-/* Copyright (C) 2021-2022 Harry Godden (hgn) - All Rights Reserved */
+/* Copyright (C) 2021-2023 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
+ * 6. Statistics
+ * 6.a Random numbers
+ **/
#ifndef VG_M_H
#define VG_M_H
#define VG_PIf 3.14159265358979323846264338327950288f
#define VG_TAUf 6.28318530717958647692528676655900576f
+/*
+ * -----------------------------------------------------------------------------
+ * Section 0. Misc Operations
+ * -----------------------------------------------------------------------------
+ */
-static u32 vg_ftu32( float a )
+/* get the f32 as the raw bits in a u32 without converting */
+static u32 vg_ftu32( f32 a )
{
u32 *ptr = (u32 *)(&a);
return *ptr;
}
-static int vg_isinff( float a )
+/* check if f32 is infinite */
+static int vg_isinff( f32 a )
{
return ((vg_ftu32(a)) & 0x7FFFFFFFU) == 0x7F800000U;
}
-static int vg_isnanf( float a )
+/* check if f32 is not a number */
+static int vg_isnanf( f32 a )
{
return !vg_isinff(a) && ((vg_ftu32(a)) & 0x7F800000U) == 0x7F800000U;
}
-static int vg_validf( float a )
+/* check if f32 is a number and is not infinite */
+static int vg_validf( f32 a )
{
return ((vg_ftu32(a)) & 0x7F800000U) != 0x7F800000U;
}
-static inline float vg_minf( float a, float b )
-{
- return a < b? a: b;
-}
+/*
+ * -----------------------------------------------------------------------------
+ * Section 1. Scalar Operations
+ * -----------------------------------------------------------------------------
+ */
-static inline float vg_maxf( float a, float b )
-{
- return a > b? a: b;
-}
+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 float vg_clampf( float a, float min, float max )
+static inline f32 vg_clampf( f32 a, f32 min, f32 max )
{
return vg_minf( max, vg_maxf( a, min ) );
}
-static inline float vg_signf( float a )
+static inline f32 vg_signf( f32 a )
{
return a < 0.0f? -1.0f: 1.0f;
}
-static inline float vg_fractf( float a )
+static inline f32 vg_fractf( f32 a )
{
return a - floorf( a );
}
-
-__attribute__ ((deprecated))
-static float stable_force( float current, float diff )
-{
- float fnew = current + diff;
-
- if( fnew * current < 0.0f )
- return 0.0f;
-
- return fnew;
-}
-
-static float vg_cfrictf( float current, float F )
-{
- return -vg_signf(current) * vg_minf( F, fabsf(current) );
-}
-
-static inline int vg_min( int a, int b )
-{
- return a < b? a: b;
-}
-
-static inline int vg_max( int a, int b )
+static f32 vg_cfrictf( f32 velocity, f32 F )
{
- return a > b? a: b;
+ return -vg_signf(velocity) * vg_minf( F, fabsf(velocity) );
}
-static inline float vg_rad( float deg )
+static inline f32 vg_rad( f32 deg )
{
return deg * VG_PIf / 180.0f;
}
/*
- * Vector 3
+ * -----------------------------------------------------------------------------
+ * Section 2.a 2D Vectors
+ * -----------------------------------------------------------------------------
*/
-static inline void v2_copy( v2f a, v2f b )
+
+static inline void v2_copy( v2f a, v2f d )
{
- b[0] = a[0]; b[1] = a[1];
+ 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 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 )
+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 v2i_sub( v2i a, v2i b, v2i d )
+static inline void v2_sub( v2f a, v2f b, v2f d )
{
d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
}
dest[1] = vg_maxf(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 float v2_dot( v2f a, v2f b )
+static inline f32 v2_dot( v2f a, v2f b )
{
return a[0] * b[0] + a[1] * b[1];
}
-static inline float v2_cross( v2f a, v2f b )
+static inline f32 v2_cross( v2f a, v2f b )
{
return a[0]*b[1] - a[1]*b[0];
}
-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_abs( v2f a, v2f d )
{
d[0] = fabsf( a[0] );
d[1] = fabsf( a[1] );
}
-static inline void v2_muls( v2f a, float s, v2f d )
+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, float s, v2f d )
+static inline void v2_divs( v2f a, f32 s, v2f d )
{
d[0] = a[0]/s; d[1] = a[1]/s;
}
d[1] = a[1]+b[1]*s[1];
}
-static inline void v2_muladds( v2f a, v2f b, float s, v2f d )
+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 float v2_length2( v2f a )
+static inline f32 v2_length2( v2f a )
{
return a[0]*a[0] + a[1]*a[1];
}
-static inline float v2_length( v2f a )
+static inline f32 v2_length( v2f a )
{
return sqrtf( v2_length2( a ) );
}
-static inline float v2_dist2( v2f a, v2f b )
+static inline f32 v2_dist2( v2f a, v2f b )
{
v2f delta;
v2_sub( a, b, delta );
return v2_length2( delta );
}
-static inline float v2_dist( v2f a, v2f b )
+static inline f32 v2_dist( v2f a, v2f b )
{
return sqrtf( v2_dist2( a, b ) );
}
-static inline void v2_lerp( v2f a, v2f b, float t, v2f d )
+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 void v2_normalize_clamp( v2f a )
{
- float l2 = v2_length2( a );
+ f32 l2 = v2_length2( a );
if( l2 > 1.0f )
v2_muls( a, 1.0f/sqrtf(l2), a );
}
b[1] = floorf( a[1] );
}
-static inline void v2_fill( v2f a, float v )
+static inline void v2_fill( v2f a, f32 v )
{
a[0] = v;
a[1] = v;
}
-/* copysign of b to a */
static inline void v2_copysign( v2f a, v2f b )
{
a[0] = copysignf( a[0], b[0] );
a[1] = copysignf( a[1], b[1] );
}
-/*
- * Vector 3
- */
-static inline void v3_zero( v3f a )
+/* integer variants
+ * ---------------- */
+
+static inline void v2i_copy( v2i a, v2i b )
{
- a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
+ 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_add( v3f a, v3f b, v3f d )
+static inline void v3_zero( v3f a )
{
- d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
+ a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
}
-static inline void v3i_add( v3i a, v3i b, v3i d )
+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 v4_add( v4f a, v4f b, v4f d )
+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];
- d[3] = a[3]+b[3];
+ 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[2] = b[2]!=0.0f? a[2]/b[2]: INFINITY;
}
-static inline void v3_muls( v3f a, float s, v3f d )
+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, float v )
+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, float s, v3f d )
+static inline void v3_divs( v3f a, f32 s, v3f d )
{
if( s == 0.0f )
v3_fill( d, INFINITY );
}
}
-static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
+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;
}
d[2] = a[2]+b[2]*s[2];
}
-static inline float v3_dot( v3f a, v3f b )
+static inline f32 v3_dot( v3f a, v3f b )
{
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
v3_copy( d, dest );
}
-static inline float v3_length2( v3f a )
+static inline f32 v3_length2( v3f a )
{
return v3_dot( a, a );
}
-static inline float v3_length( v3f a )
+static inline f32 v3_length( v3f a )
{
return sqrtf( v3_length2( a ) );
}
-static inline float v3_dist2( v3f a, v3f b )
+static inline f32 v3_dist2( v3f a, v3f b )
{
v3f delta;
v3_sub( a, b, delta );
return v3_length2( delta );
}
-static inline float v3_dist( v3f a, v3f b )
+static inline f32 v3_dist( v3f a, v3f b )
{
return sqrtf( v3_dist2( a, b ) );
}
v3_muls( a, 1.f / v3_length( a ), a );
}
-static inline float vg_lerpf( float a, float b, float t )
+static inline f32 vg_lerpf( f32 a, f32 b, f32 t )
{
return a + t*(b-a);
}
-static inline double vg_lerp( double a, double b, double t )
+static inline f64 vg_lerp( f64 a, f64 b, f64 t )
{
return a + t*(b-a);
}
/* correctly lerp around circular period -pi -> pi */
-static float vg_alerpf( float a, float b, float t )
+static f32 vg_alerpf( f32 a, f32 b, f32 t )
{
- float d = fmodf( b-a, VG_TAUf ),
+ 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, float t, v3f d )
+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]);
dest[2] = vg_maxf(a[2], b[2]);
}
-static inline float v3_minf( v3f a )
+static inline f32 v3_minf( v3f a )
{
return vg_minf( vg_minf( a[0], a[1] ), a[2] );
}
-static inline float v3_maxf( v3f a )
+static inline f32 v3_maxf( v3f a )
{
return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
}
b[2] = -a[2];
}
-static inline void v3_rotate( v3f v, float angle, v3f axis, v3f d )
+static inline void v3_rotate( v3f v, f32 angle, v3f axis, v3f d )
{
v3f v1, v2, k;
- float c, s;
+ f32 c, s;
c = cosf( angle );
s = sinf( angle );
}
/*
- * Vector 4
+ * -----------------------------------------------------------------------------
+ * 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, float s, v4f d )
+static inline void v4_muls( v4f a, f32 s, v4f d )
{
d[0] = a[0]*s;
d[1] = a[1]*s;
d[3] = a[3]*s;
}
-static inline void v4_muladds( v4f a, v4f b, float s, v4f d )
+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[3] = a[3]+b[3]*s;
}
-static inline void v4_lerp( v4f a, v4f b, float t, v4f d )
+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[3] = a[3] + t*(b[3]-a[3]);
}
-static inline float v4_dot( v4f a, v4f b )
+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 float v4_length( v4f a )
+static inline f32 v4_length( v4f a )
{
return sqrtf( v4_dot(a,a) );
}
/*
- * Matrix 2x2
+ * -----------------------------------------------------------------------------
+ * 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 s = 1.0f/ sqrtf(v4_dot(q,q));
+ 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 ){
+ v4_muls( b, -1.0f, d );
+ v4_lerp( a, d, 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 );
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Section 4.a 2x2 matrices
+ * -----------------------------------------------------------------------------
*/
-#define M2X2_INDENTIY {{1.0f, 0.0f, }, \
- { 0.0f, 1.0f, }}
+#define M2X2_INDENTIY {{1.0f, 0.0f, }, \
+ {0.0f, 1.0f, }}
-#define M2X2_ZERO {{0.0f, 0.0f, }, \
- { 0.0f, 0.0f, }}
+#define M2X2_ZERO {{0.0f, 0.0f, }, \
+ {0.0f, 0.0f, }}
static inline void m2x2_copy( m2x2f a, m2x2f b )
{
m2x2_copy( id, a );
}
-static inline void m2x2_create_rotation( m2x2f a, float theta )
+static inline void m2x2_create_rotation( m2x2f a, f32 theta )
{
- float s, c;
+ f32 s, c;
s = sinf( theta );
c = cosf( theta );
}
/*
- * Matrix 3x3
+ * -----------------------------------------------------------------------------
+ * 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, },\
+#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 )
{
m3x3_copy( id, a );
}
-static void m3x3_diagonal( m3x3f a, float v )
+static void m3x3_diagonal( m3x3f a, f32 v )
{
m3x3_identity( a );
a[0][0] = v;
static inline void m3x3_inv( m3x3f src, m3x3f dest )
{
- float a = src[0][0], b = src[0][1], c = src[0][2],
+ 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];
- float det = 1.f /
+ f32 det = 1.f /
(+a*(e*i-h*f)
-b*(d*i-f*g)
+c*(d*h-e*g));
dest[2][2] = (a*e-d*b)*det;
}
-static float m3x3_det( m3x3f m )
+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])
static inline void m3x3_transpose( m3x3f src, m3x3f dest )
{
- float a = src[0][0], b = src[0][1], c = src[0][2],
+ 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];
static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
{
- float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
+ 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],
}
static inline void m3x3_projection( m3x3f dst,
- float const left, float const right, float const bottom, float const top )
+ f32 const left, f32 const right, f32 const bottom, f32 const top )
{
- float rl, tb;
+ f32 rl, tb;
m3x3_zero( dst );
v3_muls( m[2], v[2], m[2] );
}
-static inline void m3x3_scalef( m3x3f m, float f )
+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, float angle )
+static inline void m3x3_rotate( m3x3f m, f32 angle )
{
- float m00 = m[0][0], m10 = m[1][0],
+ 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];
- float c, s;
+ f32 c, s;
s = sinf( angle );
c = cosf( angle );
m[1][2] = m02 * -s + m12 * c;
}
-static inline void box_addpt( boxf a, v3f pt )
-{
- v3_minv( a[0], pt, a[0] );
- v3_maxv( a[1], pt, a[1] );
+/*
+ * -----------------------------------------------------------------------------
+ * 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 box_concat( boxf a, boxf b )
+static inline void m4x3_invert_affine( m4x3f a, m4x3f b )
{
- v3_minv( a[0], b[0], a[0] );
- v3_maxv( a[1], b[1], a[1] );
+ m3x3_transpose( a, b );
+ m3x3_mulv( b, a[3], b[3] );
+ v3_negate( b[3], b[3] );
}
-static inline void box_copy( boxf a, boxf b )
+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 int box_overlap( boxf a, boxf b )
+static inline void m4x3_identity( m4x3f a )
{
- 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] )
- ;
+ m4x3f id = M4X3_IDENTITY;
+ m4x3_copy( id, a );
}
-static int box_within( boxf greater, boxf lesser )
+static void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
{
- v3f a, b;
- v3_sub( lesser[0], greater[0], a );
- v3_sub( lesser[1], greater[1], b );
+ 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( (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;
- }
+#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];
- return 0;
+ v3_copy( res, d );
}
-static inline void box_init_inf( boxf box )
+/*
+ * Transform plane ( xyz, distance )
+ */
+static void m4x3_mulp( m4x3f m, v4f p, v4f d )
{
- v3_fill( box[0], INFINITY );
- v3_fill( box[1], -INFINITY );
+ v3f o;
+
+ v3_muls( p, p[3], o );
+ m4x3_mulv( m, o, o );
+ m3x3_mulv( m, p, d );
+
+ d[3] = v3_dot( o, d );
}
-int ray_aabb1( boxf box, v3f co, v3f dir_inv, float dist )
+/*
+ * Affine transforms
+ */
+
+static void m4x3_translate( m4x3f m, v3f v )
{
- v3f v0, v1;
- float tmin, tmax;
+ 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] );
+}
- v3_sub( box[0], co, v0 );
- v3_sub( box[1], co, v1 );
+static void m4x3_rotate_x( m4x3f m, f32 angle )
+{
+ m4x3f t = M4X3_IDENTITY;
+ f32 c, s;
- v3_mul( v0, dir_inv, v0 );
- v3_mul( v1, dir_inv, v1 );
+ 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_transform_aabb( m4x3f m, boxf box )
+{
+ v3f a; v3f b;
- 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] ));
+ v3_copy( box[0], a );
+ v3_copy( box[1], b );
+ v3_fill( box[0], INFINITY );
+ v3_fill( box[1], -INFINITY );
- return (tmax >= tmin) && (tmin <= dist) && (tmax >= 0.0f);
+ m4x3_expand_aabb_point( m, box, (v3f){ a[0], a[1], a[2] } );
+ m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
+ m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
+ m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
+
+ m4x3_expand_aabb_point( m, box, (v3f){ a[0], a[1], b[2] } );
+ m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
+ m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
+ m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
}
static inline void m4x3_lookat( m4x3f m, v3f pos, v3f target, v3f up )
}
/*
- * Matrix 4x4
+ * -----------------------------------------------------------------------------
+ * 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 },\
+#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, float angle,
- float ratio, float fnear, float ffar )
+static void m4x4_projection( m4x4f m, f32 angle,
+ f32 ratio, f32 fnear, f32 ffar )
{
- float scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * fnear,
+ f32 scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * fnear,
r = ratio * scale,
l = -r,
t = scale,
static inline void m4x4_mul( m4x4f a, m4x4f b, m4x4f d )
{
- float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3],
+ 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],
static inline void m4x4_inv( m4x4f a, m4x4f d )
{
- float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3],
+ 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],
}
/*
- * Planes (double precision)
+ * -----------------------------------------------------------------------------
+ * Section 5.a Boxes
+ * -----------------------------------------------------------------------------
*/
-static inline void tri_to_plane( double a[3], double b[3],
- double c[3], double p[4] )
+
+static inline void box_addpt( boxf a, v3f pt )
{
- double edge0[3];
- double edge1[3];
- double 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 )
-{
- float const epsilon = 1e-6f;
-
- v3f x;
- v3_cross( a, b, x );
- float 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;
+ v3_minv( a[0], pt, a[0] );
+ v3_maxv( a[1], pt, a[1] );
}
-int plane_intersect2( v4f a, v4f b, v3f p, v3f n )
+static inline void box_concat( boxf a, boxf b )
{
- float const epsilon = 1e-6f;
-
- v4f c;
- v3_cross( a, b, c );
- float 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;
+ v3_minv( a[0], b[0], a[0] );
+ v3_maxv( a[1], b[1], a[1] );
}
-static int plane_segment( v4f plane, v3f a, v3f b, v3f co )
+static inline void box_copy( boxf a, boxf b )
{
- float d0 = v3_dot( a, plane ) - plane[3],
- d1 = v3_dot( b, plane ) - plane[3];
-
- if( d0*d1 < 0.0f )
- {
- float 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;
+ v3_copy( a[0], b[0] );
+ v3_copy( a[1], b[1] );
}
-static inline double plane_polarity( double p[4], double a[3] )
+static inline int box_overlap( boxf a, boxf b )
{
- 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])
+ 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] )
;
}
-/* 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, float angle )
-{
- float 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 )
-{
- float s = 1.0f/ sqrtf(v4_dot(q,q));
- q[0] *= s;
- q[1] *= s;
- q[2] *= s;
- q[3] *= s;
-}
-
-static inline void q_inv( v4f q, v4f d )
-{
- float 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, float t, v4f d )
-{
- if( v4_dot(a,b) < 0.0f ){
- v4_muls( b, -1.0f, d );
- v4_lerp( a, d, t, d );
- }
- else
- v4_lerp( a, b, t, d );
-
- q_normalize( d );
-}
-
-static void euler_m3x3( v3f angles, m3x3f d )
-{
- float 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 inline void q_m3x3( v4f q, m3x3f d )
-{
- float
- 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 m3x3_q( m3x3f m, v4f q )
+static int box_within( boxf greater, boxf lesser )
{
- float diag, r, rinv;
+ v3f a, b;
+ v3_sub( lesser[0], greater[0], a );
+ v3_sub( lesser[1], greater[1], b );
- 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
+ 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) )
{
- 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]);
+ return 1;
}
-}
-
-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 );
-}
-
-enum contact_type
-{
- k_contact_type_default,
- k_contact_type_disabled,
- k_contact_type_edge
-};
-
-/*
- * Matrix 4x3
- */
-
-#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 )
-{
- float 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 )
-{
- float
- 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 );
+ return 0;
}
-/*
- * Transform plane ( xyz, distance )
- */
-static void m4x3_mulp( m4x3f m, v4f p, v4f d )
+static inline void box_init_inf( boxf box )
{
- v3f o;
-
- v3_muls( p, p[3], o );
- m4x3_mulv( m, o, o );
- m3x3_mulv( m, p, d );
-
- d[3] = v3_dot( o, d );
+ v3_fill( box[0], INFINITY );
+ v3_fill( box[1], -INFINITY );
}
/*
- * Affine transforms
+ * -----------------------------------------------------------------------------
+ * Section 5.b Planes
+ * -----------------------------------------------------------------------------
*/
-static void m4x3_translate( m4x3f m, v3f v )
+static inline void tri_to_plane( f64 a[3], f64 b[3],
+ f64 c[3], f64 p[4] )
{
- 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] );
+ 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 void m4x3_rotate_x( m4x3f m, float angle )
+static int plane_intersect3( v4f a, v4f b, v4f c, v3f p )
{
- m4x3f t = M4X3_IDENTITY;
- float c, s;
-
- c = cosf( angle );
- s = sinf( angle );
+ 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;
- t[1][1] = c;
- t[1][2] = s;
- t[2][1] = -s;
- t[2][2] = c;
+ v3f v0, v1, v2;
+ v3_cross( b, c, v0 );
+ v3_cross( c, a, v1 );
+ v3_cross( a, b, v2 );
- m4x3_mul( m, t, m );
+ 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 void m4x3_rotate_y( m4x3f m, float angle )
+int plane_intersect2( v4f a, v4f b, v3f p, v3f n )
{
- m4x3f t = M4X3_IDENTITY;
- float c, s;
-
- c = cosf( angle );
- s = sinf( angle );
-
- t[0][0] = c;
- t[0][2] = -s;
- t[2][0] = s;
- t[2][2] = c;
+ f32 const epsilon = 1e-6f;
- m4x3_mul( m, t, m );
-}
-
-static void m4x3_rotate_z( m4x3f m, float angle )
-{
- m4x3f t = M4X3_IDENTITY;
- float c, s;
+ v4f c;
+ v3_cross( a, b, c );
+ f32 d = v3_length2( c );
- c = cosf( angle );
- s = sinf( angle );
+ if( (d < epsilon) && (d > -epsilon) )
+ return 0;
- t[0][0] = c;
- t[0][1] = s;
- t[1][0] = -s;
- t[1][1] = c;
+ v3f v0, v1, vx;
+ v3_cross( c, b, v0 );
+ v3_cross( a, c, v1 );
- m4x3_mul( m, t, m );
-}
+ v3_muls( v0, a[3], vx );
+ v3_muladds( vx, v1, b[3], vx );
+ v3_divs( vx, d, p );
+ v3_copy( c, n );
-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;
+ return 1;
}
-static void m4x3_decompose( m4x3f m, v3f co, v4f q, v3f s )
+static int plane_segment( v4f plane, v3f a, v3f b, v3f co )
{
- 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] );
+ f32 d0 = v3_dot( a, plane ) - plane[3],
+ d1 = v3_dot( b, plane ) - plane[3];
- m3x3_q( rot, q );
-}
+ if( d0*d1 < 0.0f )
+ {
+ f32 tot = 1.0f/( fabsf(d0)+fabsf(d1) );
-static void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
-{
- v3f v;
- m4x3_mulv( m, point, v );
+ v3_muls( a, fabsf(d1) * tot, co );
+ v3_muladds( co, b, fabsf(d0) * tot, co );
+ return 1;
+ }
- v3_minv( box[0], v, box[0] );
- v3_maxv( box[1], v, box[1] );
+ return 0;
}
-static void m4x3_transform_aabb( m4x3f m, boxf box )
+static inline f64 plane_polarity( f64 p[4], f64 a[3] )
{
- v3f a; v3f b;
-
- v3_copy( box[0], a );
- v3_copy( box[1], b );
- v3_fill( box[0], INFINITY );
- v3_fill( box[1], -INFINITY );
-
- m4x3_expand_aabb_point( m, box, (v3f){ a[0], a[1], a[2] } );
- m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
- m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
- m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
-
- m4x3_expand_aabb_point( m, box, (v3f){ a[0], a[1], b[2] } );
- m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
- m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
- m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
+ 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])
+ ;
}
/*
* -----------------------------------------------------------------------------
- * Closest point functions
+ * Section 5.c Closest point functions
* -----------------------------------------------------------------------------
*/
* These closest point tests were learned from Real-Time Collision Detection by
* Christer Ericson
*/
-VG_STATIC float closest_segment_segment( v3f p1, v3f q1, v3f p2, v3f q2,
- float *s, float *t, v3f c1, v3f c2)
+VG_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 );
- float a = v3_length2( d1 ),
+ f32 a = v3_length2( d1 ),
e = v3_length2( d2 ),
f = v3_dot( d2, r );
- const float kEpsilon = 0.0001f;
+ const f32 kEpsilon = 0.0001f;
if( a <= kEpsilon && e <= kEpsilon )
{
}
else
{
- float c = v3_dot( d1, r );
+ f32 c = v3_dot( d1, r );
if( e <= kEpsilon )
{
*t = 0.0f;
}
else
{
- float b = v3_dot(d1,d2),
+ f32 b = v3_dot(d1,d2),
d = a*e-b*b;
if( d != 0.0f )
m4x3_mulv( mtx, local, dest );
}
-VG_STATIC float closest_point_segment( v3f a, v3f b, v3f point, v3f dest )
+VG_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 );
- float t = v3_dot( v1, v0 ) / v3_length2(v0);
+ 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;
VG_STATIC void closest_on_triangle( v3f p, v3f tri[3], v3f dest )
{
v3f ab, ac, ap;
- float d1, d2;
+ f32 d1, d2;
/* Region outside A */
v3_sub( tri[1], tri[0], ab );
/* Region outside B */
v3f bp;
- float d3, d4;
+ f32 d3, d4;
v3_sub( p, tri[1], bp );
d3 = v3_dot( ab, bp );
}
/* Edge region of AB */
- float vc = d1*d4 - d3*d2;
+ f32 vc = d1*d4 - d3*d2;
if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
{
- float v = d1 / (d1-d3);
+ 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;
- float d5, d6;
+ f32 d5, d6;
v3_sub( p, tri[2], cp );
d5 = v3_dot(ab, cp);
d6 = v3_dot(ac, cp);
}
/* Region of AC */
- float vb = d5*d2 - d1*d6;
+ f32 vb = d5*d2 - d1*d6;
if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
{
- float w = d2 / (d2-d6);
+ f32 w = d2 / (d2-d6);
v3_muladds( tri[0], ac, w, dest );
v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
return;
}
/* Region of BC */
- float va = d3*d6 - d5*d4;
+ f32 va = d3*d6 - d5*d4;
if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
{
- float w = (d4-d3) / ((d4-d3) + (d5-d6));
+ f32 w = (d4-d3) / ((d4-d3) + (d5-d6));
v3f bc;
v3_sub( tri[2], tri[1], bc );
v3_muladds( tri[1], bc, w, dest );
}
/* P inside region, Q via barycentric coordinates uvw */
- float d = 1.0f/(va+vb+vc),
+ f32 d = 1.0f/(va+vb+vc),
v = vb*d,
w = vc*d;
v3_muladds( dest, ac, w, dest );
}
+enum contact_type
+{
+ k_contact_type_default,
+ k_contact_type_disabled,
+ k_contact_type_edge
+};
+
VG_STATIC enum contact_type closest_on_triangle_1( v3f p, v3f tri[3], v3f dest )
{
v3f ab, ac, ap;
- float d1, d2;
+ f32 d1, d2;
/* Region outside A */
v3_sub( tri[1], tri[0], ab );
/* Region outside B */
v3f bp;
- float d3, d4;
+ f32 d3, d4;
v3_sub( p, tri[1], bp );
d3 = v3_dot( ab, bp );
}
/* Edge region of AB */
- float vc = d1*d4 - d3*d2;
+ f32 vc = d1*d4 - d3*d2;
if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
{
- float v = d1 / (d1-d3);
+ f32 v = d1 / (d1-d3);
v3_muladds( tri[0], ab, v, dest );
return k_contact_type_edge;
}
/* Region outside C */
v3f cp;
- float d5, d6;
+ f32 d5, d6;
v3_sub( p, tri[2], cp );
d5 = v3_dot(ab, cp);
d6 = v3_dot(ac, cp);
}
/* Region of AC */
- float vb = d5*d2 - d1*d6;
+ f32 vb = d5*d2 - d1*d6;
if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
{
- float w = d2 / (d2-d6);
+ f32 w = d2 / (d2-d6);
v3_muladds( tri[0], ac, w, dest );
return k_contact_type_edge;
}
/* Region of BC */
- float va = d3*d6 - d5*d4;
+ f32 va = d3*d6 - d5*d4;
if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
{
- float w = (d4-d3) / ((d4-d3) + (d5-d6));
+ f32 w = (d4-d3) / ((d4-d3) + (d5-d6));
v3f bc;
v3_sub( tri[2], tri[1], bc );
v3_muladds( tri[1], bc, w, dest );
}
/* P inside region, Q via barycentric coordinates uvw */
- float d = 1.0f/(va+vb+vc),
+ f32 d = 1.0f/(va+vb+vc),
v = vb*d,
w = vc*d;
return k_contact_type_default;
}
-
static void closest_point_elipse( v2f p, v2f e, v2f o )
{
v2f pabs, ei, e2, ve, t;
v2_fill( t, 0.70710678118654752f );
- for( int i=0; i<3; i++ )
- {
+ for( int i=0; i<3; i++ ){
v2f v, u, ud, w;
v2_mul( ve, t, v ); /* ve*t*t*t */
}
/*
- * Raycasts
+ * -----------------------------------------------------------------------------
+ * Section 5.d Raycasts & Spherecasts
+ * -----------------------------------------------------------------------------
*/
+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, float *dist )
+ v3f dir, f32 *dist )
{
- float const kEpsilon = 0.00001f;
+ f32 const kEpsilon = 0.00001f;
v3f v0, v1, h, s, q, n;
- float a,f,u,v,t;
+ f32 a,f,u,v,t;
- float *pa = tri[0],
+ f32 *pa = tri[0],
*pb = tri[1],
*pc = tri[2];
}
/* time of intersection with ray vs sphere */
-static int ray_sphere( v3f c, float r,
- v3f co, v3f dir, float *t )
+static int ray_sphere( v3f c, f32 r,
+ v3f co, v3f dir, f32 *t )
{
v3f m;
v3_sub( co, c, m );
- float b = v3_dot( m, dir ),
+ 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;
- float discr = b*b - c1;
+ f32 discr = b*b - c1;
/* A negative discriminant corresponds to ray missing sphere */
if( discr < 0.0f )
* Heavily adapted from regular segment vs cylinder from:
* Real-Time Collision Detection
*/
-static int ray_uncapped_finite_cylinder( v3f q, v3f p, float r,
- v3f co, v3f dir, float *t )
+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( co, p, m );
v3_sub( sb, co, n );
- float md = v3_dot( m, d ),
+ f32 md = v3_dot( m, d ),
nd = v3_dot( n, d ),
dd = v3_dot( d, d ),
nn = v3_dot( n, n ),
return 0;
}
- float b = dd*mn - nd*md,
+ f32 b = dd*mn - nd*md,
discr = b*b - a*c;
if( discr < 0.0f )
* colliding area. This is a fairly long procedure.
*/
static int spherecast_triangle( v3f tri[3],
- v3f co, v3f dir, float r, float *t, v3f n )
+ v3f co, v3f dir, f32 r, f32 *t, v3f n )
{
v3f sum[3];
v3f v0, v1;
v3_muladds( tri[2], n, r, sum[2] );
int hit = 0;
- float t_min = INFINITY,
+ f32 t_min = INFINITY,
t1;
- if( ray_tri( sum, co, dir, &t1 ) )
- {
+ if( ray_tri( sum, co, dir, &t1 ) ){
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 ) )
- {
+ 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++ )
- {
+ 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 )
- {
+ if( ray_uncapped_finite_cylinder( tri[i0], tri[i1], r, co, dir, &t1 ) ){
+ if( t1 < t_min ){
t_min = t1;
v3f co1, ct, cx;
return hit;
}
-static inline float vg_randf(void)
+/*
+ * -----------------------------------------------------------------------------
+ * Section 5.e Curves
+ * -----------------------------------------------------------------------------
+ */
+
+static void eval_bezier_time( v3f p0, v3f p1, v3f h0, v3f h1, f32 t, v3f p )
{
- /* TODO: replace with our own rand */
- return (float)rand()/(float)(RAND_MAX);
+ 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 inline void vg_rand_dir(v3f dir)
+static void eval_bezier3( v3f p0, v3f p1, v3f p2, f32 t, v3f p )
{
- dir[0] = vg_randf();
- dir[1] = vg_randf();
- dir[2] = vg_randf();
+ f32 u = 1.0f-t;
- v3_muls( dir, 2.0f, dir );
- v3_sub( dir, (v3f){1.0f,1.0f,1.0f}, dir );
+ v3_muls( p0, u*u, p );
+ v3_muladds( p, p1, 2.0f*u*t, p );
+ v3_muladds( p, p2, t*t, p );
+}
- v3_normalize( dir );
+/*
+ * -----------------------------------------------------------------------------
+ * 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
+
+struct {
+ u32 mt[MT_STATE_VECTOR_LENGTH];
+ i32 index;
+}
+static vg_rand;
+
+static void vg_rand_seed( 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;
+ }
}
-static inline void vg_rand_sphere( v3f co )
+/*
+ * Generates a pseudo-randomly generated long.
+ */
+static u32 vg_randu32(void)
+{
+ 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 ){
+ /* 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 );
+ }
+ 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];
+ }
+ 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 >> 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 = vg_rand.mt[vg_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(void)
{
- vg_rand_dir(co);
- v3_muls( co, cbrtf( vg_randf() ), co );
+ return (f64)vg_randu32()/(f64)0xffffffff;
}
-static inline int vg_randint(int max)
+static inline f64 vg_randf64_range( f64 min, f64 max )
{
- return rand()%max;
+ return vg_lerp( min, max, (f64)vg_randf64() );
}
-static void eval_bezier_time( v3f p0, v3f p1, v3f h0, v3f h1, float t, v3f p )
+static inline void vg_rand_dir( v3f dir )
{
- float tt = t*t,
- ttt = tt*t;
+ dir[0] = vg_randf64();
+ dir[1] = vg_randf64();
+ dir[2] = vg_randf64();
- 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 );
+ v3_muls( dir, 2.0f, dir );
+ v3_sub( dir, (v3f){1.0f,1.0f,1.0f}, dir );
+
+ v3_normalize( dir );
}
-static void eval_bezier3( v3f p0, v3f p1, v3f p2, float t, v3f p )
+static inline void vg_rand_sphere( v3f co )
{
- float 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 );
+ vg_rand_dir(co);
+ v3_muls( co, cbrtf( vg_randf64() ), co );
}
#endif /* VG_M_H */
projects / vg.git / commitdiff