[3] ); -} - -static inline void m4x3_identity( m4x3f a ) -{ - m4x3f id = M4X3_IDENTITY; - m4x3_copy( id, a ); -} - -static void m4x3_mul( m4x3f a, m4x3f b, m4x3f d ) -{ - f32 - a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], - a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], - a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], - a30 = a[3][0], a31 = a[3][1], a32 = a[3][2], - b00 = b[0][0], b01 = b[0][1], b02 = b[0][2], - b10 = b[1][0], b11 = b[1][1], b12 = b[1][2], - b20 = b[2][0], b21 = b[2][1], b22 = b[2][2], - b30 = b[3][0], b31 = b[3][1], b32 = b[3][2]; - - d[0][0] = a00*b00 + a10*b01 + a20*b02; - d[0][1] = a01*b00 + a11*b01 + a21*b02; - d[0][2] = a02*b00 + a12*b01 + a22*b02; - d[1][0] = a00*b10 + a10*b11 + a20*b12; - d[1][1] = a01*b10 + a11*b11 + a21*b12; - d[1][2] = a02*b10 + a12*b11 + a22*b12; - d[2][0] = a00*b20 + a10*b21 + a20*b22; - d[2][1] = a01*b20 + a11*b21 + a21*b22; - d[2][2] = a02*b20 + a12*b21 + a22*b22; - d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30; - d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31; - d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32; -} - -#if 0 /* shat appf mingw wstringop-overflow */ -inline -#endif -static void m4x3_mulv( m4x3f m, v3f v, v3f d ) -{ - v3f res; - - res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0]; - res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1]; - res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2]; - - v3_copy( res, d ); -} - -/* - * Transform plane ( xyz, distance ) - */ -static void m4x3_mulp( m4x3f m, v4f p, v4f d ) -{ - v3f o; - - v3_muls( p, p[3], o ); - m4x3_mulv( m, o, o ); - m3x3_mulv( m, p, d ); - - d[3] = v3_dot( o, d ); -} - -/* - * Affine transforms - */ - -static void m4x3_translate( m4x3f m, v3f v ) -{ - v3_muladds( m[3], m[0], v[0], m[3] ); - v3_muladds( m[3], m[1], v[1], m[3] ); - v3_muladds( m[3], m[2], v[2], m[3] ); -} - -static void m4x3_rotate_x( m4x3f m, f32 angle ) -{ - m4x3f t = M4X3_IDENTITY; - f32 c, s; - - c = cosf( angle ); - s = sinf( angle ); - - t[1][1] = c; - t[1][2] = s; - t[2][1] = -s; - t[2][2] = c; - - m4x3_mul( m, t, m ); -} - -static void m4x3_rotate_y( m4x3f m, f32 angle ) -{ - m4x3f t = M4X3_IDENTITY; - f32 c, s; - - c = cosf( angle ); - s = sinf( angle ); - - t[0][0] = c; - t[0][2] = -s; - t[2][0] = s; - t[2][2] = c; - - m4x3_mul( m, t, m ); -} - -static void m4x3_rotate_z( m4x3f m, f32 angle ) -{ - m4x3f t = M4X3_IDENTITY; - f32 c, s; - - c = cosf( angle ); - s = sinf( angle ); - - t[0][0] = c; - t[0][1] = s; - t[1][0] = -s; - t[1][1] = c; - - m4x3_mul( m, t, m ); -} - -static void m4x3_expand( m4x3f m, m4x4f d ) -{ - v3_copy( m[0], d[0] ); - v3_copy( m[1], d[1] ); - v3_copy( m[2], d[2] ); - v3_copy( m[3], d[3] ); - d[0][3] = 0.0f; - d[1][3] = 0.0f; - d[2][3] = 0.0f; - d[3][3] = 1.0f; -} - -static void m4x3_decompose( m4x3f m, v3f co, v4f q, v3f s ) -{ - v3_copy( m[3], co ); - s[0] = v3_length(m[0]); - s[1] = v3_length(m[1]); - s[2] = v3_length(m[2]); - - m3x3f rot; - v3_divs( m[0], s[0], rot[0] ); - v3_divs( m[1], s[1], rot[1] ); - v3_divs( m[2], s[2], rot[2] ); - - m3x3_q( rot, q ); -} - -static void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point ){ - v3f v; - m4x3_mulv( m, point, v ); - - v3_minv( box[0], v, box[0] ); - v3_maxv( box[1], v, box[1] ); -} - -static void m4x3_expand_aabb_aabb( m4x3f m, boxf boxa, boxf boxb ){ - v3f a; v3f b; - v3_copy( boxb[0], a ); - v3_copy( boxb[1], b ); - m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], a[1], a[2] } ); - m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], b[1], a[2] } ); - m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], b[1], a[2] } ); - m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], a[1], a[2] } ); - m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], a[1], b[2] } ); - m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], b[1], b[2] } ); - m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], b[1], b[2] } ); - m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], a[1], b[2] } ); -} -static inline void m4x3_lookat( m4x3f m, v3f pos, v3f target, v3f up ) -{ - v3f dir; - v3_sub( target, pos, dir ); - v3_normalize( dir ); - - v3_copy( dir, m[2] ); - - v3_cross( up, m[2], m[0] ); - v3_normalize( m[0] ); - - v3_cross( m[2], m[0], m[1] ); - v3_copy( pos, m[3] ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 4.d 4x4 matrices - * ----------------------------------------------------------------------------- - */ - -#define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\ - { 0.0f, 1.0f, 0.0f, 0.0f },\ - { 0.0f, 0.0f, 1.0f, 0.0f },\ - { 0.0f, 0.0f, 0.0f, 1.0f }} -#define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\ - { 0.0f, 0.0f, 0.0f, 0.0f },\ - { 0.0f, 0.0f, 0.0f, 0.0f },\ - { 0.0f, 0.0f, 0.0f, 0.0f }} - -static void m4x4_projection( m4x4f m, f32 angle, - f32 ratio, f32 fnear, f32 ffar ) -{ - f32 scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * fnear, - r = ratio * scale, - l = -r, - t = scale, - b = -t; - - m[0][0] = 2.0f * fnear / (r - l); - m[0][1] = 0.0f; - m[0][2] = 0.0f; - m[0][3] = 0.0f; - - m[1][0] = 0.0f; - m[1][1] = 2.0f * fnear / (t - b); - m[1][2] = 0.0f; - m[1][3] = 0.0f; - - m[2][0] = (r + l) / (r - l); - m[2][1] = (t + b) / (t - b); - m[2][2] = -(ffar + fnear) / (ffar - fnear); - m[2][3] = -1.0f; - - m[3][0] = 0.0f; - m[3][1] = 0.0f; - m[3][2] = -2.0f * ffar * fnear / (ffar - fnear); - m[3][3] = 0.0f; -} - -static void m4x4_translate( m4x4f m, v3f v ) -{ - v4_muladds( m[3], m[0], v[0], m[3] ); - v4_muladds( m[3], m[1], v[1], m[3] ); - v4_muladds( m[3], m[2], v[2], m[3] ); -} - -static inline void m4x4_copy( m4x4f a, m4x4f b ) -{ - v4_copy( a[0], b[0] ); - v4_copy( a[1], b[1] ); - v4_copy( a[2], b[2] ); - v4_copy( a[3], b[3] ); -} - -static inline void m4x4_identity( m4x4f a ) -{ - m4x4f id = M4X4_IDENTITY; - m4x4_copy( id, a ); -} - -static inline void m4x4_zero( m4x4f a ) -{ - m4x4f zero = M4X4_ZERO; - m4x4_copy( zero, a ); -} - -static inline void m4x4_mul( m4x4f a, m4x4f b, m4x4f d ) -{ - f32 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3], - a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], a13 = a[1][3], - a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], a23 = a[2][3], - a30 = a[3][0], a31 = a[3][1], a32 = a[3][2], a33 = a[3][3], - - b00 = b[0][0], b01 = b[0][1], b02 = b[0][2], b03 = b[0][3], - b10 = b[1][0], b11 = b[1][1], b12 = b[1][2], b13 = b[1][3], - b20 = b[2][0], b21 = b[2][1], b22 = b[2][2], b23 = b[2][3], - b30 = b[3][0], b31 = b[3][1], b32 = b[3][2], b33 = b[3][3]; - - d[0][0] = a00*b00 + a10*b01 + a20*b02 + a30*b03; - d[0][1] = a01*b00 + a11*b01 + a21*b02 + a31*b03; - d[0][2] = a02*b00 + a12*b01 + a22*b02 + a32*b03; - d[0][3] = a03*b00 + a13*b01 + a23*b02 + a33*b03; - d[1][0] = a00*b10 + a10*b11 + a20*b12 + a30*b13; - d[1][1] = a01*b10 + a11*b11 + a21*b12 + a31*b13; - d[1][2] = a02*b10 + a12*b11 + a22*b12 + a32*b13; - d[1][3] = a03*b10 + a13*b11 + a23*b12 + a33*b13; - d[2][0] = a00*b20 + a10*b21 + a20*b22 + a30*b23; - d[2][1] = a01*b20 + a11*b21 + a21*b22 + a31*b23; - d[2][2] = a02*b20 + a12*b21 + a22*b22 + a32*b23; - d[2][3] = a03*b20 + a13*b21 + a23*b22 + a33*b23; - d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30*b33; - d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31*b33; - d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32*b33; - d[3][3] = a03*b30 + a13*b31 + a23*b32 + a33*b33; -} - -static inline void m4x4_mulv( m4x4f m, v4f v, v4f d ) -{ - v4f res; - - res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0]*v[3]; - res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1]*v[3]; - res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2]*v[3]; - res[3] = m[0][3]*v[0] + m[1][3]*v[1] + m[2][3]*v[2] + m[3][3]*v[3]; - - v4_copy( res, d ); -} - -static inline void m4x4_inv( m4x4f a, m4x4f d ) -{ - f32 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3], - a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], a13 = a[1][3], - a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], a23 = a[2][3], - a30 = a[3][0], a31 = a[3][1], a32 = a[3][2], a33 = a[3][3], - det, - t[6]; - - t[0] = a22*a33 - a32*a23; - t[1] = a21*a33 - a31*a23; - t[2] = a21*a32 - a31*a22; - t[3] = a20*a33 - a30*a23; - t[4] = a20*a32 - a30*a22; - t[5] = a20*a31 - a30*a21; - - d[0][0] = a11*t[0] - a12*t[1] + a13*t[2]; - d[1][0] =-(a10*t[0] - a12*t[3] + a13*t[4]); - d[2][0] = a10*t[1] - a11*t[3] + a13*t[5]; - d[3][0] =-(a10*t[2] - a11*t[4] + a12*t[5]); - - d[0][1] =-(a01*t[0] - a02*t[1] + a03*t[2]); - d[1][1] = a00*t[0] - a02*t[3] + a03*t[4]; - d[2][1] =-(a00*t[1] - a01*t[3] + a03*t[5]); - d[3][1] = a00*t[2] - a01*t[4] + a02*t[5]; - - t[0] = a12*a33 - a32*a13; - t[1] = a11*a33 - a31*a13; - t[2] = a11*a32 - a31*a12; - t[3] = a10*a33 - a30*a13; - t[4] = a10*a32 - a30*a12; - t[5] = a10*a31 - a30*a11; - - d[0][2] = a01*t[0] - a02*t[1] + a03*t[2]; - d[1][2] =-(a00*t[0] - a02*t[3] + a03*t[4]); - d[2][2] = a00*t[1] - a01*t[3] + a03*t[5]; - d[3][2] =-(a00*t[2] - a01*t[4] + a02*t[5]); - - t[0] = a12*a23 - a22*a13; - t[1] = a11*a23 - a21*a13; - t[2] = a11*a22 - a21*a12; - t[3] = a10*a23 - a20*a13; - t[4] = a10*a22 - a20*a12; - t[5] = a10*a21 - a20*a11; - - d[0][3] =-(a01*t[0] - a02*t[1] + a03*t[2]); - d[1][3] = a00*t[0] - a02*t[3] + a03*t[4]; - d[2][3] =-(a00*t[1] - a01*t[3] + a03*t[5]); - d[3][3] = a00*t[2] - a01*t[4] + a02*t[5]; - - det = 1.0f / (a00*d[0][0] + a01*d[1][0] + a02*d[2][0] + a03*d[3][0]); - v4_muls( d[0], det, d[0] ); - v4_muls( d[1], det, d[1] ); - v4_muls( d[2], det, d[2] ); - v4_muls( d[3], det, d[3] ); -} - -/* - * http://www.terathon.com/lengyel/Lengyel-Oblique.pdf - */ -static void m4x4_clip_projection( m4x4f mat, v4f plane ){ - v4f c = - { - (vg_signf(plane[0]) + mat[2][0]) / mat[0][0], - (vg_signf(plane[1]) + mat[2][1]) / mat[1][1], - -1.0f, - (1.0f + mat[2][2]) / mat[3][2] - }; - - v4_muls( plane, 2.0f / v4_dot(plane,c), c ); - - mat[0][2] = c[0]; - mat[1][2] = c[1]; - mat[2][2] = c[2] + 1.0f; - mat[3][2] = c[3]; -} - -/* - * Undoes the above operation - */ -static void m4x4_reset_clipping( m4x4f mat, float ffar, float fnear ){ - mat[0][2] = 0.0f; - mat[1][2] = 0.0f; - mat[2][2] = -(ffar + fnear) / (ffar - fnear); - mat[3][2] = -2.0f * ffar * fnear / (ffar - fnear); -} - -/* - * ----------------------------------------------------------------------------- - * Section 5.a Boxes - * ----------------------------------------------------------------------------- - */ - -static inline void box_addpt( boxf a, v3f pt ) -{ - v3_minv( a[0], pt, a[0] ); - v3_maxv( a[1], pt, a[1] ); -} - -static inline void box_concat( boxf a, boxf b ) -{ - v3_minv( a[0], b[0], a[0] ); - v3_maxv( a[1], b[1], a[1] ); -} - -static inline void box_copy( boxf a, boxf b ) -{ - v3_copy( a[0], b[0] ); - v3_copy( a[1], b[1] ); -} - -static inline int box_overlap( boxf a, boxf b ) -{ - return - ( a[0][0] <= b[1][0] && a[1][0] >= b[0][0] ) && - ( a[0][1] <= b[1][1] && a[1][1] >= b[0][1] ) && - ( a[0][2] <= b[1][2] && a[1][2] >= b[0][2] ) - ; -} - -static int box_within( boxf greater, boxf lesser ) -{ - v3f a, b; - v3_sub( lesser[0], greater[0], a ); - v3_sub( lesser[1], greater[1], b ); - - if( (a[0] >= 0.0f) && (a[1] >= 0.0f) && (a[2] >= 0.0f) && - (b[0] <= 0.0f) && (b[1] <= 0.0f) && (b[2] <= 0.0f) ) - { - return 1; - } - - return 0; -} - -static inline void box_init_inf( boxf box ){ - v3_fill( box[0], INFINITY ); - v3_fill( box[1], -INFINITY ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 5.b Planes - * ----------------------------------------------------------------------------- - */ - -static inline void tri_to_plane( f64 a[3], f64 b[3], - f64 c[3], f64 p[4] ) -{ - f64 edge0[3]; - f64 edge1[3]; - f64 l; - - edge0[0] = b[0] - a[0]; - edge0[1] = b[1] - a[1]; - edge0[2] = b[2] - a[2]; - - edge1[0] = c[0] - a[0]; - edge1[1] = c[1] - a[1]; - edge1[2] = c[2] - a[2]; - - p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1]; - p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2]; - p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0]; - - l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]); - p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l; - - p[0] = p[0] / l; - p[1] = p[1] / l; - p[2] = p[2] / l; -} - -static int plane_intersect3( v4f a, v4f b, v4f c, v3f p ) -{ - f32 const epsilon = 1e-6f; - - v3f x; - v3_cross( a, b, x ); - f32 d = v3_dot( x, c ); - - if( (d < epsilon) && (d > -epsilon) ) return 0; - - v3f v0, v1, v2; - v3_cross( b, c, v0 ); - v3_cross( c, a, v1 ); - v3_cross( a, b, v2 ); - - v3_muls( v0, a[3], p ); - v3_muladds( p, v1, b[3], p ); - v3_muladds( p, v2, c[3], p ); - v3_divs( p, d, p ); - - return 1; -} - -static int plane_intersect2( v4f a, v4f b, v3f p, v3f n ) -{ - f32 const epsilon = 1e-6f; - - v4f c; - v3_cross( a, b, c ); - f32 d = v3_length2( c ); - - if( (d < epsilon) && (d > -epsilon) ) - return 0; - - v3f v0, v1, vx; - v3_cross( c, b, v0 ); - v3_cross( a, c, v1 ); - - v3_muls( v0, a[3], vx ); - v3_muladds( vx, v1, b[3], vx ); - v3_divs( vx, d, p ); - v3_copy( c, n ); - - return 1; -} - -static int plane_segment( v4f plane, v3f a, v3f b, v3f co ) -{ - f32 d0 = v3_dot( a, plane ) - plane[3], - d1 = v3_dot( b, plane ) - plane[3]; - - if( d0*d1 < 0.0f ) - { - f32 tot = 1.0f/( fabsf(d0)+fabsf(d1) ); - - v3_muls( a, fabsf(d1) * tot, co ); - v3_muladds( co, b, fabsf(d0) * tot, co ); - return 1; - } - - return 0; -} - -static inline f64 plane_polarity( f64 p[4], f64 a[3] ) -{ - return - (a[0] * p[0] + a[1] * p[1] + a[2] * p[2]) - -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2]) - ; -} - -static f32 ray_plane( v4f plane, v3f co, v3f dir ){ - f32 d = v3_dot( plane, dir ); - if( fabsf(d) > 1e-6f ){ - v3f v0; - v3_muls( plane, plane[3], v0 ); - v3_sub( v0, co, v0 ); - return v3_dot( v0, plane ) / d; - } - else return INFINITY; -} - -/* - * ----------------------------------------------------------------------------- - * Section 5.c Closest point functions - * ----------------------------------------------------------------------------- - */ - -/* - * These closest point tests were learned from Real-Time Collision Detection by - * Christer Ericson - */ -static f32 closest_segment_segment( v3f p1, v3f q1, v3f p2, v3f q2, - f32 *s, f32 *t, v3f c1, v3f c2) -{ - v3f d1,d2,r; - v3_sub( q1, p1, d1 ); - v3_sub( q2, p2, d2 ); - v3_sub( p1, p2, r ); - - f32 a = v3_length2( d1 ), - e = v3_length2( d2 ), - f = v3_dot( d2, r ); - - const f32 kEpsilon = 0.0001f; - - if( a <= kEpsilon && e <= kEpsilon ) - { - *s = 0.0f; - *t = 0.0f; - v3_copy( p1, c1 ); - v3_copy( p2, c2 ); - - v3f v0; - v3_sub( c1, c2, v0 ); - - return v3_length2( v0 ); - } - - if( a<= kEpsilon ) - { - *s = 0.0f; - *t = vg_clampf( f / e, 0.0f, 1.0f ); - } - else - { - f32 c = v3_dot( d1, r ); - if( e <= kEpsilon ) - { - *t = 0.0f; - *s = vg_clampf( -c / a, 0.0f, 1.0f ); - } - else - { - f32 b = v3_dot(d1,d2), - d = a*e-b*b; - - if( d != 0.0f ) - { - *s = vg_clampf((b*f - c*e)/d, 0.0f, 1.0f); - } - else - { - *s = 0.0f; - } - - *t = (b*(*s)+f) / e; - - if( *t < 0.0f ) - { - *t = 0.0f; - *s = vg_clampf( -c / a, 0.0f, 1.0f ); - } - else if( *t > 1.0f ) - { - *t = 1.0f; - *s = vg_clampf((b-c)/a,0.0f,1.0f); - } - } - } - - v3_muladds( p1, d1, *s, c1 ); - v3_muladds( p2, d2, *t, c2 ); - - v3f v0; - v3_sub( c1, c2, v0 ); - return v3_length2( v0 ); -} - -static int point_inside_aabb( boxf box, v3f point ) -{ - if((point[0]<=box[1][0]) && (point[1]<=box[1][1]) && (point[2]<=box[1][2]) && - (point[0]>=box[0][0]) && (point[1]>=box[0][1]) && (point[2]>=box[0][2]) ) - return 1; - else - return 0; -} - -static void closest_point_aabb( v3f p, boxf box, v3f dest ) -{ - v3_maxv( p, box[0], dest ); - v3_minv( dest, box[1], dest ); -} - -static void closest_point_obb( v3f p, boxf box, - m4x3f mtx, m4x3f inv_mtx, v3f dest ) -{ - v3f local; - m4x3_mulv( inv_mtx, p, local ); - closest_point_aabb( local, box, local ); - m4x3_mulv( mtx, local, dest ); -} - -static f32 closest_point_segment( v3f a, v3f b, v3f point, v3f dest ) -{ - v3f v0, v1; - v3_sub( b, a, v0 ); - v3_sub( point, a, v1 ); - - f32 t = v3_dot( v1, v0 ) / v3_length2(v0); - t = vg_clampf(t,0.0f,1.0f); - v3_muladds( a, v0, t, dest ); - return t; -} - -static void closest_on_triangle( v3f p, v3f tri[3], v3f dest ) -{ - v3f ab, ac, ap; - f32 d1, d2; - - /* Region outside A */ - v3_sub( tri[1], tri[0], ab ); - v3_sub( tri[2], tri[0], ac ); - v3_sub( p, tri[0], ap ); - - d1 = v3_dot(ab,ap); - d2 = v3_dot(ac,ap); - if( d1 <= 0.0f && d2 <= 0.0f ) - { - v3_copy( tri[0], dest ); - v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest ); - return; - } - - /* Region outside B */ - v3f bp; - f32 d3, d4; - - v3_sub( p, tri[1], bp ); - d3 = v3_dot( ab, bp ); - d4 = v3_dot( ac, bp ); - - if( d3 >= 0.0f && d4 <= d3 ) - { - v3_copy( tri[1], dest ); - v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest ); - return; - } - - /* Edge region of AB */ - f32 vc = d1*d4 - d3*d2; - if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f ) - { - f32 v = d1 / (d1-d3); - v3_muladds( tri[0], ab, v, dest ); - v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest ); - return; - } - - /* Region outside C */ - v3f cp; - f32 d5, d6; - v3_sub( p, tri[2], cp ); - d5 = v3_dot(ab, cp); - d6 = v3_dot(ac, cp); - - if( d6 >= 0.0f && d5 <= d6 ) - { - v3_copy( tri[2], dest ); - v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest ); - return; - } - - /* Region of AC */ - f32 vb = d5*d2 - d1*d6; - if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f ) - { - f32 w = d2 / (d2-d6); - v3_muladds( tri[0], ac, w, dest ); - v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest ); - return; - } - - /* Region of BC */ - f32 va = d3*d6 - d5*d4; - if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f ) - { - f32 w = (d4-d3) / ((d4-d3) + (d5-d6)); - v3f bc; - v3_sub( tri[2], tri[1], bc ); - v3_muladds( tri[1], bc, w, dest ); - v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest ); - return; - } - - /* P inside region, Q via barycentric coordinates uvw */ - f32 d = 1.0f/(va+vb+vc), - v = vb*d, - w = vc*d; - - v3_muladds( tri[0], ab, v, dest ); - v3_muladds( dest, ac, w, dest ); -} - -enum contact_type -{ - k_contact_type_default, - k_contact_type_disabled, - k_contact_type_edge -}; - -static enum contact_type closest_on_triangle_1( v3f p, v3f tri[3], v3f dest ) -{ - v3f ab, ac, ap; - f32 d1, d2; - - /* Region outside A */ - v3_sub( tri[1], tri[0], ab ); - v3_sub( tri[2], tri[0], ac ); - v3_sub( p, tri[0], ap ); - - d1 = v3_dot(ab,ap); - d2 = v3_dot(ac,ap); - if( d1 <= 0.0f && d2 <= 0.0f ) - { - v3_copy( tri[0], dest ); - return k_contact_type_default; - } - - /* Region outside B */ - v3f bp; - f32 d3, d4; - - v3_sub( p, tri[1], bp ); - d3 = v3_dot( ab, bp ); - d4 = v3_dot( ac, bp ); - - if( d3 >= 0.0f && d4 <= d3 ) - { - v3_copy( tri[1], dest ); - return k_contact_type_edge; - } - - /* Edge region of AB */ - f32 vc = d1*d4 - d3*d2; - if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f ) - { - f32 v = d1 / (d1-d3); - v3_muladds( tri[0], ab, v, dest ); - return k_contact_type_edge; - } - - /* Region outside C */ - v3f cp; - f32 d5, d6; - v3_sub( p, tri[2], cp ); - d5 = v3_dot(ab, cp); - d6 = v3_dot(ac, cp); - - if( d6 >= 0.0f && d5 <= d6 ) - { - v3_copy( tri[2], dest ); - return k_contact_type_edge; - } - - /* Region of AC */ - f32 vb = d5*d2 - d1*d6; - if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f ) - { - f32 w = d2 / (d2-d6); - v3_muladds( tri[0], ac, w, dest ); - return k_contact_type_edge; - } - - /* Region of BC */ - f32 va = d3*d6 - d5*d4; - if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f ) - { - f32 w = (d4-d3) / ((d4-d3) + (d5-d6)); - v3f bc; - v3_sub( tri[2], tri[1], bc ); - v3_muladds( tri[1], bc, w, dest ); - return k_contact_type_edge; - } - - /* P inside region, Q via barycentric coordinates uvw */ - f32 d = 1.0f/(va+vb+vc), - v = vb*d, - w = vc*d; - - v3_muladds( tri[0], ab, v, dest ); - v3_muladds( dest, ac, w, dest ); - - return k_contact_type_default; -} - -static void closest_point_elipse( v2f p, v2f e, v2f o ) -{ - v2f pabs, ei, e2, ve, t; - - v2_abs( p, pabs ); - v2_div( (v2f){ 1.0f, 1.0f }, e, ei ); - v2_mul( e, e, e2 ); - v2_mul( ei, (v2f){ e2[0]-e2[1], e2[1]-e2[0] }, ve ); - - v2_fill( t, 0.70710678118654752f ); - - for( int i=0; i<3; i++ ){ - v2f v, u, ud, w; - - v2_mul( ve, t, v ); /* ve*t*t*t */ - v2_mul( v, t, v ); - v2_mul( v, t, v ); - - v2_sub( pabs, v, u ); - v2_normalize( u ); - - v2_mul( t, e, ud ); - v2_sub( ud, v, ud ); - - v2_muls( u, v2_length( ud ), u ); - - v2_add( v, u, w ); - v2_mul( w, ei, w ); - - v2_maxv( (v2f){0.0f,0.0f}, w, t ); - v2_normalize( t ); - } - - v2_mul( t, e, o ); - v2_copysign( o, p ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 5.d Raycasts & Spherecasts - * ----------------------------------------------------------------------------- - */ - -static int ray_aabb1( boxf box, v3f co, v3f dir_inv, f32 dist ) -{ - v3f v0, v1; - f32 tmin, tmax; - - v3_sub( box[0], co, v0 ); - v3_sub( box[1], co, v1 ); - - v3_mul( v0, dir_inv, v0 ); - v3_mul( v1, dir_inv, v1 ); - - tmin = vg_minf( v0[0], v1[0] ); - tmax = vg_maxf( v0[0], v1[0] ); - tmin = vg_maxf( tmin, vg_minf( v0[1], v1[1] )); - tmax = vg_minf( tmax, vg_maxf( v0[1], v1[1] )); - tmin = vg_maxf( tmin, vg_minf( v0[2], v1[2] )); - tmax = vg_minf( tmax, vg_maxf( v0[2], v1[2] )); - - return (tmax >= tmin) && (tmin <= dist) && (tmax >= 0.0f); -} - -/* Time of intersection with ray vs triangle */ -static int ray_tri( v3f tri[3], v3f co, - v3f dir, f32 *dist, int backfaces ) -{ - f32 const kEpsilon = 0.00001f; - - v3f v0, v1, h, s, q, n; - f32 a,f,u,v,t; - - f32 *pa = tri[0], - *pb = tri[1], - *pc = tri[2]; - - v3_sub( pb, pa, v0 ); - v3_sub( pc, pa, v1 ); - v3_cross( dir, v1, h ); - v3_cross( v0, v1, n ); - - if( (v3_dot( n, dir ) > 0.0f) && !backfaces ) /* Backface culling */ - return 0; - - /* Parralel */ - a = v3_dot( v0, h ); - - if( a > -kEpsilon && a < kEpsilon ) - return 0; - - f = 1.0f/a; - v3_sub( co, pa, s ); - - u = f * v3_dot(s, h); - if( u < 0.0f || u > 1.0f ) - return 0; - - v3_cross( s, v0, q ); - v = f * v3_dot( dir, q ); - if( v < 0.0f || u+v > 1.0f ) - return 0; - - t = f * v3_dot(v1, q); - if( t > kEpsilon ) - { - *dist = t; - return 1; - } - else return 0; -} - -/* time of intersection with ray vs sphere */ -static int ray_sphere( v3f c, f32 r, - v3f co, v3f dir, f32 *t ) -{ - v3f m; - v3_sub( co, c, m ); - - f32 b = v3_dot( m, dir ), - c1 = v3_dot( m, m ) - r*r; - - /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */ - if( c1 > 0.0f && b > 0.0f ) - return 0; - - f32 discr = b*b - c1; - - /* A negative discriminant corresponds to ray missing sphere */ - if( discr < 0.0f ) - return 0; - - /* - * Ray now found to intersect sphere, compute smallest t value of - * intersection - */ - *t = -b - sqrtf( discr ); - - /* If t is negative, ray started inside sphere so clamp t to zero */ - if( *t < 0.0f ) - *t = 0.0f; - - return 1; -} - -/* - * time of intersection of ray vs cylinder - * The cylinder does not have caps but is finite - * - * Heavily adapted from regular segment vs cylinder from: - * Real-Time Collision Detection - */ -static int ray_uncapped_finite_cylinder( v3f q, v3f p, f32 r, - v3f co, v3f dir, f32 *t ) -{ - v3f d, m, n, sb; - v3_muladds( co, dir, 1.0f, sb ); - - v3_sub( q, p, d ); - v3_sub( co, p, m ); - v3_sub( sb, co, n ); - - f32 md = v3_dot( m, d ), - nd = v3_dot( n, d ), - dd = v3_dot( d, d ), - nn = v3_dot( n, n ), - mn = v3_dot( m, n ), - a = dd*nn - nd*nd, - k = v3_dot( m, m ) - r*r, - c = dd*k - md*md; - - if( fabsf(a) < 0.00001f ) - { - /* Segment runs parallel to cylinder axis */ - return 0; - } - - f32 b = dd*mn - nd*md, - discr = b*b - a*c; - - if( discr < 0.0f ) - return 0; /* No real roots; no intersection */ - - *t = (-b - sqrtf(discr)) / a; - if( *t < 0.0f ) - return 0; /* Intersection behind ray */ - - /* Check within cylinder segment */ - if( md + (*t)*nd < 0.0f ) - return 0; - - if( md + (*t)*nd > dd ) - return 0; - - /* Segment intersects cylinder between the endcaps; t is correct */ - return 1; -} - -/* - * Time of intersection of sphere and triangle. Origin must be outside the - * colliding area. This is a fairly long procedure. - */ -static int spherecast_triangle( v3f tri[3], - v3f co, v3f dir, f32 r, f32 *t, v3f n ) -{ - v3f sum[3]; - v3f v0, v1; - - v3_sub( tri[1], tri[0], v0 ); - v3_sub( tri[2], tri[0], v1 ); - v3_cross( v0, v1, n ); - v3_normalize( n ); - v3_muladds( tri[0], n, r, sum[0] ); - v3_muladds( tri[1], n, r, sum[1] ); - v3_muladds( tri[2], n, r, sum[2] ); - - int hit = 0; - f32 t_min = INFINITY, - t1; - - if( ray_tri( sum, co, dir, &t1, 0 ) ){ - t_min = vg_minf( t_min, t1 ); - hit = 1; - } - - /* - * Currently disabled; ray_sphere requires |d| = 1. it is not very important. - */ -#if 0 - for( int i=0; i<3; i++ ){ - if( ray_sphere( tri[i], r, co, dir, &t1 ) ){ - t_min = vg_minf( t_min, t1 ); - hit = 1; - } - } -#endif - - for( int i=0; i<3; i++ ){ - int i0 = i, - i1 = (i+1)%3; - - if( ray_uncapped_finite_cylinder( tri[i0], tri[i1], r, co, dir, &t1 ) ){ - if( t1 < t_min ){ - t_min = t1; - - v3f co1, ct, cx; - v3_add( dir, co, co1 ); - v3_lerp( co, co1, t_min, ct ); - - closest_point_segment( tri[i0], tri[i1], ct, cx ); - v3_sub( ct, cx, n ); - v3_normalize( n ); - } - - hit = 1; - } - } - - *t = t_min; - return hit; -} - -/* - * ----------------------------------------------------------------------------- - * Section 5.e Curves - * ----------------------------------------------------------------------------- - */ - -static void eval_bezier_time( v3f p0, v3f p1, v3f h0, v3f h1, f32 t, v3f p ) -{ - f32 tt = t*t, - ttt = tt*t; - - v3_muls( p1, ttt, p ); - v3_muladds( p, h1, 3.0f*tt -3.0f*ttt, p ); - v3_muladds( p, h0, 3.0f*ttt -6.0f*tt +3.0f*t, p ); - v3_muladds( p, p0, 3.0f*tt -ttt -3.0f*t +1.0f, p ); -} - -static void eval_bezier3( v3f p0, v3f p1, v3f p2, f32 t, v3f p ) -{ - f32 u = 1.0f-t; - - v3_muls( p0, u*u, p ); - v3_muladds( p, p1, 2.0f*u*t, p ); - v3_muladds( p, p2, t*t, p ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 5.f Volumes - * ----------------------------------------------------------------------------- - */ - -static f32 vg_sphere_volume( f32 r ){ - return (4.0f/3.0f) * VG_PIf * r*r*r; -} - -static f32 vg_box_volume( boxf box ){ - v3f e; - v3_sub( box[1], box[0], e ); - return e[0]*e[1]*e[2]; -} - -static f32 vg_cylinder_volume( f32 r, f32 h ){ - return VG_PIf * r*r * h; -} - -static f32 vg_capsule_volume( f32 r, f32 h ){ - return vg_sphere_volume( r ) + vg_cylinder_volume( r, h-r*2.0f ); -} - -static void vg_sphere_bound( f32 r, boxf out_box ){ - v3_fill( out_box[0], -r ); - v3_fill( out_box[1], r ); -} - -static void vg_capsule_bound( f32 r, f32 h, boxf out_box ){ - v3_copy( (v3f){-r,-h*0.5f,r}, out_box[0] ); - v3_copy( (v3f){-r, h*0.5f,r}, out_box[1] ); -} - - -/* - * ----------------------------------------------------------------------------- - * Section 5.g Inertia Tensors - * ----------------------------------------------------------------------------- - */ - -/* - * Translate existing inertia tensor - */ -static void vg_translate_inertia( m3x3f inout_inertia, f32 mass, v3f d ){ - /* - * I = I_0 + m*[(d.d)E_3 - d(X)d] - * - * I: updated tensor - * I_0: original tensor - * m: scalar mass - * d: translation vector - * (X): outer product - * E_3: identity matrix - */ - m3x3f t, outer, scale; - m3x3_diagonal( t, v3_dot(d,d) ); - m3x3_outer_product( outer, d, d ); - m3x3_sub( t, outer, t ); - m3x3_diagonal( scale, mass ); - m3x3_mul( scale, t, t ); - m3x3_add( inout_inertia, t, inout_inertia ); -} - -/* - * Rotate existing inertia tensor - */ -static void vg_rotate_inertia( m3x3f inout_inertia, m3x3f rotation ){ - /* - * I = R I_0 R^T - * - * I: updated tensor - * I_0: original tensor - * R: rotation matrix - * R^T: tranposed rotation matrix - */ - - m3x3f Rt; - m3x3_transpose( rotation, Rt ); - m3x3_mul( rotation, inout_inertia, inout_inertia ); - m3x3_mul( inout_inertia, Rt, inout_inertia ); -} -/* - * Create inertia tensor for box - */ -static void vg_box_inertia( boxf box, f32 mass, m3x3f out_inertia ){ - v3f e, com; - v3_sub( box[1], box[0], e ); - v3_muladds( box[0], e, 0.5f, com ); - - f32 ex2 = e[0]*e[0], - ey2 = e[1]*e[1], - ez2 = e[2]*e[2], - ix = (ey2+ez2) * mass * (1.0f/12.0f), - iy = (ex2+ez2) * mass * (1.0f/12.0f), - iz = (ex2+ey2) * mass * (1.0f/12.0f); - - m3x3_identity( out_inertia ); - m3x3_setdiagonalv3( out_inertia, (v3f){ ix, iy, iz } ); - vg_translate_inertia( out_inertia, mass, com ); -} - -/* - * Create inertia tensor for sphere - */ -static void vg_sphere_inertia( f32 r, f32 mass, m3x3f out_inertia ){ - f32 ixyz = r*r * mass * (2.0f/5.0f); - - m3x3_identity( out_inertia ); - m3x3_setdiagonalv3( out_inertia, (v3f){ ixyz, ixyz, ixyz } ); -} - -/* - * Create inertia tensor for capsule - */ -static void vg_capsule_inertia( f32 r, f32 h, f32 mass, m3x3f out_inertia ){ - f32 density = mass / vg_capsule_volume( r, h ), - ch = h-r*2.0f, /* cylinder height */ - cm = VG_PIf * ch*r*r * density, /* cylinder mass */ - hm = VG_TAUf * (1.0f/3.0f) * r*r*r * density, /* hemisphere mass */ - - iy = r*r*cm * 0.5f, - ixz = iy * 0.5f + cm*ch*ch*(1.0f/12.0f), - - aux0= (hm*2.0f*r*r)/5.0f; - - iy += aux0 * 2.0f; - - f32 aux1= ch*0.5f, - aux2= aux0 + hm*(aux1*aux1 + 3.0f*(1.0f/8.0f)*ch*r); - - ixz += aux2*2.0f; - - m3x3_identity( out_inertia ); - m3x3_setdiagonalv3( out_inertia, (v3f){ ixz, iy, ixz } ); -} - -/* - * ----------------------------------------------------------------------------- - * Section 6.a PSRNG and some distributions - * ----------------------------------------------------------------------------- - */ - -/* An implementation of the MT19937 Algorithm for the Mersenne Twister - * by Evan Sultanik. Based upon the pseudocode in: M. Matsumoto and - * T. Nishimura, "Mersenne Twister: A 623-dimensionally - * equidistributed uniform pseudorandom number generator," ACM - * Transactions on Modeling and Computer Simulation Vol. 8, No. 1, - * January pp.3-30 1998. - * - * http://www.sultanik.com/Mersenne_twister - * https://github.com/ESultanik/mtwister/blob/master/mtwister.c - */ - -#define MT_UPPER_MASK 0x80000000 -#define MT_LOWER_MASK 0x7fffffff -#define MT_TEMPERING_MASK_B 0x9d2c5680 -#define MT_TEMPERING_MASK_C 0xefc60000 - -#define MT_STATE_VECTOR_LENGTH 624 - -/* changes to STATE_VECTOR_LENGTH also require changes to this */ -#define MT_STATE_VECTOR_M 397 - -typedef struct vg_rand vg_rand; -struct vg_rand { - u32 mt[MT_STATE_VECTOR_LENGTH]; - i32 index; -}; - -static void vg_rand_seed( vg_rand *rand, unsigned long seed ) { - /* set initial seeds to mt[STATE_VECTOR_LENGTH] using the generator - * from Line 25 of Table 1 in: Donald Knuth, "The Art of Computer - * Programming," Vol. 2 (2nd Ed.) pp.102. - */ - rand->mt[0] = seed & 0xffffffff; - for( rand->index=1; rand->indexindex++){ - rand->mt[rand->index] = (6069 * rand->mt[rand->index-1]) & 0xffffffff; - } -} - -/* - * Generates a pseudo-randomly generated long. - */ -static u32 vg_randu32( vg_rand *rand ) { - u32 y; - /* mag[x] = x * 0x9908b0df for x = 0,1 */ - static u32 mag[2] = {0x0, 0x9908b0df}; - if( rand->index >= MT_STATE_VECTOR_LENGTH || rand->index < 0 ){ - /* generate STATE_VECTOR_LENGTH words at a time */ - int kk; - if( rand->index >= MT_STATE_VECTOR_LENGTH+1 || rand->index < 0 ){ - vg_rand_seed( rand, 4357 ); - } - for( kk=0; kkmt[kk] & MT_UPPER_MASK) | - (rand->mt[kk+1] & MT_LOWER_MASK); - rand->mt[kk] = rand->mt[kk+MT_STATE_VECTOR_M] ^ (y>>1) ^ mag[y & 0x1]; - } - for( ; kkmt[kk] & MT_UPPER_MASK) | - (rand->mt[kk+1] & MT_LOWER_MASK); - rand->mt[kk] = - rand->mt[ kk+(MT_STATE_VECTOR_M-MT_STATE_VECTOR_LENGTH)] ^ - (y >> 1) ^ mag[y & 0x1]; - } - y = (rand->mt[MT_STATE_VECTOR_LENGTH-1] & MT_UPPER_MASK) | - (rand->mt[0] & MT_LOWER_MASK); - rand->mt[MT_STATE_VECTOR_LENGTH-1] = - rand->mt[MT_STATE_VECTOR_M-1] ^ (y >> 1) ^ mag[y & 0x1]; - rand->index = 0; - } - y = rand->mt[rand->index++]; - y ^= (y >> 11); - y ^= (y << 7) & MT_TEMPERING_MASK_B; - y ^= (y << 15) & MT_TEMPERING_MASK_C; - y ^= (y >> 18); - return y; -} - -/* - * Generates a pseudo-randomly generated f64 in the range [0..1]. - */ -static inline f64 vg_randf64( vg_rand *rand ){ - return (f64)vg_randu32(rand)/(f64)0xffffffff; -} - -static inline f64 vg_randf64_range( vg_rand *rand, f64 min, f64 max ){ - return vg_lerp( min, max, (f64)vg_randf64(rand) ); -} - -static inline void vg_rand_dir( vg_rand *rand, v3f dir ){ - dir[0] = vg_randf64(rand); - dir[1] = vg_randf64(rand); - dir[2] = vg_randf64(rand); - - /* warning: *could* be 0 length. - * very unlikely.. 1 in (2^32)^3. but its mathematically wrong. */ - - v3_muls( dir, 2.0f, dir ); - v3_sub( dir, (v3f){1.0f,1.0f,1.0f}, dir ); - - v3_normalize( dir ); -} - -static inline void vg_rand_sphere( vg_rand *rand, v3f co ){ - vg_rand_dir(rand,co); - v3_muls( co, cbrtf( vg_randf64(rand) ), co ); -} - -static void vg_rand_disc( vg_rand *rand, v2f co ){ - f32 a = vg_randf64(rand) * VG_TAUf; - co[0] = sinf(a); - co[1] = cosf(a); - v2_muls( co, sqrtf( vg_randf64(rand) ), co ); -} - -static void vg_rand_cone( vg_rand *rand, v3f out_dir, f32 angle ){ - f32 r = sqrtf(vg_randf64(rand)) * angle * 0.5f, - a = vg_randf64(rand) * VG_TAUf; - - out_dir[0] = sinf(a) * sinf(r); - out_dir[1] = cosf(a) * sinf(r); - out_dir[2] = cosf(r); -} - -static void vg_hsv_rgb( v3f hsv, v3f rgb ){ - i32 i = floorf( hsv[0]*6.0f ); - f32 v = hsv[2], - f = hsv[0] * 6.0f - (f32)i, - p = v * (1.0f-hsv[1]), - q = v * (1.0f-f*hsv[1]), - t = v * (1.0f-(1.0f-f)*hsv[1]); - - switch( i % 6 ){ - case 0: rgb[0] = v; rgb[1] = t; rgb[2] = p; break; - case 1: rgb[0] = q; rgb[1] = v; rgb[2] = p; break; - case 2: rgb[0] = p; rgb[1] = v; rgb[2] = t; break; - case 3: rgb[0] = p; rgb[1] = q; rgb[2] = v; break; - case 4: rgb[0] = t; rgb[1] = p; rgb[2] = v; break; - case 5: rgb[0] = v; rgb[1] = p; rgb[2] = q; break; - } -} - -static void vg_rgb_hsv( v3f rgb, v3f hsv ){ - f32 min = v3_minf( rgb ), - max = v3_maxf( rgb ), - range = max-min, - k_epsilon = 0.00001f; - - hsv[2] = max; - if( range < k_epsilon ){ - hsv[0] = 0.0f; - hsv[1] = 0.0f; - return; - } - - if( max > k_epsilon ){ - hsv[1] = range/max; - } - else { - hsv[0] = 0.0f; - hsv[1] = 0.0f; - return; - } - - if( rgb[0] >= max ) - hsv[0] = (rgb[1]-rgb[2])/range; - else if( max == rgb[1] ) - hsv[0] = 2.0f+(rgb[2]-rgb[0])/range; - else - hsv[0] = 4.0f+(rgb[0]-rgb[1])/range; - - hsv[0] = vg_fractf( hsv[0] * (60.0f/360.0f) ); -} -- 2.25.1