+static bh_system bh_system_rigidbodies;
+
+#ifndef RIGIDBODY_H
+#define RIGIDBODY_H
+
+/*
+ * -----------------------------------------------------------------------------
+ * (K)onstants
+ * -----------------------------------------------------------------------------
+ */
+
+static const float
+ k_rb_rate = 60.0f,
+ k_rb_delta = (1.0f/k_rb_rate),
+ k_friction = 0.6f,
+ k_damp_linear = 0.05f, /* scale velocity 1/(1+x) */
+ k_damp_angular = 0.1f, /* scale angular 1/(1+x) */
+ k_limit_bias = 0.02f,
+ k_joint_bias = 0.08f, /* positional joints */
+ k_joint_correction = 0.01f,
+ k_penetration_slop = 0.01f,
+ k_inertia_scale = 4.0f;
+
+/*
+ * -----------------------------------------------------------------------------
+ * structure definitions
+ * -----------------------------------------------------------------------------
+ */
+
+typedef struct rigidbody rigidbody;
+typedef struct contact rb_ct;
+
+struct rigidbody
+{
+ v3f co, v, w;
+ v4f q;
+
+ enum rb_shape
+ {
+ k_rb_shape_box = 0,
+ k_rb_shape_sphere = 1,
+ k_rb_shape_capsule = 2,
+ k_rb_shape_scene = 3
+ }
+ type;
+
+ union
+ {
+ struct rb_sphere
+ {
+ float radius;
+ }
+ sphere;
+
+ struct rb_capsule
+ {
+ float height, radius;
+ }
+ capsule;
+
+ struct rb_scene
+ {
+ scene *pscene;
+ }
+ scene;
+ }
+ inf;
+
+ v3f right, up, forward;
+
+ int is_world;
+
+ boxf bbx, bbx_world;
+ float inv_mass;
+
+ /* inertia model and inverse world tensor */
+ v3f I;
+ m3x3f iI, iIw;
+
+ m4x3f to_world, to_local;
+};
+
+static struct contact
+{
+ rigidbody *rba, *rbb;
+ v3f co, n;
+ v3f t[2];
+ float p, bias, norm_impulse, tangent_impulse[2],
+ normal_mass, tangent_mass[2];
+
+ u32 element_id;
+}
+rb_contact_buffer[256];
+static int rb_contact_count = 0;
+
+/*
+ * -----------------------------------------------------------------------------
+ * Math Utils
+ * -----------------------------------------------------------------------------
+ */
+
+static float sphere_volume( float radius )
+{
+ float r3 = radius*radius*radius;
+ return (4.0f/3.0f) * VG_PIf * r3;
+}
+
+static void rb_tangent_basis( v3f n, v3f tx, v3f ty )
+{
+ /* Compute tangent basis (box2d) */
+ if( fabsf( n[0] ) >= 0.57735027f )
+ {
+ tx[0] = n[1];
+ tx[1] = -n[0];
+ tx[2] = 0.0f;
+ }
+ else
+ {
+ tx[0] = 0.0f;
+ tx[1] = n[2];
+ tx[2] = -n[1];
+ }
+
+ v3_normalize( tx );
+ v3_cross( n, tx, ty );
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Debugging
+ * -----------------------------------------------------------------------------
+ */
+
+static void rb_debug_contact( rb_ct *ct )
+{
+ v3f p1;
+ v3_muladds( ct->co, ct->n, 0.1f, p1 );
+ vg_line_pt3( ct->co, 0.025f, 0xff0000ff );
+ vg_line( ct->co, p1, 0xffffffff );
+}
+
+static void debug_sphere( m4x3f m, float radius, u32 colour )
+{
+ v3f ly = { 0.0f, 0.0f, radius },
+ lx = { 0.0f, radius, 0.0f },
+ lz = { 0.0f, 0.0f, radius };
+
+ for( int i=0; i<16; i++ )
+ {
+ float t = ((float)(i+1) * (1.0f/16.0f)) * VG_PIf * 2.0f,
+ s = sinf(t),
+ c = cosf(t);
+
+ v3f py = { s*radius, 0.0f, c*radius },
+ px = { s*radius, c*radius, 0.0f },
+ pz = { 0.0f, s*radius, c*radius };
+
+ v3f p0, p1, p2, p3, p4, p5;
+ m4x3_mulv( m, py, p0 );
+ m4x3_mulv( m, ly, p1 );
+ m4x3_mulv( m, px, p2 );
+ m4x3_mulv( m, lx, p3 );
+ m4x3_mulv( m, pz, p4 );
+ m4x3_mulv( m, lz, p5 );
+
+ vg_line( p0, p1, colour == 0x00? 0xff00ff00: colour );
+ vg_line( p2, p3, colour == 0x00? 0xff0000ff: colour );
+ vg_line( p4, p5, colour == 0x00? 0xffff0000: colour );
+
+ v3_copy( py, ly );
+ v3_copy( px, lx );
+ v3_copy( pz, lz );
+ }
+}
+
+static void debug_capsule( m4x3f m, float radius, float h, u32 colour )
+{
+ v3f ly = { 0.0f, 0.0f, radius },
+ lx = { 0.0f, radius, 0.0f },
+ lz = { 0.0f, 0.0f, radius };
+
+ float s0 = sinf(0.0f)*radius,
+ c0 = cosf(0.0f)*radius;
+
+ v3f p0, p1, up, right, forward;
+ m3x3_mulv( m, (v3f){0.0f,1.0f,0.0f}, up );
+ m3x3_mulv( m, (v3f){1.0f,0.0f,0.0f}, right );
+ m3x3_mulv( m, (v3f){0.0f,0.0f,-1.0f}, forward );
+ v3_muladds( m[3], up, -h*0.5f+radius, p0 );
+ v3_muladds( m[3], up, h*0.5f-radius, p1 );
+
+ v3f a0, a1, b0, b1;
+ v3_muladds( p0, right, radius, a0 );
+ v3_muladds( p1, right, radius, a1 );
+ v3_muladds( p0, forward, radius, b0 );
+ v3_muladds( p1, forward, radius, b1 );
+ vg_line( a0, a1, colour );
+ vg_line( b0, b1, colour );
+
+ v3_muladds( p0, right, -radius, a0 );
+ v3_muladds( p1, right, -radius, a1 );
+ v3_muladds( p0, forward, -radius, b0 );
+ v3_muladds( p1, forward, -radius, b1 );
+ vg_line( a0, a1, colour );
+ vg_line( b0, b1, colour );
+
+ for( int i=0; i<16; i++ )
+ {
+ float t = ((float)(i+1) * (1.0f/16.0f)) * VG_PIf * 2.0f,
+ s1 = sinf(t)*radius,
+ c1 = cosf(t)*radius;
+
+ v3f e0 = { s0, 0.0f, c0 },
+ e1 = { s1, 0.0f, c1 },
+ e2 = { s0, c0, 0.0f },
+ e3 = { s1, c1, 0.0f },
+ e4 = { 0.0f, c0, s0 },
+ e5 = { 0.0f, c1, s1 };
+
+ m3x3_mulv( m, e0, e0 );
+ m3x3_mulv( m, e1, e1 );
+ m3x3_mulv( m, e2, e2 );
+ m3x3_mulv( m, e3, e3 );
+ m3x3_mulv( m, e4, e4 );
+ m3x3_mulv( m, e5, e5 );
+
+ v3_add( p0, e0, a0 );
+ v3_add( p0, e1, a1 );
+ v3_add( p1, e0, b0 );
+ v3_add( p1, e1, b1 );
+
+ vg_line( a0, a1, colour );
+ vg_line( b0, b1, colour );
+
+ if( c0 < 0.0f )
+ {
+ v3_add( p0, e2, a0 );
+ v3_add( p0, e3, a1 );
+ v3_add( p0, e4, b0 );
+ v3_add( p0, e5, b1 );
+ }
+ else
+ {
+ v3_add( p1, e2, a0 );
+ v3_add( p1, e3, a1 );
+ v3_add( p1, e4, b0 );
+ v3_add( p1, e5, b1 );
+ }
+
+ vg_line( a0, a1, colour );
+ vg_line( b0, b1, colour );
+
+ s0 = s1;
+ c0 = c1;
+ }
+}
+
+static void rb_debug( rigidbody *rb, u32 colour )
+{
+ if( rb->type == k_rb_shape_box )
+ {
+ v3f *box = rb->bbx;
+ vg_line_boxf_transformed( rb->to_world, rb->bbx, colour );
+ }
+ else if( rb->type == k_rb_shape_sphere )
+ {
+ debug_sphere( rb->to_world, rb->inf.sphere.radius, colour );
+ }
+ else if( rb->type == k_rb_shape_capsule )
+ {
+ m4x3f m0, m1;
+ float h = rb->inf.capsule.height,
+ r = rb->inf.capsule.radius;
+
+ debug_capsule( rb->to_world, r, h, colour );
+ }
+ else if( rb->type == k_rb_shape_scene )
+ {
+ vg_line_boxf( rb->bbx, colour );
+ }
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Integration
+ * -----------------------------------------------------------------------------
+ */
+
+/*
+ * Update world space bounding box based on local one
+ */
+static void rb_update_bounds( rigidbody *rb )
+{
+ box_copy( rb->bbx, rb->bbx_world );
+ m4x3_transform_aabb( rb->to_world, rb->bbx_world );
+}
+
+/*
+ * Commit transform to rigidbody. Updates matrices
+ */
+static void rb_update_transform( rigidbody *rb )
+{
+ q_normalize( rb->q );
+ q_m3x3( rb->q, rb->to_world );
+ v3_copy( rb->co, rb->to_world[3] );
+
+ m4x3_invert_affine( rb->to_world, rb->to_local );
+
+ m3x3_mulv( rb->to_world, (v3f){1.0f,0.0f, 0.0f}, rb->right );
+ m3x3_mulv( rb->to_world, (v3f){0.0f,1.0f, 0.0f}, rb->up );
+ m3x3_mulv( rb->to_world, (v3f){0.0f,0.0f,-1.0f}, rb->forward );
+
+ m3x3_mul( rb->iI, rb->to_local, rb->iIw );
+ m3x3_mul( rb->to_world, rb->iIw, rb->iIw );
+
+ rb_update_bounds( rb );
+}
+
+/*
+ * Initialize rigidbody and calculate masses, inertia
+ */
+static void rb_init( rigidbody *rb )
+{
+ float volume = 1.0f;
+
+ if( rb->type == k_rb_shape_box )
+ {
+ v3f dims;
+ v3_sub( rb->bbx[1], rb->bbx[0], dims );
+ volume = dims[0]*dims[1]*dims[2];
+
+ if( !rb->is_world )
+ vg_info( "Box volume: %f\n", volume );
+ }
+ else if( rb->type == k_rb_shape_sphere )
+ {
+ volume = sphere_volume( rb->inf.sphere.radius );
+ v3_fill( rb->bbx[0], -rb->inf.sphere.radius );
+ v3_fill( rb->bbx[1], rb->inf.sphere.radius );
+
+ vg_info( "Sphere volume: %f\n", volume );
+ }
+ else if( rb->type == k_rb_shape_capsule )
+ {
+ float r = rb->inf.capsule.radius,
+ h = rb->inf.capsule.height;
+ volume = sphere_volume( r ) + VG_PIf * r*r * (h - r*2.0f);
+
+ v3_fill( rb->bbx[0], -rb->inf.sphere.radius );
+ v3_fill( rb->bbx[1], rb->inf.sphere.radius );
+ rb->bbx[0][1] = -h;
+ rb->bbx[1][1] = h;
+ }
+ else if( rb->type == k_rb_shape_scene )
+ {
+ rb->is_world = 1;
+ box_copy( rb->inf.scene.pscene->bbx, rb->bbx );
+ }
+
+ if( rb->is_world )
+ {
+ rb->inv_mass = 0.0f;
+ v3_zero( rb->I );
+ m3x3_zero(rb->iI);
+ }
+ else
+ {
+ float mass = 2.0f*volume;
+ rb->inv_mass = 1.0f/mass;
+
+ v3f extent;
+ v3_sub( rb->bbx[1], rb->bbx[0], extent );
+ v3_muls( extent, 0.5f, extent );
+
+ /* local intertia tensor */
+ float scale = k_inertia_scale;
+ float ex2 = scale*extent[0]*extent[0],
+ ey2 = scale*extent[1]*extent[1],
+ ez2 = scale*extent[2]*extent[2];
+
+ rb->I[0] = ((1.0f/12.0f) * mass * (ey2+ez2));
+ rb->I[1] = ((1.0f/12.0f) * mass * (ex2+ez2));
+ rb->I[2] = ((1.0f/12.0f) * mass * (ex2+ey2));
+
+ m3x3_identity( rb->iI );
+ rb->iI[0][0] = rb->I[0];
+ rb->iI[1][1] = rb->I[1];
+ rb->iI[2][2] = rb->I[2];
+ m3x3_inv( rb->iI, rb->iI );
+ }
+
+ v3_zero( rb->v );
+ v3_zero( rb->w );
+
+ rb_update_transform( rb );
+}
+
+static void rb_iter( rigidbody *rb )
+{
+ v3f gravity = { 0.0f, -9.8f, 0.0f };
+ v3_muladds( rb->v, gravity, k_rb_delta, rb->v );
+
+ /* intergrate velocity */
+ v3_muladds( rb->co, rb->v, k_rb_delta, rb->co );
+ v3_lerp( rb->w, (v3f){0.0f,0.0f,0.0f}, 0.0025f, rb->w );
+
+ /* inegrate inertia */
+ if( v3_length2( rb->w ) > 0.0f )
+ {
+ v4f rotation;
+ v3f axis;
+ v3_copy( rb->w, axis );
+
+ float mag = v3_length( axis );
+ v3_divs( axis, mag, axis );
+ q_axis_angle( rotation, axis, mag*k_rb_delta );
+ q_mul( rotation, rb->q, rb->q );
+ }
+
+ /* damping */
+ v3_muls( rb->v, 1.0f/(1.0f+k_rb_delta*k_damp_linear), rb->v );
+ v3_muls( rb->w, 1.0f/(1.0f+k_rb_delta*k_damp_angular), rb->w );
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Closest point functions
+ * -----------------------------------------------------------------------------
+ */
+
+/*
+ * These closest point tests were learned from Real-Time Collision Detection by
+ * Christer Ericson
+ */
+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 );
+}
+
+static void closest_point_aabb( v3f p, boxf box, v3f dest )
+{
+ v3_maxv( p, box[0], dest );
+ v3_minv( dest, box[1], dest );
+}
+
+static void closest_point_obb( v3f p, rigidbody *rb, v3f dest )
+{
+ v3f local;
+ m4x3_mulv( rb->to_local, p, local );
+ closest_point_aabb( local, rb->bbx, local );
+ m4x3_mulv( rb->to_world, local, dest );
+}
+
+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;
+}
+
+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 );
+}
+
+/* TODO */
+static void 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;
+ }
+
+ /* 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;
+ }
+
+ /* 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;
+ }
+
+ /* 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;
+ }
+
+ /* 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;
+ }
+
+ /* 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;
+ }
+
+ /* 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 );
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Boolean shape overlap functions
+ * -----------------------------------------------------------------------------
+ */
+
+/*
+ * Project AABB, and triangle interval onto axis to check if they overlap
+ */
+static int rb_box_triangle_interval( v3f extent, v3f axis, v3f tri[3] )
+{
+ float
+
+ r = extent[0] * fabsf(axis[0]) +
+ extent[1] * fabsf(axis[1]) +
+ extent[2] * fabsf(axis[2]),
+
+ p0 = v3_dot( axis, tri[0] ),
+ p1 = v3_dot( axis, tri[1] ),
+ p2 = v3_dot( axis, tri[2] ),
+
+ e = vg_maxf(-vg_maxf(p0,vg_maxf(p1,p2)), vg_minf(p0,vg_minf(p1,p2)));
+
+ if( e > r ) return 0;
+ else return 1;
+}
+
+/*
+ * Seperating axis test box vs triangle
+ */
+static int rb_box_triangle_sat( rigidbody *rba, v3f tri_src[3] )
+{
+ v3f tri[3];
+
+ v3f extent, c;
+ v3_sub( rba->bbx[1], rba->bbx[0], extent );
+ v3_muls( extent, 0.5f, extent );
+ v3_add( rba->bbx[0], extent, c );
+
+ for( int i=0; i<3; i++ )
+ {
+ m4x3_mulv( rba->to_local, tri_src[i], tri[i] );
+ v3_sub( tri[i], c, tri[i] );
+ }
+
+ /* u0, u1, u2 */
+ if(!rb_box_triangle_interval( extent, (v3f){1.0f,0.0f,0.0f}, tri )) return 0;
+ if(!rb_box_triangle_interval( extent, (v3f){0.0f,1.0f,0.0f}, tri )) return 0;
+ if(!rb_box_triangle_interval( extent, (v3f){0.0f,0.0f,1.0f}, tri )) return 0;
+
+ v3f v0,v1,v2,n, e0,e1,e2;
+ v3_sub( tri[1], tri[0], v0 );
+ v3_sub( tri[2], tri[0], v1 );
+ v3_sub( tri[2], tri[1], v2 );
+ v3_normalize( v0 );
+ v3_normalize( v1 );
+ v3_normalize( v2 );
+ v3_cross( v0, v1, n );
+ v3_cross( v0, n, e0 );
+ v3_cross( n, v1, e1 );
+ v3_cross( v2, n, e2 );
+
+ /* normal */
+ if(!rb_box_triangle_interval( extent, n, tri )) return 0;
+
+ v3f axis[9];
+ v3_cross( e0, (v3f){1.0f,0.0f,0.0f}, axis[0] );
+ v3_cross( e0, (v3f){0.0f,1.0f,0.0f}, axis[1] );
+ v3_cross( e0, (v3f){0.0f,0.0f,1.0f}, axis[2] );
+ v3_cross( e1, (v3f){1.0f,0.0f,0.0f}, axis[3] );
+ v3_cross( e1, (v3f){0.0f,1.0f,0.0f}, axis[4] );
+ v3_cross( e1, (v3f){0.0f,0.0f,1.0f}, axis[5] );
+ v3_cross( e2, (v3f){1.0f,0.0f,0.0f}, axis[6] );
+ v3_cross( e2, (v3f){0.0f,1.0f,0.0f}, axis[7] );
+ v3_cross( e2, (v3f){0.0f,0.0f,1.0f}, axis[8] );
+
+ for( int i=0; i<9; i++ )
+ if(!rb_box_triangle_interval( extent, axis[i], tri )) return 0;
+
+ return 1;
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Collision matrix
+ * -----------------------------------------------------------------------------
+ */
+
+/*
+ * Contact generators
+ *
+ * These do not automatically allocate contacts, an appropriately sized
+ * buffer must be supplied. The function returns the size of the manifold
+ * which was generated.
+ *
+ * The values set on the contacts are: n, co, p, rba, rbb
+ */
+
+/*
+ * By collecting the minimum(time) and maximum(time) pairs of points, we
+ * build a reduced and stable exact manifold.
+ *
+ * tx: time at point
+ * rx: minimum distance of these points
+ * dx: the delta between the two points
+ *
+ * pairs will only ammend these if they are creating a collision
+ */
+typedef struct capsule_manifold capsule_manifold;
+struct capsule_manifold
+{
+ float t0, t1;
+ float r0, r1;
+ v3f d0, d1;
+};
+
+/*
+ * Expand a line manifold with a new pair. t value is the time along segment
+ * on the oriented object which created this pair.
+ */
+static void rb_capsule_manifold( v3f pa, v3f pb, float t, float r,
+ capsule_manifold *manifold )
+{
+ v3f delta;
+ v3_sub( pa, pb, delta );
+
+ if( v3_length2(delta) < r*r )
+ {
+ if( t < manifold->t0 )
+ {
+ v3_copy( delta, manifold->d0 );
+ manifold->t0 = t;
+ manifold->r0 = r;
+ }
+
+ if( t > manifold->t1 )
+ {
+ v3_copy( delta, manifold->d1 );
+ manifold->t1 = t;
+ manifold->r1 = r;
+ }
+ }
+}
+
+static void rb_capsule_manifold_init( capsule_manifold *manifold )
+{
+ manifold->t0 = INFINITY;
+ manifold->t1 = -INFINITY;
+}
+
+static int rb_capsule_manifold_done( rigidbody *rba, rigidbody *rbb,
+ capsule_manifold *manifold, rb_ct *buf )
+{
+ float h = rba->inf.capsule.height,
+ ra = rba->inf.capsule.radius;
+
+ v3f p0, p1;
+ v3_muladds( rba->co, rba->up, -h*0.5f+ra, p0 );
+ v3_muladds( rba->co, rba->up, h*0.5f-ra, p1 );
+
+ int count = 0;
+ if( manifold->t0 <= 1.0f )
+ {
+ rb_ct *ct = buf;
+
+ v3f pa;
+ v3_muls( p0, 1.0f-manifold->t0, pa );
+ v3_muladds( pa, p1, manifold->t0, pa );
+
+ float d = v3_length( manifold->d0 );
+ v3_muls( manifold->d0, 1.0f/d, ct->n );
+ v3_muladds( pa, ct->n, -ra, ct->co );
+
+ ct->p = manifold->r0 - d;
+ ct->rba = rba;
+ ct->rbb = rbb;
+
+ count ++;
+ }
+
+ if( (manifold->t1 >= 0.0f) && (manifold->t0 != manifold->t1) )
+ {
+ rb_ct *ct = buf+count;
+
+ v3f pa;
+ v3_muls( p0, 1.0f-manifold->t1, pa );
+ v3_muladds( pa, p1, manifold->t1, pa );
+
+ float d = v3_length( manifold->d1 );
+ v3_muls( manifold->d1, 1.0f/d, ct->n );
+ v3_muladds( pa, ct->n, -ra, ct->co );
+
+ ct->p = manifold->r1 - d;
+ ct->rba = rba;
+ ct->rbb = rbb;
+
+ count ++;
+ }
+
+ /*
+ * Debugging
+ */
+
+ if( count == 2 )
+ vg_line( buf[0].co, buf[1].co, 0xff0000ff );
+
+ return count;
+}
+
+static int rb_capsule_sphere( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
+{
+ float h = rba->inf.capsule.height,
+ ra = rba->inf.capsule.radius,
+ rb = rbb->inf.sphere.radius;
+
+ v3f p0, p1;
+ v3_muladds( rba->co, rba->up, -h*0.5f+ra, p0 );
+ v3_muladds( rba->co, rba->up, h*0.5f-ra, p1 );
+
+ v3f c, delta;
+ closest_point_segment( p0, p1, rbb->co, c );
+ v3_sub( c, rbb->co, delta );
+
+ float d2 = v3_length2(delta),
+ r = ra + rb;
+
+ if( d2 < r*r )
+ {
+ float d = sqrtf(d2);
+
+ rb_ct *ct = buf;
+ v3_muls( delta, 1.0f/d, ct->n );
+ ct->p = r-d;
+
+ v3f p0, p1;
+ v3_muladds( c, ct->n, -ra, p0 );
+ v3_muladds( rbb->co, ct->n, rb, p1 );
+ v3_add( p0, p1, ct->co );
+ v3_muls( ct->co, 0.5f, ct->co );
+
+ ct->rba = rba;
+ ct->rbb = rbb;
+
+ return 1;
+ }
+
+ return 0;
+}
+
+static int rb_capsule_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
+{
+ float ha = rba->inf.capsule.height,
+ hb = rbb->inf.capsule.height,
+ ra = rba->inf.capsule.radius,
+ rb = rbb->inf.capsule.radius,
+ r = ra+rb;
+
+ v3f p0, p1, p2, p3;
+ v3_muladds( rba->co, rba->up, -ha*0.5f+ra, p0 );
+ v3_muladds( rba->co, rba->up, ha*0.5f-ra, p1 );
+ v3_muladds( rbb->co, rbb->up, -hb*0.5f+rb, p2 );
+ v3_muladds( rbb->co, rbb->up, hb*0.5f-rb, p3 );
+
+ capsule_manifold manifold;
+ rb_capsule_manifold_init( &manifold );
+
+ v3f pa, pb;
+ float ta, tb;
+ closest_segment_segment( p0, p1, p2, p3, &ta, &tb, pa, pb );
+ rb_capsule_manifold( pa, pb, ta, r, &manifold );
+
+ ta = closest_point_segment( p0, p1, p2, pa );
+ tb = closest_point_segment( p0, p1, p3, pb );
+ rb_capsule_manifold( pa, p2, ta, r, &manifold );
+ rb_capsule_manifold( pb, p3, tb, r, &manifold );
+
+ closest_point_segment( p2, p3, p0, pa );
+ closest_point_segment( p2, p3, p1, pb );
+ rb_capsule_manifold( p0, pa, 0.0f, r, &manifold );
+ rb_capsule_manifold( p1, pb, 1.0f, r, &manifold );
+
+ return rb_capsule_manifold_done( rba, rbb, &manifold, buf );
+}
+
+/*
+ * Generates up to two contacts; optimised for the most stable manifold
+ */
+static int rb_capsule_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
+{
+ float h = rba->inf.capsule.height,
+ r = rba->inf.capsule.radius;
+
+ /*
+ * Solving this in symetric local space of the cube saves us some time and a
+ * couple branches when it comes to the quad stage.
+ */
+ v3f centroid;
+ v3_add( rbb->bbx[0], rbb->bbx[1], centroid );
+ v3_muls( centroid, 0.5f, centroid );
+
+ boxf bbx;
+ v3_sub( rbb->bbx[0], centroid, bbx[0] );
+ v3_sub( rbb->bbx[1], centroid, bbx[1] );
+
+ v3f pc, p0w, p1w, p0, p1;
+ v3_muladds( rba->co, rba->up, -h*0.5f+r, p0w );
+ v3_muladds( rba->co, rba->up, h*0.5f-r, p1w );
+
+ m4x3_mulv( rbb->to_local, p0w, p0 );
+ m4x3_mulv( rbb->to_local, p1w, p1 );
+ v3_sub( p0, centroid, p0 );
+ v3_sub( p1, centroid, p1 );
+ v3_add( p0, p1, pc );
+ v3_muls( pc, 0.5f, pc );
+
+ /*
+ * Finding an appropriate quad to collide lines with
+ */
+ v3f region;
+ v3_div( pc, bbx[1], region );
+
+ v3f quad[4];
+ if( (fabsf(region[0]) > fabsf(region[1])) &&
+ (fabsf(region[0]) > fabsf(region[2])) )
+ {
+ float px = vg_signf(region[0]) * bbx[1][0];
+ v3_copy( (v3f){ px, bbx[0][1], bbx[0][2] }, quad[0] );
+ v3_copy( (v3f){ px, bbx[1][1], bbx[0][2] }, quad[1] );
+ v3_copy( (v3f){ px, bbx[1][1], bbx[1][2] }, quad[2] );
+ v3_copy( (v3f){ px, bbx[0][1], bbx[1][2] }, quad[3] );
+ }
+ else if( fabsf(region[1]) > fabsf(region[2]) )
+ {
+ float py = vg_signf(region[1]) * bbx[1][1];
+ v3_copy( (v3f){ bbx[0][0], py, bbx[0][2] }, quad[0] );
+ v3_copy( (v3f){ bbx[1][0], py, bbx[0][2] }, quad[1] );
+ v3_copy( (v3f){ bbx[1][0], py, bbx[1][2] }, quad[2] );
+ v3_copy( (v3f){ bbx[0][0], py, bbx[1][2] }, quad[3] );
+ }
+ else
+ {
+ float pz = vg_signf(region[2]) * bbx[1][2];
+ v3_copy( (v3f){ bbx[0][0], bbx[0][1], pz }, quad[0] );
+ v3_copy( (v3f){ bbx[1][0], bbx[0][1], pz }, quad[1] );
+ v3_copy( (v3f){ bbx[1][0], bbx[1][1], pz }, quad[2] );
+ v3_copy( (v3f){ bbx[0][0], bbx[1][1], pz }, quad[3] );
+ }
+
+ capsule_manifold manifold;
+ rb_capsule_manifold_init( &manifold );
+
+ v3f c0, c1;
+ closest_point_aabb( p0, bbx, c0 );
+ closest_point_aabb( p1, bbx, c1 );
+
+ v3f d0, d1, da;
+ v3_sub( c0, p0, d0 );
+ v3_sub( c1, p1, d1 );
+ v3_sub( p1, p0, da );
+
+ /* TODO: ? */
+ v3_normalize(d0);
+ v3_normalize(d1);
+ v3_normalize(da);
+
+ if( v3_dot( da, d0 ) <= 0.01f )
+ rb_capsule_manifold( p0, c0, 0.0f, r, &manifold );
+
+ if( v3_dot( da, d1 ) >= -0.01f )
+ rb_capsule_manifold( p1, c1, 1.0f, r, &manifold );
+
+ for( int i=0; i<4; i++ )
+ {
+ int i0 = i,
+ i1 = (i+1)%4;
+
+ v3f ca, cb;
+ float ta, tb;
+ closest_segment_segment( p0, p1, quad[i0], quad[i1], &ta, &tb, ca, cb );
+ rb_capsule_manifold( ca, cb, ta, r, &manifold );
+ }
+
+ /*
+ * Create final contacts based on line manifold
+ */
+ m3x3_mulv( rbb->to_world, manifold.d0, manifold.d0 );
+ m3x3_mulv( rbb->to_world, manifold.d1, manifold.d1 );
+
+ /*
+ * Debugging
+ */
+
+#if 0
+ for( int i=0; i<4; i++ )
+ {
+ v3f q0, q1;
+ int i0 = i,
+ i1 = (i+1)%4;
+
+ v3_add( quad[i0], centroid, q0 );
+ v3_add( quad[i1], centroid, q1 );
+
+ m4x3_mulv( rbb->to_world, q0, q0 );
+ m4x3_mulv( rbb->to_world, q1, q1 );
+
+ vg_line( q0, q1, 0xffffffff );
+ }
+#endif