// Util // ================================================================================================================== #define CSR_PIf 3.14159265358979323846264338327950288f // Simple min/max replacements float csr_minf( float a, float b ) { return a < b? a: b; } float csr_maxf( float a, float b ) { return a > b? a: b; } int csr_min( int a, int b ) { return a < b? a: b; } int csr_max( int a, int b ) { return a > b? a: b; } // Convert double precision vec3 into single void v3d_v3f( double a[3], float b[3] ) { b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; } // Convert degrees to radians float csr_rad( float deg ) { return deg * CSR_PIf / 180.0f; } // Vector 2 // ================================================================================================================== void v2_copy( v2f a, v2f b ) { b[0] = a[0]; b[1] = a[1]; } void v2_minv( v2f a, v2f b, v2f dest ) { dest[0] = csr_minf(a[0], b[0]); dest[1] = csr_minf(a[1], b[1]); } void v2_maxv( v2f a, v2f b, v2f dest ) { dest[0] = csr_maxf(a[0], b[0]); dest[1] = csr_maxf(a[1], b[1]); } void v2_sub( v2f a, v2f b, v2f d ) { d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; } float v2_cross( v2f a, v2f b ) { return a[0] * b[1] - a[1] * b[0]; } void v2_add( v2f a, v2f b, v2f d ) { d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; } // Vector 3 // ================================================================================================================== void v3_zero( v3f a ) { a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; } void v3_copy( v3f a, v3f b ) { b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; } 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]; } 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]; } 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]; } void v3_div( v3f a, v3f b, v3f d ) { d[0] = a[0]/b[0]; d[1] = a[1]/b[1]; d[2] = a[2]/b[2]; } void v3_muls( v3f a, float s, v3f d ) { d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s; } void v3_divs( v3f a, float s, v3f d ) { d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s; } void v3_muladds( v3f a, v3f b, float s, v3f d ) { d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s; } float v3_dot( v3f a, v3f b ) { return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; } void v3_cross( v3f a, v3f b, 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]; } float v3_length2( v3f a ) { return v3_dot( a, a ); } float v3_length( v3f a ) { return sqrtf( v3_length2( a ) ); } float v3_dist2( v3f a, v3f b ) { v3f delta; v3_sub( a, b, delta ); return v3_length2( delta ); } float v3_dist( v3f a, v3f b ) { return sqrtf( v3_dist2( a, b ) ); } void v3_normalize( v3f a ) { v3_muls( a, 1.f / v3_length( a ), a ); } float csr_lerpf( float a, float b, float t ) { return a + t*(b-a); } void v3_lerp( v3f a, v3f b, float 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]); } void v3_minv( v3f a, v3f b, v3f dest ) { dest[0] = csr_minf(a[0], b[0]); dest[1] = csr_minf(a[1], b[1]); dest[2] = csr_minf(a[2], b[2]); } void v3_maxv( v3f a, v3f b, v3f dest ) { dest[0] = csr_maxf(a[0], b[0]); dest[1] = csr_maxf(a[1], b[1]); dest[2] = csr_maxf(a[2], b[2]); } float v3_minf( v3f a ) { return csr_minf( csr_minf( a[0], a[1] ), a[2] ); } float v3_maxf( v3f a ) { return csr_maxf( csr_maxf( a[0], a[1] ), a[2] ); } void v3_fill( v3f a, float v ) { a[0] = v; a[1] = v; a[2] = v; } // Vector 4 void v4_copy( v4f a, v4f b ) { b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3]; } // Matrix 3x3 //====================================================================================================== void m3x3_inv_transpose( m3x3f src, m3x3f dest ) { float 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 / (+a*(e*i-h*f) -b*(d*i-f*g) +c*(d*h-e*g)); dest[0][0] = (e*i-h*f)*det; dest[1][0] = -(b*i-c*h)*det; dest[2][0] = (b*f-c*e)*det; dest[0][1] = -(d*i-f*g)*det; dest[1][1] = (a*i-c*g)*det; dest[2][1] = -(a*f-d*c)*det; dest[0][2] = (d*h-g*e)*det; dest[1][2] = -(a*h-g*b)*det; dest[2][2] = (a*e-d*b)*det; } 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 ); } // 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 }} 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] ); } 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] ); } void m4x3_identity( m4x3f a ) { m4x3f id = M4X3_IDENTITY; m4x3_copy( id, a ); } 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; } 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 ); } // Affine transforms 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] ); } void m4x3_scale( m4x3f m, float s ) { v3_muls( m[0], s, m[0] ); v3_muls( m[1], s, m[1] ); v3_muls( m[2], s, m[2] ); } void m4x3_rotate_x( m4x3f m, float angle ) { m4x3f t = M4X3_IDENTITY; float 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 ); } void m4x3_rotate_y( m4x3f m, float angle ) { 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; m4x3_mul( m, t, m ); } void m4x3_rotate_z( m4x3f m, float angle ) { m4x3f t = M4X3_IDENTITY; float 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 ); } // Warning: These functions are unoptimized.. 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] ); } void box_concat( boxf a, boxf b ) { v3_minv( a[0], b[0], a[0] ); v3_maxv( a[1], b[1], a[1] ); } void box_copy( boxf a, boxf b ) { v3_copy( a[0], b[0] ); v3_copy( a[1], b[1] ); } void m4x3_transform_aabb( m4x3f m, boxf box ) { 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, a ); m4x3_expand_aabb_point( m, box, (v3f){ a[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){ b[0], b[1], a[2] } ); m4x3_expand_aabb_point( m, box, b ); m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } ); m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } ); m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } ); } // Planes (double precision) // ================================================================================================================== void tri_to_plane( double a[3], double b[3], double c[3], double p[4] ) { 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; } int plane_intersect( double a[4], double b[4], double c[4], double p[4] ) { double const epsilon = 1e-8f; double x[3]; double d; x[0] = a[1] * b[2] - a[2] * b[1]; x[1] = a[2] * b[0] - a[0] * b[2]; x[2] = a[0] * b[1] - a[1] * b[0]; d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2]; if( d < epsilon && d > -epsilon ) return 0; p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3]; p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3]; p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3]; p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3]; p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3]; p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3]; p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3]; p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3]; p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3]; p[0] = -p[0] / d; p[1] = -p[1] / d; p[2] = -p[2] / d; return 1; } double plane_polarity( double p[4], double 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]) ; }