-/* Copyright (C) 2021-2023 Harry Godden (hgn) - All Rights Reserved
+/* Copyright (C) 2021-2024 Harry Godden (hgn) - All Rights Reserved
*
* 0. Misc
* 1. Scalar operations
* 5.d Raycast & Spherecasts
* 5.e Curves
* 5.f Volumes
+ * 5.g Inertia tensors
* 6. Statistics
* 6.a Random numbers
- **/
+ */
-#ifndef VG_M_H
-#define VG_M_H
+#pragma once
#include "vg_platform.h"
#include <math.h>
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) );
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
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[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] );
m3x3_copy( id, a );
}
-static void m3x3_diagonal( m3x3f a, f32 v )
+static void m3x3_diagonal( m3x3f out_a, f32 v )
{
- m3x3_identity( a );
- a[0][0] = v;
- a[1][1] = v;
- a[2][2] = 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 )
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
return 1;
}
-int plane_intersect2( v4f a, v4f b, v3f p, v3f n )
+static int plane_intersect2( v4f a, v4f b, v3f p, v3f n )
{
f32 const epsilon = 1e-6f;
* -----------------------------------------------------------------------------
*/
-int ray_aabb1( boxf box, v3f co, v3f dir_inv, f32 dist )
+static int ray_aabb1( boxf box, v3f co, v3f dir_inv, f32 dist )
{
v3f v0, v1;
f32 tmin, tmax;
/* Time of intersection with ray vs triangle */
static int ray_tri( v3f tri[3], v3f co,
- v3f dir, f32 *dist )
+ v3f dir, f32 *dist, int backfaces )
{
f32 const kEpsilon = 0.00001f;
v3_cross( dir, v1, h );
v3_cross( v0, v1, n );
- if( v3_dot( n, dir ) > 0.0f ) /* Backface culling */
+ if( (v3_dot( n, dir ) > 0.0f) && !backfaces ) /* Backface culling */
return 0;
/* Parralel */
f32 t_min = INFINITY,
t1;
- if( ray_tri( sum, co, dir, &t1 ) ){
+ if( ray_tri( sum, co, dir, &t1, 0 ) ){
t_min = vg_minf( t_min, t1 );
hit = 1;
}
* -----------------------------------------------------------------------------
*/
-static float vg_sphere_volume( float radius ){
- float r3 = radius*radius*radius;
- return (4.0f/3.0f) * VG_PIf * r3;
+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 } );
}
/*
/* changes to STATE_VECTOR_LENGTH also require changes to this */
#define MT_STATE_VECTOR_M 397
-struct {
+typedef struct vg_rand vg_rand;
+struct vg_rand {
u32 mt[MT_STATE_VECTOR_LENGTH];
i32 index;
-}
-static vg_rand;
+};
-static void vg_rand_seed( unsigned long seed )
-{
+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.
*/
- vg_rand.mt[0] = seed & 0xffffffff;
- for( vg_rand.index=1; vg_rand.index<MT_STATE_VECTOR_LENGTH; vg_rand.index++){
- vg_rand.mt[vg_rand.index] =
- (6069 * vg_rand.mt[vg_rand.index-1]) & 0xffffffff;
+ rand->mt[0] = seed & 0xffffffff;
+ for( rand->index=1; rand->index<MT_STATE_VECTOR_LENGTH; rand->index++){
+ rand->mt[rand->index] = (6069 * rand->mt[rand->index-1]) & 0xffffffff;
}
}
/*
* Generates a pseudo-randomly generated long.
*/
-static u32 vg_randu32(void)
-{
+static u32 vg_randu32( vg_rand *rand ) {
u32 y;
/* mag[x] = x * 0x9908b0df for x = 0,1 */
static u32 mag[2] = {0x0, 0x9908b0df};
- if( vg_rand.index >= MT_STATE_VECTOR_LENGTH || vg_rand.index < 0 ){
+ if( rand->index >= MT_STATE_VECTOR_LENGTH || rand->index < 0 ){
/* generate STATE_VECTOR_LENGTH words at a time */
int kk;
- if( vg_rand.index >= MT_STATE_VECTOR_LENGTH+1 || vg_rand.index < 0 ){
- vg_rand_seed( 4357 );
+ if( rand->index >= MT_STATE_VECTOR_LENGTH+1 || rand->index < 0 ){
+ vg_rand_seed( rand, 4357 );
}
for( kk=0; kk<MT_STATE_VECTOR_LENGTH-MT_STATE_VECTOR_M; kk++ ){
- y = (vg_rand.mt[kk] & MT_UPPER_MASK) |
- (vg_rand.mt[kk+1] & MT_LOWER_MASK);
- vg_rand.mt[kk] = vg_rand.mt[kk+MT_STATE_VECTOR_M] ^
- (y >> 1) ^ mag[y & 0x1];
+ y = (rand->mt[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( ; kk<MT_STATE_VECTOR_LENGTH-1; kk++ ){
- y = (vg_rand.mt[kk] & MT_UPPER_MASK) |
- (vg_rand.mt[kk+1] & MT_LOWER_MASK);
- vg_rand.mt[kk] =
- vg_rand.mt[ kk+(MT_STATE_VECTOR_M-MT_STATE_VECTOR_LENGTH)] ^
+ y = (rand->mt[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 = (vg_rand.mt[MT_STATE_VECTOR_LENGTH-1] & MT_UPPER_MASK) |
- (vg_rand.mt[0] & MT_LOWER_MASK);
- vg_rand.mt[MT_STATE_VECTOR_LENGTH-1] =
- vg_rand.mt[MT_STATE_VECTOR_M-1] ^ (y >> 1) ^ mag[y & 0x1];
- vg_rand.index = 0;
+ 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 = vg_rand.mt[vg_rand.index++];
+ y = rand->mt[rand->index++];
y ^= (y >> 11);
y ^= (y << 7) & MT_TEMPERING_MASK_B;
y ^= (y << 15) & MT_TEMPERING_MASK_C;
/*
* Generates a pseudo-randomly generated f64 in the range [0..1].
*/
-static inline f64 vg_randf64(void)
-{
- return (f64)vg_randu32()/(f64)0xffffffff;
+static inline f64 vg_randf64( vg_rand *rand ){
+ return (f64)vg_randu32(rand)/(f64)0xffffffff;
}
-static inline f64 vg_randf64_range( f64 min, f64 max )
-{
- return vg_lerp( min, max, (f64)vg_randf64() );
+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( v3f dir )
-{
- dir[0] = vg_randf64();
- dir[1] = vg_randf64();
- dir[2] = vg_randf64();
+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( v3f co )
-{
- vg_rand_dir(co);
- v3_muls( co, cbrtf( vg_randf64() ), co );
+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;
+ }
}
-#endif /* VG_M_H */
+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) );
+}
projects / vg.git / blobdiff