more physics shapes

[carveJwlIkooP6JGAAIwe30JlM.git] / rigidbody.h

/* 
 * Resources: Box2D - Erin Catto
 *            qu3e  - Randy Gaul
 */

#include "common.h"
#include "bvh.h"

static void rb_tangent_basis( v3f n, v3f tx, v3f ty );
static bh_system bh_system_rigidbodies;

#ifndef RIGIDBODY_H
#define RIGIDBODY_H

#define RB_DEPR 
#define k_rb_rate  60.0f
#define k_rb_delta (1.0f/k_rb_rate)

typedef struct rigidbody rigidbody;
typedef struct contact rb_ct;

struct rigidbody
{
   v3f co, v, w;
   v4f q;

   enum rb_shape
   {
      k_rb_shape_box,
      k_rb_shape_sphere,
      k_rb_shape_capsule
   } 
   type;
   
   union
   {
      struct rb_sphere
      {
         float radius;
      }
      sphere;

      struct rb_capsule
      {
         float height, radius;
      } 
      capsule;
   }
   inf;

   v3f right, up, forward;
   
   int is_world;

   boxf bbx, bbx_world;
   float inv_mass;

   v3f delta;  /* where is the origin of this in relation to a parent body */
   m4x3f to_world, to_local;
};

static rigidbody rb_static_null = 
{
   .co={0.0f,0.0f,0.0f},
   .q={0.0f,0.0f,0.0f,1.0f},
   .v={0.0f,0.0f,0.0f},
   .w={0.0f,0.0f,0.0f},
   .is_world = 1,
   .inv_mass = 0.0f
};

static void rb_debug( rigidbody *rb, u32 colour );

static struct contact
{
   rigidbody *rba, *rbb;
   v3f co, n;
   v3f t[2];
   float mass_total, p, bias, norm_impulse, tangent_impulse[2];
}
rb_contact_buffer[256];
static int rb_contact_count = 0;

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 );

   box_copy( rb->bbx, rb->bbx_world );
   m4x3_transform_aabb( rb->to_world, rb->bbx_world );

   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 );
}

static float sphere_volume( float radius )
{
   float r3 = radius*radius*radius;
   return (4.0f/3.0f) * VG_PIf * r3;
}

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];
   }
   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 );
   }
   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;
   }

   if( rb->is_world )
   {
      rb->inv_mass = 0.0f;
   }
   else
   {
      rb->inv_mass = 1.0f/(8.0f*volume);
   }

   v3_zero( rb->v );
   v3_zero( rb->w );

   rb_update_transform( rb );
}

static void rb_iter( rigidbody *rb )
{
   v3f gravity = { 0.0f, -9.6f, 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 );
   }
}

static void rb_torque( rigidbody *rb, v3f axis, float mag )
{
   v3_muladds( rb->w, axis, mag*k_rb_delta, rb->w );
}

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 );
}

static void rb_solver_reset(void);
static void rb_build_manifold_terrain( rigidbody *rb );
static void rb_build_manifold_terrain_sphere( rigidbody *rb );
static void rb_solve_contacts( rb_ct *buf, int len );
static void rb_presolve_contacts( rb_ct *buffer, int len );

/* 
 * 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 );
}

/*
 * 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
 */

static void rb_debug_contact( rb_ct *ct )
{
   v3f p1;
   v3_muladds( ct->co, ct->n, 0.2f, p1 );
   vg_line_pt3( ct->co, 0.1f, 0xff0000ff );
   vg_line( ct->co, p1, 0xffffffff );
}

/* 
 * 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_vs_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_vs_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_vs_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

   return rb_capsule_manifold_done( rba, rbb, &manifold, buf );
}

static int rb_sphere_vs_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   v3f co, delta;

   closest_point_obb( rba->co, rbb, co );
   v3_sub( rba->co, co, delta );

   float d2 = v3_length2(delta),
          r = rba->inf.sphere.radius;

   if( d2 <= r*r )
   {
      float d;

      rb_ct *ct = buf;
      if( d2 <= 0.0001f )
      {
         v3_sub( rba->co, rbb->co, delta );

         /* 
          * some extra testing is required to find the best axis to push the
          * object back outside the box. Since there isnt a clear seperating
          * vector already, especially on really high aspect boxes.
          */
         float lx = v3_dot( rbb->right, delta ),
               ly = v3_dot( rbb->up, delta ),
               lz = v3_dot( rbb->forward, delta ),
               px = rbb->bbx[1][0] - fabsf(lx),
               py = rbb->bbx[1][1] - fabsf(ly),
               pz = rbb->bbx[1][2] - fabsf(lz);

         if( px < py && px < pz )
            v3_muls( rbb->right, vg_signf(lx), ct->n );
         else if( py < pz )
            v3_muls( rbb->up, vg_signf(ly), ct->n );
         else
            v3_muls( rbb->forward, vg_signf(lz), ct->n );

         v3_muladds( rba->co, ct->n, -r, ct->co );
         ct->p = r;
      }
      else
      {
         d = sqrtf(d2);
         v3_muls( delta, 1.0f/d, ct->n );
         ct->p = r-d;
         v3_copy( co, ct->co );
      }

      ct->rba = rba;
      ct->rbb = rbb;
      return 1;
   }

   return 0;
}

static int rb_sphere_vs_sphere( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   v3f delta;
   v3_sub( rba->co, rbb->co, delta );

   float d2 = v3_length2(delta),
          r = rba->inf.sphere.radius + rbb->inf.sphere.radius;

   if( d2 < r*r )
   {
      float d = sqrtf(d2);

      rb_ct *ct = buf;
      v3_muls( delta, 1.0f/d, ct->n );

      v3f p0, p1;
      v3_muladds( rba->co, ct->n,-rba->inf.sphere.radius, p0 );
      v3_muladds( rbb->co, ct->n, rbb->inf.sphere.radius, p1 );
      v3_add( p0, p1, ct->co );
      v3_muls( ct->co, 0.5f, ct->co );
      ct->p = r-d;
      ct->rba = rba;
      ct->rbb = rbb;
      return 1;
   }

   return 0;
}

static int RB_MATRIX_ERROR( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   vg_error( "Collision type is unimplemented between types %d and %d\n",
             rba->type, rbb->type );

   return 0;
}

static int rb_sphere_vs_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_capsule_vs_sphere( rbb, rba, buf );
}

static int rb_box_vs_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_capsule_vs_box( rbb, rba, buf );
}

static int rb_box_vs_sphere( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_sphere_vs_box( rbb, rba, buf );
}

static int (*rb_jump_table[4][4])( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
= {
              /* box */         /* Sphere */         /* Capsule */
/*box    */ { RB_MATRIX_ERROR,  rb_box_vs_sphere,    rb_box_vs_capsule,    RB_MATRIX_ERROR },
/*sphere */ { rb_sphere_vs_box, rb_sphere_vs_sphere, rb_sphere_vs_capsule, RB_MATRIX_ERROR },
/*capsule*/ { rb_capsule_vs_box,rb_capsule_vs_sphere,rb_capsule_vs_capsule,RB_MATRIX_ERROR },
/*mesh   */ { RB_MATRIX_ERROR,  RB_MATRIX_ERROR,     RB_MATRIX_ERROR,      RB_MATRIX_ERROR }
};


/*
 * Generic functions
 */

/* 
 * This function does not accept triangle as a dynamic object, it is assumed
 * to always be static.
 * 
 * The triangle is also assumed to be one sided for better detection
 */
static int rb_sphere_vs_triangle( rigidbody *rba, v3f tri[3], rb_ct *buf )
{
   v3f delta, co;

   closest_on_triangle( rba->co, tri, co );
   v3_sub( rba->co, co, delta );

   float d2 = v3_length2( delta ),
          r = rba->inf.sphere.radius;

   if( d2 < r*r )
   {
      v3f ab, ac, tn;
      v3_sub( tri[1], tri[0], ab );
      v3_sub( tri[2], tri[0], ac );
      v3_cross( ac, ab, tn );

      if( v3_dot( delta, tn ) > 0.0f )
         v3_muls( delta, -1.0f, delta );

      float d = sqrtf(d2);

      rb_ct *ct = buf;
      v3_muls( delta, 1.0f/d, ct->n );
      v3_copy( co, ct->co );
      ct->p = r-d;
      ct->rba = rba;
      ct->rbb = &rb_static_null;
      return 1;
   }

   return 0;
}


RB_DEPR
static int sphere_vs_triangle( v3f c, float r, v3f tri[3], 
      v3f co, v3f norm, float *p )
{
   v3f delta;
   closest_on_triangle( c, tri, co );

   v3_sub( c, co, delta );


   float d = v3_length2( delta );
   if( d < r*r )
   {
      v3f ab, ac, tn;
      v3_sub( tri[1], tri[0], ab );
      v3_sub( tri[2], tri[0], ac );
      v3_cross( ac, ab, tn );

      if( v3_dot( delta, tn ) > 0.0f )
         v3_muls( delta, -1.0f, delta );

      vg_line_pt3( co, 0.05f, 0xff00ff00 );

      d = sqrtf(d);
      v3_muls( delta, 1.0f/d, norm );

      *p = r-d;
      return 1;
   }

   return 0;
}

#include "world.h"

static void rb_solver_reset(void)
{
   rb_contact_count = 0;
}

static rb_ct *rb_global_ct(void)
{
   return rb_contact_buffer + rb_contact_count;
}

static struct contact *rb_start_contact(void)
{
   if( rb_contact_count == vg_list_size(rb_contact_buffer) )
   {
      vg_error( "rigidbody: too many contacts generated (%u)\n", 
            rb_contact_count );
      return NULL;
   }

   return &rb_contact_buffer[ rb_contact_count ];
}

static void rb_commit_contact( struct contact *ct, float p )
{
   ct->bias = -0.2f*k_rb_rate*vg_minf(0.0f,-p+0.04f);
   rb_tangent_basis( ct->n, ct->t[0], ct->t[1] );

   ct->norm_impulse = 0.0f;
   ct->tangent_impulse[0] = 0.0f;
   ct->tangent_impulse[1] = 0.0f;

   rb_contact_count ++;
}

static void rb_build_manifold_terrain_sphere( rigidbody *rb )
{
   u32 geo[256];
   v3f tri[3];
   int len = bh_select( &world.geo.bhtris, rb->bbx_world, geo, 256 );
   
   for( int i=0; i<len; i++ )
   {
      u32 *ptri = &world.geo.indices[ geo[i]*3 ];

      for( int j=0; j<3; j++ )
         v3_copy( world.geo.verts[ptri[j]].co, tri[j] );

      vg_line(tri[0],tri[1],0xff00ff00 );
      vg_line(tri[1],tri[2],0xff00ff00 );
      vg_line(tri[2],tri[0],0xff00ff00 );

      v3f co, norm;
      float p;

      for( int j=0; j<2; j++ )
      {
         if( sphere_vs_triangle( rb->co, rb->inf.sphere.radius, tri,co,norm,&p))
         {
            struct contact *ct = rb_start_contact();

            if( !ct )
               return;

            v3f p1;
            v3_muladds( rb->co, norm, p, p1 );
            vg_line( rb->co, p1, 0xffffffff );

            ct->rba = rb;
            v3_copy( co, ct->co );
            v3_copy( norm, ct->n );
            rb_commit_contact( ct, p );
         }
      }
   }

}

RB_DEPR
static void rb_build_manifold_terrain( rigidbody *rb )
{
   v3f *box = rb->bbx;
   v3f pts[8]; 
   float *p000 = pts[0], *p001 = pts[1], *p010 = pts[2], *p011 = pts[3],
         *p100 = pts[4], *p101 = pts[5], *p110 = pts[6], *p111 = pts[7];
                     
   p000[0]=box[0][0];p000[1]=box[0][1];p000[2]=box[0][2];
   p001[0]=box[0][0];p001[1]=box[0][1];p001[2]=box[1][2];
   p010[0]=box[0][0];p010[1]=box[1][1];p010[2]=box[0][2];
   p011[0]=box[0][0];p011[1]=box[1][1];p011[2]=box[1][2];

   p100[0]=box[1][0];p100[1]=box[0][1];p100[2]=box[0][2];
   p101[0]=box[1][0];p101[1]=box[0][1];p101[2]=box[1][2];
   p110[0]=box[1][0];p110[1]=box[1][1];p110[2]=box[0][2];
   p111[0]=box[1][0];p111[1]=box[1][1];p111[2]=box[1][2];

   m4x3_mulv( rb->to_world, p000, p000 );
   m4x3_mulv( rb->to_world, p001, p001 );
   m4x3_mulv( rb->to_world, p010, p010 );
   m4x3_mulv( rb->to_world, p011, p011 );
   m4x3_mulv( rb->to_world, p100, p100 );
   m4x3_mulv( rb->to_world, p101, p101 );
   m4x3_mulv( rb->to_world, p110, p110 );
   m4x3_mulv( rb->to_world, p111, p111 );

   int count = 0;

   for( int i=0; i<8; i++ )
   {
      float *point = pts[i];
      struct contact *ct = rb_start_contact();

      if( !ct )
         return;

      ct->rba = rb;
      
      v3f surface;
      v3_copy( point, surface );
      surface[1] += 4.0f;

      ray_hit hit;
      hit.dist = INFINITY;
      if( !ray_world( surface, (v3f){0.0f,-1.0f,0.0f}, &hit ))
         continue;

      v3_copy( hit.pos, surface );

      float p = vg_minf( surface[1] - point[1], 1.0f );

      if( p > 0.0f )
      {
         v3_copy( hit.normal, ct->n );
         v3_add( point, surface, ct->co );
         v3_muls( ct->co, 0.5f, ct->co );

         rb_commit_contact( ct, p );
         count ++;
         if( count == 4 )
            break;
      }
   }
}

/*
 * Initializing things like tangent vectors
 */

static void rb_presolve_contacts( rb_ct *buffer, int len )
{
   for( int i=0; i<len; i++ )
   {
      rb_ct *ct = &buffer[i];
      ct->bias = -0.2f * k_rb_rate * vg_minf(0.0f,-ct->p+0.04f);
      rb_tangent_basis( ct->n, ct->t[0], ct->t[1] );

      ct->norm_impulse = 0.0f;
      ct->tangent_impulse[0] = 0.0f;
      ct->tangent_impulse[1] = 0.0f;
      ct->mass_total = 1.0f/(ct->rba->inv_mass + ct->rbb->inv_mass);

      rb_debug_contact( ct );
   }
}

/*
 * Creates relative contact velocity vector, and offsets between each body
 */
static void rb_rcv( rb_ct *ct, v3f rv, v3f da, v3f db )
{
   rigidbody *rba = ct->rba,
             *rbb = ct->rbb;

   v3_sub( ct->co, rba->co, da );
   v3_sub( ct->co, rbb->co, db );
   
   v3f rva, rvb;
   v3_cross( rba->w, da, rva );
   v3_add( rba->v, rva, rva );
   v3_cross( rbb->w, db, rvb );
   v3_add( rbb->v, rvb, rvb );

   v3_sub( rva, rvb, rv );
}

/*
 * Apply regular and angular velocity impulses to objects involved in contact
 */
static void rb_standard_impulse( rb_ct *ct, v3f da, v3f db, v3f impulse )
{
   rigidbody *rba = ct->rba,
             *rbb = ct->rbb;

   v3f ia, ib;
   v3_muls( impulse,  ct->mass_total*rba->inv_mass, ia );
   v3_muls( impulse, -ct->mass_total*rbb->inv_mass, ib );

   /* response */
   v3_add( rba->v, ia, rba->v );
   v3_add( rbb->v, ib, rbb->v );
   
   /* Angular velocity */
   v3f wa, wb;
   v3_cross( da, ia, wa );
   v3_cross( db, ib, wb );
   v3_add( rba->w, wa, rba->w );
   v3_add( rbb->w, wb, rbb->w );
}

/*
 * One iteration to solve the contact constraint
 */
static void rb_solve_contacts( rb_ct *buf, int len )
{
   float k_friction = 0.1f;

   /* Friction Impulse */
   for( int i=0; i<len; i++ )
   {
      struct contact *ct = &buf[i];
      rigidbody *rb = ct->rba;

      v3f rv, da, db;
      rb_rcv( ct, rv, da, db );
      
      for( int j=0; j<2; j++ )
      {
         float f = k_friction * ct->norm_impulse,
              vt = -v3_dot( rv, ct->t[j] );
         
         float temp = ct->tangent_impulse[j];
         ct->tangent_impulse[j] = vg_clampf( temp+vt, -f, f );
         vt = ct->tangent_impulse[j] - temp;

         v3f impulse;
         v3_muls( ct->t[j], vt, impulse );
         rb_standard_impulse( ct, da, db, impulse );
      }
   }

   /* Normal Impulse */
   for( int i=0; i<len; i++ )
   {
      struct contact *ct = &buf[i];
      rigidbody *rba = ct->rba,
                *rbb = ct->rbb;

      v3f rv, da, db;
      rb_rcv( ct, rv, da, db );

      float vn = -v3_dot( rv, ct->n ) + ct->bias;

      float temp = ct->norm_impulse;
      ct->norm_impulse = vg_maxf( temp + vn, 0.0f );
      vn = ct->norm_impulse - temp;

      v3f impulse;
      v3_muls( ct->n, vn, impulse );
      rb_standard_impulse( ct, da, db, impulse );
   }
}

/*
 * The following ventures into not really very sophisticated at all maths
 */

struct rb_angle_limit
{
   rigidbody *rba, *rbb;
   v3f axis;
   float impulse, bias;
};

static int rb_angle_limit_force(  rigidbody *rba, v3f va, 
                                  rigidbody *rbb, v3f vb,
                                  float max )
{
   v3f wva, wvb;
   m3x3_mulv( rba->to_world, va, wva );
   m3x3_mulv( rbb->to_world, vb, wvb );

   float dt = v3_dot(wva,wvb)*0.999f,
        ang = fabsf(dt);
   ang = acosf( dt );
   if( ang > max )
   {
      float correction = max-ang;

      v3f axis;
      v3_cross( wva, wvb, axis );
      
      v4f rotation;
      q_axis_angle( rotation, axis, -correction*0.25f );
      q_mul( rotation, rba->q, rba->q );

      q_axis_angle( rotation, axis,  correction*0.25f );
      q_mul( rotation, rbb->q, rbb->q );

      return 1;
   }

   return 0;
}

static void rb_constraint_angle_limit( struct rb_angle_limit *limit )
{

}

RB_DEPR
static void rb_constraint_angle( rigidbody *rba, v3f va,
                                 rigidbody *rbb, v3f vb, 
                                 float max, float spring )
{
   v3f wva, wvb;
   m3x3_mulv( rba->to_world, va, wva );
   m3x3_mulv( rbb->to_world, vb, wvb );

   float dt = v3_dot(wva,wvb)*0.999f,
        ang = fabsf(dt);

   v3f axis;
   v3_cross( wva, wvb, axis );
   v3_muladds( rba->w, axis,  ang*spring*0.5f, rba->w );
   v3_muladds( rbb->w, axis, -ang*spring*0.5f, rbb->w );

   return;
   
   /* TODO: convert max into the dot product value so we dont have to always
    *       evaluate acosf, only if its greater than the angle specified */
   ang = acosf( dt );
   if( ang > max )
   {
      float correction = max-ang;
      
      v4f rotation;
      q_axis_angle( rotation, axis, -correction*0.125f );
      q_mul( rotation, rba->q, rba->q );

      q_axis_angle( rotation, axis,  correction*0.125f );
      q_mul( rotation, rbb->q, rbb->q );
   }
}

static void rb_relative_velocity( rigidbody *ra, v3f lca,
                                  rigidbody *rb, v3f lcb, v3f rcv )
{
   v3f wca, wcb;
   m3x3_mulv( ra->to_world, lca, wca );
   m3x3_mulv( rb->to_world, lcb, wcb );

   v3_sub( ra->v, rb->v, rcv );

   v3f rcv_Ra, rcv_Rb;
   v3_cross( ra->w, wca, rcv_Ra );
   v3_cross( rb->w, wcb, rcv_Rb );
   v3_add( rcv_Ra, rcv, rcv );
   v3_sub( rcv, rcv_Rb, rcv );
}

static void rb_constraint_position( rigidbody *ra, v3f lca,
                                    rigidbody *rb, v3f lcb )
{
   /* C = (COa + Ra*LCa) - (COb + Rb*LCb) = 0 */
   v3f wca, wcb;
   m3x3_mulv( ra->to_world, lca, wca );
   m3x3_mulv( rb->to_world, lcb, wcb );

   v3f delta;
   v3_add( wcb, rb->co, delta );
   v3_sub( delta, wca, delta );
   v3_sub( delta, ra->co, delta );

   v3_muladds( ra->co, delta,  0.5f, ra->co );
   v3_muladds( rb->co, delta, -0.5f, rb->co );

   v3f rcv;
   v3_sub( ra->v, rb->v, rcv );

   v3f rcv_Ra, rcv_Rb;
   v3_cross( ra->w, wca, rcv_Ra );
   v3_cross( rb->w, wcb, rcv_Rb );
   v3_add( rcv_Ra, rcv, rcv );
   v3_sub( rcv, rcv_Rb, rcv );

   float nm = 0.5f/(rb->inv_mass + ra->inv_mass);

   float mass_a = 1.0f/ra->inv_mass,
         mass_b = 1.0f/rb->inv_mass,
         total_mass = mass_a+mass_b;
   
   v3f impulse;
   v3_muls( rcv, 1.0f, impulse );
   v3_muladds( rb->v, impulse, mass_b/total_mass, rb->v );
   v3_cross( wcb, impulse, impulse );
   v3_add( impulse, rb->w, rb->w );

   v3_muls( rcv, -1.0f, impulse );
   v3_muladds( ra->v, impulse, mass_a/total_mass, ra->v );
   v3_cross( wca, impulse, impulse );
   v3_add( impulse, ra->w, ra->w );

#if 0
   /*
    * this could be used for spring joints
    * its not good for position constraint
    */
   v3f impulse;
   v3_muls( delta, 0.5f*spring, impulse );

   v3_add( impulse, ra->v, ra->v );
   v3_cross( wca, impulse, impulse );
   v3_add( impulse, ra->w, ra->w );

   v3_muls( delta, -0.5f*spring, impulse );

   v3_add( impulse, rb->v, rb->v );
   v3_cross( wcb, impulse, impulse );
   v3_add( impulse, rb->w, rb->w );
#endif
}

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 );
   }
}

/*
 * out penetration distance, normal
 */
static int rb_point_in_body( rigidbody *rb, v3f pos, float *pen, v3f normal )
{
   v3f local;
   m4x3_mulv( rb->to_local, pos, local );

   if( local[0] > rb->bbx[0][0] && local[0] < rb->bbx[1][0] &&
       local[1] > rb->bbx[0][1] && local[1] < rb->bbx[1][1] &&
       local[2] > rb->bbx[0][2] && local[2] < rb->bbx[1][2] )
   {
      v3f area, com, comrel;
      v3_add( rb->bbx[0], rb->bbx[1], com );
      v3_muls( com, 0.5f, com );

      v3_sub( rb->bbx[1], rb->bbx[0], area );
      v3_sub( local, com, comrel );
      v3_div( comrel, area, comrel );

      int axis = 0;
      float max_mag = fabsf(comrel[0]);
      
      if( fabsf(comrel[1]) > max_mag )
      {
         axis = 1;
         max_mag = fabsf(comrel[1]);
      }
      if( fabsf(comrel[2]) > max_mag )
      {
         axis = 2;
         max_mag = fabsf(comrel[2]);
      }
      
      v3_zero( normal );
      normal[axis] = vg_signf(comrel[axis]);

      if( normal[axis] < 0.0f )
         *pen = local[axis] - rb->bbx[0][axis];
      else
         *pen = rb->bbx[1][axis] - local[axis];

      m3x3_mulv( rb->to_world, normal, normal );
      return 1;
   }

   return 0;
}

/*
 * BVH implementation, this is ONLY for static rigidbodies, its to slow for
 * realtime use.
 */

static void rb_bh_expand_bound( void *user, boxf bound, u32 item_index )
{
   rigidbody *rb = &((rigidbody *)user)[ item_index ];
   box_concat( bound, rb->bbx_world );
}

static float rb_bh_centroid( void *user, u32 item_index, int axis )
{
   rigidbody *rb = &((rigidbody *)user)[ item_index ];
   return (rb->bbx_world[axis][0] + rb->bbx_world[1][axis]) * 0.5f;
}

static void rb_bh_swap( void *user, u32 ia, u32 ib )
{
   rigidbody temp, *rba, *rbb;
   rba = &((rigidbody *)user)[ ia ];
   rbb = &((rigidbody *)user)[ ib ];

   temp = *rba;
   *rba = *rbb;
   *rbb = temp;
}

static void rb_bh_debug( void *user, u32 item_index )
{
   rigidbody *rb = &((rigidbody *)user)[ item_index ];
   rb_debug( rb, 0xff00ffff );
}

static bh_system bh_system_rigidbodies =
{
   .expand_bound = rb_bh_expand_bound,
   .item_centroid = rb_bh_centroid,
   .item_swap = rb_bh_swap,
   .item_debug = rb_bh_debug,
   .cast_ray = NULL
};

#endif /* RIGIDBODY_H */