return a - floorf( a );
}
+
+__attribute__ ((deprecated))
static float stable_force( float current, float diff )
{
float fnew = current + diff;
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;
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 )
{
d[0] = a[0]*s; d[1] = a[1]*s;
b[1] = floorf( a[1] );
}
+static inline void v2_fill( v2f a, float 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
*/
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 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 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];
{ 0.0f, 0.0f, 0.0f, }}
+/* 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;
+}
+
+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 inline void m3x3_copy( m3x3f a, m3x3f b )
{
v3_copy( a[0], b[0] );
m3x3_copy( id, a );
}
+static void m3x3_diagonal( m3x3f a, float v )
+{
+ m3x3_identity( a );
+ a[0][0] = v;
+ a[1][1] = v;
+ 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;
dest[2][2] = (a*e-d*b)*det;
}
+static float 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 )
{
float a = src[0][0], b = src[0][1], c = src[0][2],
static inline void m3x3_scale( m3x3f m, v3f v )
{
- m[0][0] = m[0][0] * v[0];
- m[0][1] = m[0][1] * v[0];
- m[0][2] = m[0][2] * v[0];
+ v3_muls( m[0], v[0], m[0] );
+ v3_muls( m[1], v[1], m[1] );
+ v3_muls( m[2], v[2], m[2] );
+}
- m[1][0] = m[1][0] * v[1];
- m[1][1] = m[1][1] * v[1];
- m[1][2] = m[1][2] * v[1];
+static inline void m3x3_scalef( m3x3f m, float f )
+{
+ v3f v;
+ v3_fill( v, f );
+ m3x3_scale( m, v );
}
static inline void m3x3_rotate( m3x3f m, float angle )
m[1][2] = m02 * -s + m12 * c;
}
-/*
- * 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 inline 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;
-}
-
-static inline 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 inline 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 inline 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 inline 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] );
-}
-
-static inline void m4x3_scalev( m4x3f 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 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 );
-}
-
-static inline 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 );
-}
-
-static inline 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 );
-}
-
-static inline 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 inline 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 inline void box_addpt( boxf a, v3f pt )
{
v3_minv( a[0], pt, a[0] );
v3_fill( box[1], -INFINITY );
}
-static inline void m4x3_transform_aabb( m4x3f m, boxf box )
+int ray_aabb1( boxf box, v3f co, v3f dir_inv, float dist )
{
- 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] } );
-}
-
-int ray_aabb( boxf box, v3f co, v3f dir, float dist )
-{
- v3f v0, v1;
- float tmin, tmax;
+ v3f v0, v1;
+ float tmin, tmax;
v3_sub( box[0], co, v0 );
v3_sub( box[1], co, v1 );
- v3_div( v0, dir, v0 );
- v3_div( v1, dir, 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[2], v1[2] ));
tmax = vg_minf( tmax, vg_maxf( v0[2], v1[2] ));
- return tmax >= tmin && tmin < dist && tmax > 0;
+ return (tmax >= tmin) && (tmin <= dist) && (tmax >= 0.0f);
}
static inline void m4x3_lookat( m4x3f m, v3f pos, v3f target, v3f up )
p[2] = p[2] / l;
}
-static inline int plane_intersect( double a[4], double b[4],
- double c[4], double p[4] )
+static int plane_intersect3( v4f a, v4f b, v4f c, v3f p )
{
- 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];
+ float const epsilon = 1e-6f;
- 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];
+ v3f x;
+ v3_cross( a, b, x );
+ float d = v3_dot( x, c );
- p[0] = -p[0] / d;
- p[1] = -p[1] / d;
- p[2] = -p[2] / d;
+ 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;
}
+int plane_intersect2( v4f a, v4f b, v3f p, v3f n )
+{
+ 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;
+}
+
+static int plane_segment( v4f plane, v3f a, v3f b, v3f co )
+{
+ 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;
+}
+
static inline double plane_polarity( double p[4], double a[3] )
{
return
static inline void q_nlerp( v4f a, v4f b, float t, v4f d )
{
- if( v4_dot(a,b) < 0.0f )
- {
+ if( v4_dot(a,b) < 0.0f ){
v4_muls( b, -1.0f, d );
v4_lerp( a, d, 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
}
}
-static int ray_tri( v3f tri[3], v3f co, v3f dir, float *dist )
+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 );
+}
+
+/*
+ * 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, 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 );
+}
+
+static 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 );
+}
+
+static 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 );
+}
+
+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;
+
+ 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] } );
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * 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)
+{
+ v3f d1,d2,r;
+ v3_sub( q1, p1, d1 );
+ v3_sub( q2, p2, d2 );
+ v3_sub( p1, p2, r );
+
+ float a = v3_length2( d1 ),
+ e = v3_length2( d2 ),
+ f = v3_dot( d2, r );
+
+ const float 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
+ {
+ float c = v3_dot( d1, r );
+ if( e <= kEpsilon )
+ {
+ *t = 0.0f;
+ *s = vg_clampf( -c / a, 0.0f, 1.0f );
+ }
+ else
+ {
+ float 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 );
+}
+
+VG_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;
+}
+
+VG_STATIC void closest_point_aabb( v3f p, boxf box, v3f dest )
+{
+ v3_maxv( p, box[0], dest );
+ v3_minv( dest, box[1], dest );
+}
+
+VG_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 );
+}
+
+VG_STATIC float 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);
+ 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;
+
+ /* 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;
+ float 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 */
+ float vc = d1*d4 - d3*d2;
+ if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
+ {
+ float 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;
+ 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 */
+ float vb = d5*d2 - d1*d6;
+ if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
+ {
+ float 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;
+ if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
+ {
+ float 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 */
+ float 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 );
+}
+
+VG_STATIC enum contact_type closest_on_triangle_1( v3f p, v3f tri[3], v3f dest )
+{
+ v3f ab, ac, ap;
+ float 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;
+ float 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 */
+ float vc = d1*d4 - d3*d2;
+ if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
+ {
+ float v = d1 / (d1-d3);
+ v3_muladds( tri[0], ab, v, dest );
+ return k_contact_type_edge;
+ }
+
+ /* Region outside C */
+ v3f cp;
+ float 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 */
+ float vb = d5*d2 - d1*d6;
+ if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
+ {
+ float 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;
+ if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
+ {
+ float 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 */
+ float 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 );
+}
+
+/*
+ * Raycasts
+ */
+
+/* Time of intersection with ray vs triangle */
+static int ray_tri( v3f tri[3], v3f co,
+ v3f dir, float *dist )
{
float const kEpsilon = 0.00001f;
/* Parralel */
a = v3_dot( v0, h );
+
if( a > -kEpsilon && a < kEpsilon )
return 0;
else return 0;
}
+/* time of intersection with ray vs sphere */
+static int ray_sphere( v3f c, float r,
+ v3f co, v3f dir, float *t )
+{
+ v3f m;
+ v3_sub( co, c, m );
+
+ float 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;
+
+ /* 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, float r,
+ v3f co, v3f dir, float *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 );
+
+ float 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;
+ }
+
+ float 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, float r, float *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;
+ float t_min = INFINITY,
+ 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 ) )
+ {
+ 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;
+}
+
static inline float vg_randf(void)
{
+ /* TODO: replace with our own rand */
return (float)rand()/(float)(RAND_MAX);
}
v3_muladds( p, p0, 3.0f*tt -ttt -3.0f*t +1.0f, p );
}
+static void eval_bezier3( v3f p0, v3f p1, v3f p2, float t, v3f p )
+{
+ 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 );
+}
+
#endif /* VG_M_H */
projects / vg.git / blobdiff