LPR - Skating

[carveJwlIkooP6JGAAIwe30JlM.git] / rigidbody.h

/*
 * Copyright (C) 2021-2022 Mt.ZERO Software, Harry Godden - All Rights Reserved
 */

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

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

#include <math.h>

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



#ifndef RIGIDBODY_H
#define RIGIDBODY_H

/*
 * -----------------------------------------------------------------------------
 *                                (K)onstants
 * -----------------------------------------------------------------------------
 */

VG_STATIC const float 
   k_rb_rate          = (1.0/VG_TIMESTEP_FIXED),
   k_rb_delta         = (1.0/k_rb_rate),
   k_friction         = 0.4f,
   k_damp_linear      = 0.1f,               /* scale velocity 1/(1+x) */
   k_damp_angular     = 0.1f,                /* scale angular  1/(1+x) */
   k_penetration_slop = 0.01f,
   k_inertia_scale    = 8.0f,
   k_phys_baumgarte   = 0.2f,
   k_gravity          = 9.6f;

VG_STATIC float
   k_limit_bias       = 0.02f,
   k_joint_correction = 0.01f,
   k_joint_impulse    = 1.0f,
   k_joint_bias       = 0.08f;               /* positional joints */

VG_STATIC void rb_register_cvar(void)
{
   vg_var_push( (struct vg_var){
      .name = "k_limit_bias", .data = &k_limit_bias,
      .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
   });

   vg_var_push( (struct vg_var){
      .name = "k_joint_bias", .data = &k_joint_bias,
      .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
   });

   vg_var_push( (struct vg_var){
      .name = "k_joint_correction", .data = &k_joint_correction,
      .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
   });

   vg_var_push( (struct vg_var){
      .name = "k_joint_impulse", .data = &k_joint_impulse,
      .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
   });
}

/* 
 * -----------------------------------------------------------------------------
 *                           structure definitions
 * -----------------------------------------------------------------------------
 */

typedef struct rigidbody rigidbody;
typedef struct contact rb_ct;
typedef struct rb_sphere rb_sphere;
typedef struct rb_capsule rb_capsule;
typedef struct rb_scene rb_scene;

struct rb_sphere
{
   float radius;
};

struct rb_capsule
{
   float height, radius;
};

struct rb_scene
{
   bh_tree *bh_scene;
};

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 sphere;
      struct rb_capsule capsule;
      struct rb_scene 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;
};

VG_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;

   enum contact_type type;
}
rb_contact_buffer[256];
VG_STATIC int rb_contact_count = 0;

typedef struct rb_constr_pos rb_constr_pos;
typedef struct rb_constr_swingtwist rb_constr_swingtwist;

struct rb_constr_pos
{
   rigidbody *rba, *rbb;
   v3f lca, lcb;
};

struct rb_constr_swingtwist
{
   rigidbody *rba, *rbb;

   v4f conevx, conevy; /* relative to rba */
   v3f view_offset,    /* relative to rba */
       coneva, conevxb;/* relative to rbb */

   int tangent_violation, axis_violation;
   v3f axis, tangent_axis, tangent_target, axis_target;

   float conet;
   float tangent_mass, axis_mass;
};

struct rb_constr_spring
{
   int nothing;
};

/*
 * -----------------------------------------------------------------------------
 *                               Math Utils
 * -----------------------------------------------------------------------------
 */

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

VG_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
 * -----------------------------------------------------------------------------
 */

VG_STATIC void rb_debug_contact( rb_ct *ct )
{
   if( ct->type != k_contact_type_disabled )
   {
      v3f p1;
      v3_muladds( ct->co, ct->n, 0.05f, p1 );
      vg_line_pt3( ct->co, 0.0125f, 0xff0000ff );
      vg_line( ct->co, p1, 0xffffffff );
   }
}

VG_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 );
   }
}

VG_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;
   }
}

VG_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
 */
VG_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
 */
VG_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 );
}

/* 
 * Extrapolate rigidbody into a transform based on vg accumulator.
 * Useful for rendering
 */
VG_STATIC void rb_extrapolate_transform( rigidbody *rb, m4x3f transform )
{
   float substep = vg_clampf( vg.accumulator / k_rb_delta, 0.0f, 1.0f );

   v3f co;
   v4f q;

   v3_muladds( rb->co, rb->v, k_rb_delta*substep, co );

   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*substep );
      q_mul( rotation, rb->q, q );
      q_normalize( q );
   }
   else
   {
      v4_copy( rb->q, q );
   }

   q_m3x3( q, transform );
   v3_copy( co, transform[3] );
}

/*
 * Initialize rigidbody and calculate masses, inertia
 */
VG_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], -r );
      v3_fill( rb->bbx[1],  r );
      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.bh_scene->nodes[0].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 );
}

VG_STATIC void rb_iter( rigidbody *rb )
{
   if( !vg_validf( rb->v[0] ) ||
       !vg_validf( rb->v[1] ) ||
       !vg_validf( rb->v[2] ) )
   {
      vg_fatal_exit_loop( "NaN velocity" );
   }

   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 );
}


/*
 * -----------------------------------------------------------------------------
 *                    Boolean shape overlap functions
 * -----------------------------------------------------------------------------
 */

/* 
 * Project AABB, and triangle interval onto axis to check if they overlap
 */
VG_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
 */
VG_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;
}

/*
 * -----------------------------------------------------------------------------
 *                                Manifold
 * -----------------------------------------------------------------------------
 */

VG_STATIC int rb_manifold_apply_filtered( rb_ct *man, int len )
{
   int k = 0;

   for( int i=0; i<len; i++ )
   {
      rb_ct *ct = &man[i];

      if( ct->type == k_contact_type_disabled )
         continue;

      man[k ++] = man[i];
   }

   return k;
}

/*
 * Merge two contacts if they are within radius(r) of eachother
 */
VG_STATIC void rb_manifold_contact_weld( rb_ct *ci, rb_ct *cj, float r )
{
   if( v3_dist2( ci->co, cj->co ) < r*r )
   {
      cj->type = k_contact_type_disabled;
      ci->p = (ci->p + cj->p) * 0.5f;

      v3_add( ci->co, cj->co, ci->co );
      v3_muls( ci->co, 0.5f, ci->co );

      v3f delta;
      v3_sub( ci->rba->co, ci->co, delta );

      float c0 = v3_dot( ci->n, delta ),
            c1 = v3_dot( cj->n, delta );

      if( c0 < 0.0f || c1 < 0.0f )
      {
         /* error */
         ci->type = k_contact_type_disabled;
      }
      else
      {
         v3f n;
         v3_muls( ci->n, c0, n );
         v3_muladds( n, cj->n, c1, n );
         v3_normalize( n );
         v3_copy( n, ci->n );
      }
   }
}

/*
 * 
 */
VG_STATIC void rb_manifold_filter_joint_edges( rb_ct *man, int len, float r )
{
   for( int i=0; i<len-1; i++ )
   {
      rb_ct *ci = &man[i];
      if( ci->type != k_contact_type_edge ) 
         continue;

      for( int j=i+1; j<len; j++ )
      {
         rb_ct *cj = &man[j];
         if( cj->type != k_contact_type_edge ) 
            continue;
         
         rb_manifold_contact_weld( ci, cj, r );
      }
   }
}

/*
 * Resolve overlapping pairs
 *
 * TODO: Remove?
 */
VG_STATIC void rb_manifold_filter_pairs( rb_ct *man, int len, float r )
{
   for( int i=0; i<len-1; i++ )
   {
      rb_ct *ci = &man[i];
      int similar = 0;

      if( ci->type == k_contact_type_disabled ) continue;

      for( int j=i+1; j<len; j++ )
      {
         rb_ct *cj = &man[j];

         if( cj->type == k_contact_type_disabled ) continue;

         if( v3_dist2( ci->co, cj->co ) < r*r )
         {
            cj->type = k_contact_type_disabled;
            v3_add( cj->n, ci->n, ci->n );
            ci->p += cj->p;
            similar ++;
         }
      }

      if( similar )
      {
         float n = 1.0f/((float)similar+1.0f);
         v3_muls( ci->n, n, ci->n );
         ci->p *= n;

         if( v3_length2(ci->n) < 0.1f*0.1f )
            ci->type = k_contact_type_disabled;
         else
            v3_normalize( ci->n );
      }
   }
}

/* 
 * Remove contacts that are facing away from A
 */
VG_STATIC void rb_manifold_filter_backface( rb_ct *man, int len )
{
   for( int i=0; i<len; i++ )
   {
      rb_ct *ct = &man[i];
      if( ct->type == k_contact_type_disabled ) 
         continue;

      v3f delta;
      v3_sub( ct->co, ct->rba->co, delta );
      
      if( v3_dot( delta, ct->n ) > -0.001f )
         ct->type = k_contact_type_disabled;
   }
}

/*
 * Filter out duplicate coplanar results. Good for spheres.
 */
VG_STATIC void rb_manifold_filter_coplanar( rb_ct *man, int len, float w )
{
   for( int i=0; i<len; i++ )
   {
      rb_ct *ci = &man[i];
      if( ci->type == k_contact_type_disabled ||
          ci->type == k_contact_type_edge ) 
         continue;

      float d1 = v3_dot( ci->co, ci->n );

      for( int j=0; j<len; j++ )
      {
         if( j == i )
            continue;

         rb_ct *cj = &man[j];
         if( cj->type == k_contact_type_disabled ) 
            continue;
         
         float d2 = v3_dot( cj->co, ci->n ),
               d  = d2-d1;

         if( fabsf( d ) <= w )
         {
            cj->type = k_contact_type_disabled;
         }
      }
   }
}

/*
 * -----------------------------------------------------------------------------
 *                            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.
 */
VG_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;
      }
   }
}

VG_STATIC void rb_capsule_manifold_init( capsule_manifold *manifold )
{
   manifold->t0 =  INFINITY;
   manifold->t1 = -INFINITY;
}

__attribute__ ((deprecated))
VG_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;
      ct->type = k_contact_type_default;

      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;
      ct->type = k_contact_type_default;

      count ++;
   }

   /*
    * Debugging
    */

   if( count == 2 )
      vg_line( buf[0].co, buf[1].co, 0xff0000ff );

   return count;
}

VG_STATIC int rb_capsule__manifold_done( m4x3f mtx, rb_capsule *c,
                                         capsule_manifold *manifold,
                                         rb_ct *buf )
{
   v3f p0, p1;
   v3_muladds( mtx[3], mtx[1], -c->height*0.5f+c->radius, p0 );
   v3_muladds( mtx[3], mtx[1],  c->height*0.5f-c->radius, 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, -c->radius, ct->co );

      ct->p = manifold->r0 - d;
      ct->type = k_contact_type_default;
      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, -c->radius, ct->co );

      ct->p = manifold->r1 - d;
      ct->type = k_contact_type_default;

      count ++;
   }

   /*
    * Debugging
    */

   if( count == 2 )
      vg_line( buf[0].co, buf[1].co, 0xff0000ff );

   return count;
}

VG_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;
      ct->type = k_contact_type_default;

      return 1;
   }

   return 0;
}

VG_STATIC int rb_capsule_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   if( !box_overlap( rba->bbx_world, rbb->bbx_world ) )
      return 0;

   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
 */
VG_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 );
   
   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 );
}

VG_STATIC int rb_sphere_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   v3f co, delta;

   closest_point_obb( rba->co, rbb->bbx, rbb->to_world, rbb->to_local, 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;
      ct->type = k_contact_type_default;
      return 1;
   }

   return 0;
}

VG_STATIC int rb_sphere_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->type = k_contact_type_default;
      ct->p = r-d;
      ct->rba = rba;
      ct->rbb = rbb;
      return 1;
   }

   return 0;
}

//#define RIGIDBODY_DYNAMIC_MESH_EDGES

__attribute__ ((deprecated))
VG_STATIC int rb_sphere_triangle( rigidbody *rba, rigidbody *rbb, 
                                  v3f tri[3], rb_ct *buf )
{
   v3f delta, co;

#ifdef RIGIDBODY_DYNAMIC_MESH_EDGES
   closest_on_triangle_1( rba->co, tri, co );
#else
   enum contact_type type = closest_on_triangle_1( rba->co, tri, co );
#endif

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

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

   if( d2 < r*r )
   {
      rb_ct *ct = buf;

      v3f ab, ac, tn;
      v3_sub( tri[2], tri[0], ab );
      v3_sub( tri[1], tri[0], ac );
      v3_cross( ac, ab, tn );
      v3_copy( tn, ct->n );

      if( v3_length2( ct->n ) <= 0.00001f )
      {
         vg_error( "Zero area triangle!\n" );
         return 0;
      }

      v3_normalize( ct->n );

      float d = sqrtf(d2);

      v3_copy( co, ct->co );
      ct->type = type;
      ct->p = r-d;
      ct->rba = rba;
      ct->rbb = rbb;
      return 1;
   }

   return 0;
}

VG_STATIC int rb_sphere__triangle( m4x3f mtxA, rb_sphere *b,
                                   v3f tri[3], rb_ct *buf )
{
   v3f delta, co;
   enum contact_type type = closest_on_triangle_1( mtxA[3], tri, co );

   v3_sub( mtxA[3], co, delta );

   float d2 = v3_length2( delta ),
          r = b->radius;

   if( d2 < r*r )
   {
      rb_ct *ct = buf;

      v3f ab, ac, tn;
      v3_sub( tri[2], tri[0], ab );
      v3_sub( tri[1], tri[0], ac );
      v3_cross( ac, ab, tn );
      v3_copy( tn, ct->n );

      if( v3_length2( ct->n ) <= 0.00001f )
      {
         vg_error( "Zero area triangle!\n" );
         return 0;
      }

      v3_normalize( ct->n );

      float d = sqrtf(d2);

      v3_copy( co, ct->co );
      ct->type = type;
      ct->p = r-d;
      return 1;
   }

   return 0;
}

VG_STATIC void rb_debug_sharp_scene_edges( rigidbody *rbb, float sharp_ang,
                                           boxf box, u32 colour )
{
   sharp_ang = cosf( sharp_ang );

   scene *sc = rbb->inf.scene.bh_scene->user;
   vg_line_boxf( box, 0xff00ff00 );

   bh_iter it;
   bh_iter_init( 0, &it );
   int idx;
   
   while( bh_next( rbb->inf.scene.bh_scene, &it, box, &idx ) )
   {
      u32 *ptri = &sc->arrindices[ idx*3 ];
      v3f tri[3];

      for( int j=0; j<3; j++ )
         v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );

      for( int j=0; j<3; j++ )
      {
#if 0
         v3f edir;
         v3_sub( tri[(j+1)%3], tri[j], edir );

         if( v3_dot( edir, (v3f){ 0.5184758473652127f,
                                  0.2073903389460850f,
                                 -0.8295613557843402f } ) < 0.0f )
            continue;
#endif

         bh_iter jt;
         bh_iter_init( 0, &jt );

         boxf region;
         float const k_r = 0.02f;
         v3_add( (v3f){  k_r,  k_r,  k_r }, tri[j], region[1] );
         v3_add( (v3f){ -k_r, -k_r, -k_r }, tri[j], region[0] );

         int jdx;
         while( bh_next( rbb->inf.scene.bh_scene, &jt, region, &jdx ) )
         {
            if( idx <= jdx )
               continue;

            u32 *ptrj = &sc->arrindices[ jdx*3 ];
            v3f trj[3];

            for( int k=0; k<3; k++ )
               v3_copy( sc->arrvertices[ptrj[k]].co, trj[k] );

            for( int k=0; k<3; k++ )
            {
               if( v3_dist2( tri[j], trj[k] ) <= k_r*k_r )
               {
                  int jp1 = (j+1)%3,
                      jp2 = (j+2)%3,
                      km1 = (k+3-1)%3,
                      km2 = (k+3-2)%3;

                  if( v3_dist2( tri[jp1], trj[km1] ) <= k_r*k_r )
                  {
                     v3f b0, b1, b2;
                     v3_sub( tri[jp1], tri[j], b0 );
                     v3_sub( tri[jp2], tri[j], b1 );
                     v3_sub( trj[km2], tri[j], b2 );

                     v3f cx0, cx1;
                     v3_cross( b0, b1, cx0 );
                     v3_cross( b2, b0, cx1 );

                     float polarity = v3_dot( cx0, b2 );

                     if( polarity < 0.0f )
                     {
#if 0
                        vg_line( tri[j], tri[jp1], 0xff00ff00 );
                        float ang = v3_dot(cx0,cx1) / 
                                       (v3_length(cx0)*v3_length(cx1));
                        if( ang < sharp_ang )
                        {
                           vg_line( tri[j], tri[jp1], 0xff00ff00 );
                        }
#endif
                     }
                  }
               }
            }
         }
      }
   }
}

VG_STATIC int rb_sphere__scene( m4x3f mtxA, rb_sphere *b,
                                m4x3f mtxB, rb_scene *s, rb_ct *buf )
{
   scene *sc = s->bh_scene->user;

   bh_iter it;
   bh_iter_init( 0, &it );
   int idx;

   int count = 0;

   float r = b->radius;
   boxf box;
   v3_sub( mtxA[3], (v3f){ r,r,r }, box[0] );
   v3_add( mtxA[3], (v3f){ r,r,r }, box[1] );
   
   while( bh_next( s->bh_scene, &it, box, &idx ) )
   {
      u32 *ptri = &sc->arrindices[ idx*3 ];
      v3f tri[3];

      for( int j=0; j<3; j++ )
         v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
      
      buf[ count ].element_id = ptri[0];

      vg_line( tri[0],tri[1],0x70ff6000 );
      vg_line( tri[1],tri[2],0x70ff6000 );
      vg_line( tri[2],tri[0],0x70ff6000 );

      int contact = rb_sphere__triangle( mtxA, b, tri, &buf[count] );
      count += contact;

      if( count == 16 )
      {
         vg_warn( "Exceeding sphere_vs_scene capacity. Geometry too dense!\n" );
         return count;
      }
   }

   return count;
}

__attribute__ ((deprecated))
VG_STATIC int rb_sphere_scene( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   scene *sc = rbb->inf.scene.bh_scene->user;

   bh_iter it;
   bh_iter_init( 0, &it );
   int idx;

   int count = 0;
   
   while( bh_next( rbb->inf.scene.bh_scene, &it, rba->bbx_world, &idx ) )
   {
      u32 *ptri = &sc->arrindices[ idx*3 ];
      v3f tri[3];

      for( int j=0; j<3; j++ )
         v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
      
      buf[ count ].element_id = ptri[0];

      vg_line( tri[0],tri[1],0x70ff6000 );
      vg_line( tri[1],tri[2],0x70ff6000 );
      vg_line( tri[2],tri[0],0x70ff6000 );

      int contact = rb_sphere_triangle( rba, rbb, tri, buf+count );
      count += contact;

      if( count == 16 )
      {
         vg_warn( "Exceeding sphere_vs_scene capacity. Geometry too dense!\n" );
         return count;
      }
   }

   return count;
}

VG_STATIC int rb_box_scene( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   scene *sc = rbb->inf.scene.bh_scene->user;
   
   v3f tri[3];

   bh_iter it;
   bh_iter_init( 0, &it );
   int idx;

   int count = 0;
   
   while( bh_next( rbb->inf.scene.bh_scene, &it, rba->bbx_world, &idx ) )
   {
      u32 *ptri = &sc->arrindices[ idx*3 ];

      for( int j=0; j<3; j++ )
         v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );

      if( rb_box_triangle_sat( rba, tri ) )
      {
         vg_line(tri[0],tri[1],0xff50ff00 );
         vg_line(tri[1],tri[2],0xff50ff00 );
         vg_line(tri[2],tri[0],0xff50ff00 );
      }
      else
      {
         vg_line(tri[0],tri[1],0xff0000ff );
         vg_line(tri[1],tri[2],0xff0000ff );
         vg_line(tri[2],tri[0],0xff0000ff );

         continue;
      }

      v3f v0,v1,n;
      v3_sub( tri[1], tri[0], v0 );
      v3_sub( tri[2], tri[0], v1 );
      v3_cross( v0, v1, n );
      v3_normalize( n );

      /* find best feature */
      float best = v3_dot( rba->right, n );
      int axis = 0;
      
      float cy = v3_dot( rba->up, n );
      if( fabsf(cy) > fabsf(best) )
      {
         best = cy;
         axis = 1;
      }
      
      float cz = -v3_dot( rba->forward, n );
      if( fabsf(cz) > fabsf(best) )
      {
         best = cz;
         axis = 2;
      }

      v3f manifold[4];

      if( axis == 0 )
      {
         float px = best > 0.0f? rba->bbx[0][0]: rba->bbx[1][0];
         manifold[0][0] = px;
         manifold[0][1] = rba->bbx[0][1];
         manifold[0][2] = rba->bbx[0][2];
         manifold[1][0] = px;
         manifold[1][1] = rba->bbx[1][1];
         manifold[1][2] = rba->bbx[0][2];
         manifold[2][0] = px;
         manifold[2][1] = rba->bbx[1][1];
         manifold[2][2] = rba->bbx[1][2];
         manifold[3][0] = px;
         manifold[3][1] = rba->bbx[0][1];
         manifold[3][2] = rba->bbx[1][2];
      }
      else if( axis == 1 )
      {
         float py = best > 0.0f? rba->bbx[0][1]: rba->bbx[1][1];
         manifold[0][0] = rba->bbx[0][0];
         manifold[0][1] = py;
         manifold[0][2] = rba->bbx[0][2];
         manifold[1][0] = rba->bbx[1][0];
         manifold[1][1] = py;
         manifold[1][2] = rba->bbx[0][2];
         manifold[2][0] = rba->bbx[1][0];
         manifold[2][1] = py;
         manifold[2][2] = rba->bbx[1][2];
         manifold[3][0] = rba->bbx[0][0];
         manifold[3][1] = py;
         manifold[3][2] = rba->bbx[1][2];
      }
      else
      {
         float pz = best > 0.0f? rba->bbx[0][2]: rba->bbx[1][2];
         manifold[0][0] = rba->bbx[0][0];
         manifold[0][1] = rba->bbx[0][1];
         manifold[0][2] = pz;
         manifold[1][0] = rba->bbx[1][0];
         manifold[1][1] = rba->bbx[0][1];
         manifold[1][2] = pz;
         manifold[2][0] = rba->bbx[1][0];
         manifold[2][1] = rba->bbx[1][1];
         manifold[2][2] = pz;
         manifold[3][0] = rba->bbx[0][0];
         manifold[3][1] = rba->bbx[1][1];
         manifold[3][2] = pz;
      }
   
      for( int j=0; j<4; j++ )
         m4x3_mulv( rba->to_world, manifold[j], manifold[j] );

      vg_line( manifold[0], manifold[1], 0xffffffff );
      vg_line( manifold[1], manifold[2], 0xffffffff );
      vg_line( manifold[2], manifold[3], 0xffffffff );
      vg_line( manifold[3], manifold[0], 0xffffffff );

      for( int j=0; j<4; j++ )
      {
         rb_ct *ct = buf+count;

         v3_copy( manifold[j], ct->co );
         v3_copy( n, ct->n );

         float l0 = v3_dot( tri[0], n ),
               l1 = v3_dot( manifold[j], n );

         ct->p = (l0-l1)*0.5f;
         if( ct->p < 0.0f )
            continue;

         ct->type = k_contact_type_default;
         ct->rba = rba;
         ct->rbb = rbb;
         count ++;

         if( count >= 12 )
            return count;
      }
   }
   return count;
}

VG_STATIC int rb_capsule__triangle( m4x3f mtxA, rb_capsule *c,
                                    v3f tri[3], rb_ct *buf )
{
   v3f pc, p0w, p1w;
   v3_muladds( mtxA[3], mtxA[1], -c->height*0.5f+c->radius, p0w );
   v3_muladds( mtxA[3], mtxA[1],  c->height*0.5f-c->radius, p1w );

   capsule_manifold manifold;
   rb_capsule_manifold_init( &manifold );
   
   v3f c0, c1;
   closest_on_triangle_1( p0w, tri, c0 );
   closest_on_triangle_1( p1w, tri, c1 );

   v3f d0, d1, da;
   v3_sub( c0, p0w, d0 );
   v3_sub( c1, p1w, d1 );
   v3_sub( p1w, p0w, da );
   
   v3_normalize(d0);
   v3_normalize(d1);
   v3_normalize(da);

   if( v3_dot( da, d0 ) <= 0.01f )
      rb_capsule_manifold( p0w, c0, 0.0f, c->radius, &manifold );

   if( v3_dot( da, d1 ) >= -0.01f )
      rb_capsule_manifold( p1w, c1, 1.0f, c->radius, &manifold );

   for( int i=0; i<3; i++ )
   {
      int i0 = i,
          i1 = (i+1)%3;

      v3f ca, cb;
      float ta, tb;
      closest_segment_segment( p0w, p1w, tri[i0], tri[i1], &ta, &tb, ca, cb );
      rb_capsule_manifold( ca, cb, ta, c->radius, &manifold );
   }

   v3f v0, v1, n;
   v3_sub( tri[1], tri[0], v0 );
   v3_sub( tri[2], tri[0], v1 );
   v3_cross( v0, v1, n );
   v3_normalize( n );

   int count = rb_capsule__manifold_done( mtxA, c, &manifold, buf );
   for( int i=0; i<count; i++ )
      v3_copy( n, buf[i].n );

   return count;
}

/*
 * Generates up to two contacts; optimised for the most stable manifold
 */
__attribute__ ((deprecated))
VG_STATIC int rb_capsule_triangle( rigidbody *rba, rigidbody *rbb, 
                                   v3f tri[3], rb_ct *buf )
{
   float h = rba->inf.capsule.height,
         r = rba->inf.capsule.radius;
   
   v3f pc, p0w, p1w;
   v3_muladds( rba->co, rba->up, -h*0.5f+r, p0w );
   v3_muladds( rba->co, rba->up,  h*0.5f-r, p1w );

   capsule_manifold manifold;
   rb_capsule_manifold_init( &manifold );
   
   v3f c0, c1;
   closest_on_triangle_1( p0w, tri, c0 );
   closest_on_triangle_1( p1w, tri, c1 );

   v3f d0, d1, da;
   v3_sub( c0, p0w, d0 );
   v3_sub( c1, p1w, d1 );
   v3_sub( p1w, p0w, da );
   
   v3_normalize(d0);
   v3_normalize(d1);
   v3_normalize(da);

   if( v3_dot( da, d0 ) <= 0.01f )
      rb_capsule_manifold( p0w, c0, 0.0f, r, &manifold );

   if( v3_dot( da, d1 ) >= -0.01f )
      rb_capsule_manifold( p1w, c1, 1.0f, r, &manifold );

   for( int i=0; i<3; i++ )
   {
      int i0 = i,
          i1 = (i+1)%3;

      v3f ca, cb;
      float ta, tb;
      closest_segment_segment( p0w, p1w, tri[i0], tri[i1], &ta, &tb, ca, cb );
      rb_capsule_manifold( ca, cb, ta, r, &manifold );
   }

   v3f v0, v1, n;
   v3_sub( tri[1], tri[0], v0 );
   v3_sub( tri[2], tri[0], v1 );
   v3_cross( v0, v1, n );
   v3_normalize( n );

   int count = rb_capsule_manifold_done( rba, rbb, &manifold, buf );
   for( int i=0; i<count; i++ )
      v3_copy( n, buf[i].n );

   return count;
}

/* mtxB is defined only for tradition; it is not used currently */
VG_STATIC int rb_capsule__scene( m4x3f mtxA, rb_capsule *c,
                                 m4x3f mtxB, rb_scene *s, 
                                 rb_ct *buf )
{
   bh_iter it;
   bh_iter_init( 0, &it );
   int idx;
   int count = 0;

   boxf bbx;
   v3_sub( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[0] );
   v3_add( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[1] );
   
   scene *sc = s->bh_scene->user;
   
   while( bh_next( s->bh_scene, &it, bbx, &idx ) )
   {
      u32 *ptri = &sc->arrindices[ idx*3 ];
      v3f tri[3];

      for( int j=0; j<3; j++ )
         v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
      
      buf[ count ].element_id = ptri[0];

      int contact = rb_capsule__triangle( mtxA, c, tri, &buf[count] );
      count += contact;

      if( count == 16 )
      {
         vg_warn("Exceeding capsule_vs_scene capacity. Geometry too dense!\n");
         return count;
      }
   }

   return count;
}

__attribute__ ((deprecated))
VG_STATIC int rb_capsule_scene( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   scene *sc = rbb->inf.scene.bh_scene->user;

   bh_iter it;
   bh_iter_init( 0, &it );
   int idx;

   int count = 0;
   
   while( bh_next( rbb->inf.scene.bh_scene, &it, rba->bbx_world, &idx ) )
   {
      u32 *ptri = &sc->arrindices[ idx*3 ];
      v3f tri[3];

      for( int j=0; j<3; j++ )
         v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
      
      buf[ count ].element_id = ptri[0];

#if 0
      vg_line( tri[0],tri[1],0x70ff6000 );
      vg_line( tri[1],tri[2],0x70ff6000 );
      vg_line( tri[2],tri[0],0x70ff6000 );
#endif

      int contact = rb_capsule_triangle( rba, rbb, tri, buf+count );
      count += contact;

      if( count == 16 )
      {
         vg_warn("Exceeding capsule_vs_scene capacity. Geometry too dense!\n");
         return count;
      }
   }

   return count;
}

VG_STATIC int rb_scene_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_capsule_scene( rbb, rba, buf );
}

VG_STATIC int RB_MATRIX_ERROR( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
#if 0
   vg_error( "Collision type is unimplemented between types %d and %d\n",
             rba->type, rbb->type );
#endif

   return 0;
}

VG_STATIC int rb_sphere_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_capsule_sphere( rbb, rba, buf );
}

VG_STATIC int rb_box_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_capsule_box( rbb, rba, buf );
}

VG_STATIC int rb_box_sphere( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_sphere_box( rbb, rba, buf );
}

VG_STATIC int rb_scene_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
{
   return rb_box_scene( rbb, rba, buf );
}

VG_STATIC int (*rb_jump_table[4][4])( rigidbody *a, rigidbody *b, rb_ct *buf ) = 
{
    /* box */        /* Sphere */       /* Capsule */       /* Mesh */
  { RB_MATRIX_ERROR, rb_box_sphere,     rb_box_capsule,     rb_box_scene    },
  { rb_sphere_box,   rb_sphere_sphere,  rb_sphere_capsule,  rb_sphere_scene },
  { rb_capsule_box,  rb_capsule_sphere, rb_capsule_capsule, rb_capsule_scene },
  { rb_scene_box,    RB_MATRIX_ERROR,   rb_scene_capsule,   RB_MATRIX_ERROR }
};

VG_STATIC int rb_collide( rigidbody *rba, rigidbody *rbb )
{
   int (*collider_jump)(rigidbody *rba, rigidbody *rbb, rb_ct *buf ) 
      = rb_jump_table[rba->type][rbb->type];

   /* 
    * 12 is the maximum manifold size we can generate, so we are forced to abort
    * potentially checking any more.
    */
   if( rb_contact_count + 12 > vg_list_size(rb_contact_buffer) )
   {
      vg_warn( "Too many contacts made in global collider buffer (%d of %d\n)",
               rb_contact_count, vg_list_size(rb_contact_buffer) );
      return 0;
   }

   /*
    * FUTURE: Replace this with a more dedicated broad phase pass
    */
   if( box_overlap( rba->bbx_world, rbb->bbx_world ) )
   {
      int count = collider_jump( rba, rbb, rb_contact_buffer+rb_contact_count); 
      rb_contact_count += count;
      return count;
   }
   else
      return 0;
}

/*
 * -----------------------------------------------------------------------------
 *                                Dynamics
 * -----------------------------------------------------------------------------
 */

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

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

VG_STATIC void rb_prepare_contact( rb_ct *ct )
{
   ct->bias = -0.2f * k_rb_rate * vg_minf( 0.0f, -ct->p+k_penetration_slop );
   rb_tangent_basis( ct->n, ct->t[0], ct->t[1] );

#if 0
   ct->type = k_contact_type_default;
#endif
   ct->norm_impulse = 0.0f;
   ct->tangent_impulse[0] = 0.0f;
   ct->tangent_impulse[1] = 0.0f;
}

/*
 * Initializing things like tangent vectors
 */
VG_STATIC void rb_presolve_contacts( rb_ct *buffer, int len )
{
   for( int i=0; i<len; i++ )
   {
      rb_ct *ct = &buffer[i];
      rb_prepare_contact( ct );

      v3f ra, rb, raCn, rbCn, raCt, rbCt;
      v3_sub( ct->co, ct->rba->co, ra );
      v3_sub( ct->co, ct->rbb->co, rb );
      v3_cross( ra, ct->n, raCn );
      v3_cross( rb, ct->n, rbCn );
      
      /* orient inverse inertia tensors */
      v3f raCnI, rbCnI;
      m3x3_mulv( ct->rba->iIw, raCn, raCnI );
      m3x3_mulv( ct->rbb->iIw, rbCn, rbCnI );

      ct->normal_mass  = ct->rba->inv_mass + ct->rbb->inv_mass;
      ct->normal_mass += v3_dot( raCn, raCnI );
      ct->normal_mass += v3_dot( rbCn, rbCnI );
      ct->normal_mass  = 1.0f/ct->normal_mass;

      for( int j=0; j<2; j++ )
      {
         v3f raCtI, rbCtI;
         v3_cross( ct->t[j], ra, raCt );
         v3_cross( ct->t[j], rb, rbCt );
         m3x3_mulv( ct->rba->iIw, raCt, raCtI );
         m3x3_mulv( ct->rbb->iIw, rbCt, rbCtI );
         
         ct->tangent_mass[j]  = ct->rba->inv_mass + ct->rbb->inv_mass;
         ct->tangent_mass[j] += v3_dot( raCt, raCtI );
         ct->tangent_mass[j] += v3_dot( rbCt, rbCtI );
         ct->tangent_mass[j]  = 1.0f/ct->tangent_mass[j];
      }

      rb_debug_contact( ct );
   }
}

/*
 * Creates relative contact velocity vector
 */
VG_STATIC void rb_rcv( rigidbody *rba, rigidbody *rbb, v3f ra, v3f rb, v3f rv )
{
   v3f rva, rvb;
   v3_cross( rba->w, ra, rva );
   v3_add(   rba->v, rva, rva );
   v3_cross( rbb->w, rb, rvb );
   v3_add(   rbb->v, rvb, rvb );

   v3_sub( rva, rvb, rv );
}

/*
 * Apply impulse to object
 */
VG_STATIC void rb_linear_impulse( rigidbody *rb, v3f delta, v3f impulse )
{
   /* linear */
   v3_muladds( rb->v, impulse,  rb->inv_mass, rb->v );
   
   /* Angular velocity */
   v3f wa;
   v3_cross( delta, impulse, wa );

   m3x3_mulv( rb->iIw, wa, wa );
   v3_add( rb->w, wa, rb->w );
}

/*
 * One iteration to solve the contact constraint
 */
VG_STATIC void rb_solve_contacts( rb_ct *buf, int len )
{
   for( int i=0; i<len; i++ )
   {
      struct contact *ct = &buf[i];

      v3f rv, ra, rb;
      v3_sub( ct->co, ct->rba->co, ra );
      v3_sub( ct->co, ct->rbb->co, rb );
      rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
      
      /* Friction */
      for( int j=0; j<2; j++ )
      {
         float     f = k_friction * ct->norm_impulse,
                  vt = v3_dot( rv, ct->t[j] ),
              lambda = ct->tangent_mass[j] * -vt;
         
         float temp = ct->tangent_impulse[j];
         ct->tangent_impulse[j] = vg_clampf( temp + lambda, -f, f );
         lambda = ct->tangent_impulse[j] - temp;

         v3f impulse;
         v3_muls( ct->t[j],  lambda, impulse );
         rb_linear_impulse( ct->rba, ra, impulse );
         
         v3_muls( ct->t[j], -lambda, impulse );
         rb_linear_impulse( ct->rbb, rb, impulse );
      }

      /* Normal */
      rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
      float     vn = v3_dot( rv, ct->n ),
            lambda = ct->normal_mass * (-vn + ct->bias);

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

      v3f impulse;
      v3_muls( ct->n,  lambda, impulse );
      rb_linear_impulse( ct->rba, ra, impulse );

      v3_muls( ct->n, -lambda, impulse );
      rb_linear_impulse( ct->rbb, rb, impulse );
   }
}

/*
 * -----------------------------------------------------------------------------
 *                               Constraints
 * -----------------------------------------------------------------------------
 */

VG_STATIC void rb_debug_position_constraints( rb_constr_pos *buffer, int len )
{
   for( int i=0; i<len; i++ )
   {
      rb_constr_pos *constr = &buffer[i];
      rigidbody *rba = constr->rba, *rbb = constr->rbb;

      v3f wca, wcb;
      m3x3_mulv( rba->to_world, constr->lca, wca );
      m3x3_mulv( rbb->to_world, constr->lcb, wcb );

      v3f p0, p1;
      v3_add( wca, rba->co, p0 );
      v3_add( wcb, rbb->co, p1 );
      vg_line_pt3( p0, 0.0025f, 0xff000000 );
      vg_line_pt3( p1, 0.0025f, 0xffffffff );
      vg_line2( p0, p1, 0xff000000, 0xffffffff );
   }
}

VG_STATIC void rb_presolve_swingtwist_constraints( rb_constr_swingtwist *buf,
                                                   int len )
{
   float size = 0.12f;

   for( int i=0; i<len; i++ )
   {
      rb_constr_swingtwist *st = &buf[ i ];
      
      v3f vx, vy, va, vxb, axis, center;

      m3x3_mulv( st->rba->to_world, st->conevx, vx );
      m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
      m3x3_mulv( st->rba->to_world, st->conevy, vy );
      m3x3_mulv( st->rbb->to_world, st->coneva, va );
      m4x3_mulv( st->rba->to_world, st->view_offset, center );
      v3_cross( vy, vx, axis );

      /* Constraint violated ? */
      float fx = v3_dot( vx, va ),     /* projection world */
            fy = v3_dot( vy, va ),
            fn = v3_dot( va, axis ),

            rx = st->conevx[3],        /* elipse radii */
            ry = st->conevy[3],

            lx = fx/rx,                /* projection local (fn==lz) */
            ly = fy/ry;

      st->tangent_violation = ((lx*lx + ly*ly) > fn*fn) || (fn <= 0.0f);
      if( st->tangent_violation )
      {
         /* Calculate a good position and the axis to solve on */
         v2f closest, tangent, 
             p = { fx/fabsf(fn), fy/fabsf(fn) };

         closest_point_elipse( p, (v2f){rx,ry}, closest );
         tangent[0] = -closest[1] / (ry*ry);
         tangent[1] =  closest[0] / (rx*rx);
         v2_normalize( tangent );

         v3f v0, v1;
         v3_muladds( axis, vx, closest[0], v0 );
         v3_muladds( v0, vy, closest[1], v0 );
         v3_normalize( v0 );

         v3_muls( vx, tangent[0], v1 );
         v3_muladds( v1, vy, tangent[1], v1 );

         v3_copy( v0, st->tangent_target );
         v3_copy( v1, st->tangent_axis );

         /* calculate mass */
         v3f aIw, bIw;
         m3x3_mulv( st->rba->iIw, st->tangent_axis, aIw );
         m3x3_mulv( st->rbb->iIw, st->tangent_axis, bIw );
         st->tangent_mass = 1.0f / (v3_dot( st->tangent_axis, aIw ) +
                                    v3_dot( st->tangent_axis, bIw ));

         float angle = v3_dot( va, st->tangent_target );
      }

      v3f refaxis;
      v3_cross( vy, va, refaxis );  /* our default rotation */
      v3_normalize( refaxis );

      float angle = v3_dot( refaxis, vxb );
      st->axis_violation = fabsf(angle) < st->conet;

      if( st->axis_violation )
      {
         v3f dir_test;
         v3_cross( refaxis, vxb, dir_test );

         if( v3_dot(dir_test, va) < 0.0f )
            st->axis_violation = -st->axis_violation;

         float newang = (float)st->axis_violation * acosf(st->conet-0.0001f);

         v3f refaxis_up;
         v3_cross( va, refaxis, refaxis_up );
         v3_muls( refaxis_up, sinf(newang), st->axis_target );
         v3_muladds( st->axis_target, refaxis, -cosf(newang), st->axis_target );

         /* calculate mass */
         v3_copy( va, st->axis );
         v3f aIw, bIw;
         m3x3_mulv( st->rba->iIw, st->axis, aIw );
         m3x3_mulv( st->rbb->iIw, st->axis, bIw );
         st->axis_mass = 1.0f / (v3_dot( st->axis, aIw ) +
                                 v3_dot( st->axis, bIw ));
      }
   }
}

VG_STATIC void rb_debug_swingtwist_constraints( rb_constr_swingtwist *buf, 
                                                int len )
{
   float size = 0.12f;

   for( int i=0; i<len; i++ )
   {
      rb_constr_swingtwist *st = &buf[ i ];
      
      v3f vx, vxb, vy, va, axis, center;

      m3x3_mulv( st->rba->to_world, st->conevx, vx );
      m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
      m3x3_mulv( st->rba->to_world, st->conevy, vy );
      m3x3_mulv( st->rbb->to_world, st->coneva, va );
      m4x3_mulv( st->rba->to_world, st->view_offset, center );
      v3_cross( vy, vx, axis );

      float rx = st->conevx[3],        /* elipse radii */
            ry = st->conevy[3];

      v3f p0, p1;
      v3_muladds( center, va, size, p1 );
      vg_line( center, p1, 0xffffffff );
      vg_line_pt3( p1, 0.00025f, 0xffffffff );

      if( st->tangent_violation )
      {
         v3_muladds( center, st->tangent_target, size, p0 );

         vg_line( center, p0, 0xff00ff00 );
         vg_line_pt3( p0, 0.00025f, 0xff00ff00 );
         vg_line( p1, p0, 0xff000000 );
      }
      
      for( int x=0; x<32; x++ )
      {
         float t0 = ((float)x * (1.0f/32.0f)) * VG_TAUf,
               t1 = (((float)x+1.0f) * (1.0f/32.0f)) * VG_TAUf,
               c0 = cosf( t0 ),
               s0 = sinf( t0 ),
               c1 = cosf( t1 ),
               s1 = sinf( t1 );

         v3f v0, v1;
         v3_muladds( axis, vx, c0*rx, v0 );
         v3_muladds( v0,   vy, s0*ry, v0 );
         v3_muladds( axis, vx, c1*rx, v1 );
         v3_muladds( v1,   vy, s1*ry, v1 );

         v3_normalize( v0 );
         v3_normalize( v1 );

         v3_muladds( center, v0, size, p0 );
         v3_muladds( center, v1, size, p1 );

         u32 col0r = fabsf(c0) * 255.0f,
             col0g = fabsf(s0) * 255.0f,
             col1r = fabsf(c1) * 255.0f,
             col1g = fabsf(s1) * 255.0f,
             col   = st->tangent_violation? 0xff0000ff: 0xff000000,
             col0  = col | (col0r<<16) | (col0g << 8),
             col1  = col | (col1r<<16) | (col1g << 8);

         vg_line2( center, p0, VG__NONE, col0 );
         vg_line2( p0, p1, col0, col1 );
      }

      /* Draw twist */
      v3_muladds( center, va, size, p0 );
      v3_muladds( p0, vxb, size, p1 );

      vg_line( p0, p1, 0xff0000ff );

      if( st->axis_violation )
      {
         v3_muladds( p0, st->axis_target, size*1.25f, p1 );
         vg_line( p0, p1, 0xffffff00 );
         vg_line_pt3( p1, 0.0025f, 0xffffff80 );
      }

      v3f refaxis;
      v3_cross( vy, va, refaxis );  /* our default rotation */
      v3_normalize( refaxis );
      v3f refaxis_up;
      v3_cross( va, refaxis, refaxis_up );
      float newang = acosf(st->conet-0.0001f);

      v3_muladds( p0, refaxis_up, sinf(newang)*size, p1 );
      v3_muladds( p1, refaxis, -cosf(newang)*size, p1 );
      vg_line( p0, p1, 0xff000000 );

      v3_muladds( p0, refaxis_up, sinf(-newang)*size, p1 );
      v3_muladds( p1, refaxis, -cosf(-newang)*size, p1 );
      vg_line( p0, p1, 0xff404040 );
   }
}

/*
 * Solve a list of positional constraints
 */
VG_STATIC void rb_solve_position_constraints( rb_constr_pos *buf, int len )
{
   for( int i=0; i<len; i++ )
   {
      rb_constr_pos *constr = &buf[i];
      rigidbody *rba = constr->rba, *rbb = constr->rbb;

      v3f wa, wb;
      m3x3_mulv( rba->to_world, constr->lca, wa );
      m3x3_mulv( rbb->to_world, constr->lcb, wb );

      m3x3f ssra, ssrat, ssrb, ssrbt;
      
      m3x3_skew_symetric( ssrat, wa );
      m3x3_skew_symetric( ssrbt, wb );
      m3x3_transpose( ssrat, ssra );
      m3x3_transpose( ssrbt, ssrb );

      v3f b, b_wa, b_wb, b_a, b_b;
      m3x3_mulv( ssra, rba->w, b_wa );
      m3x3_mulv( ssrb, rbb->w, b_wb );
      v3_add( rba->v, b_wa, b );
      v3_sub( b, rbb->v, b );
      v3_sub( b, b_wb, b );
      v3_muls( b, -1.0f, b );

      m3x3f invMa, invMb;
      m3x3_diagonal( invMa, rba->inv_mass );
      m3x3_diagonal( invMb, rbb->inv_mass );

      m3x3f ia, ib;
      m3x3_mul( ssra, rba->iIw, ia );
      m3x3_mul( ia, ssrat, ia );
      m3x3_mul( ssrb, rbb->iIw, ib );
      m3x3_mul( ib, ssrbt, ib );

      m3x3f cma, cmb;
      m3x3_add( invMa, ia, cma );
      m3x3_add( invMb, ib, cmb );

      m3x3f A;
      m3x3_add( cma, cmb, A );

      /* Solve Ax = b ( A^-1*b = x ) */
      v3f impulse;
      m3x3f invA;
      m3x3_inv( A, invA );
      m3x3_mulv( invA, b, impulse );

      v3f delta_va, delta_wa, delta_vb, delta_wb;
      m3x3f iwa, iwb;
      m3x3_mul( rba->iIw, ssrat, iwa );
      m3x3_mul( rbb->iIw, ssrbt, iwb );

      m3x3_mulv( invMa, impulse, delta_va );
      m3x3_mulv( invMb, impulse, delta_vb );
      m3x3_mulv( iwa, impulse, delta_wa );
      m3x3_mulv( iwb, impulse, delta_wb );

      v3_add( rba->v, delta_va, rba->v );
      v3_add( rba->w, delta_wa, rba->w );
      v3_sub( rbb->v, delta_vb, rbb->v );
      v3_sub( rbb->w, delta_wb, rbb->w );
   }
}

VG_STATIC void rb_solve_swingtwist_constraints( rb_constr_swingtwist *buf, 
                                                int len )
{
   float size = 0.12f;

   for( int i=0; i<len; i++ )
   {
      rb_constr_swingtwist *st = &buf[ i ];

      if( !st->axis_violation )
         continue;

      float rv = v3_dot( st->axis, st->rbb->w ) - 
                 v3_dot( st->axis, st->rba->w );

      if( rv * (float)st->axis_violation > 0.0f )
         continue;

      v3f impulse, wa, wb;
      v3_muls( st->axis, rv*st->axis_mass, impulse );
      m3x3_mulv( st->rba->iIw, impulse, wa );
      v3_add( st->rba->w, wa, st->rba->w );

      v3_muls( impulse, -1.0f, impulse );
      m3x3_mulv( st->rbb->iIw, impulse, wb );
      v3_add( st->rbb->w, wb, st->rbb->w );

      float rv2 = v3_dot( st->axis, st->rbb->w ) - 
                  v3_dot( st->axis, st->rba->w );
   }

   for( int i=0; i<len; i++ )
   {
      rb_constr_swingtwist *st = &buf[ i ];

      if( !st->tangent_violation )
         continue;

      float rv = v3_dot( st->tangent_axis, st->rbb->w ) - 
                 v3_dot( st->tangent_axis, st->rba->w );

      if( rv > 0.0f )
         continue;

      v3f impulse, wa, wb;
      v3_muls( st->tangent_axis, rv*st->tangent_mass, impulse );
      m3x3_mulv( st->rba->iIw, impulse, wa );
      v3_add( st->rba->w, wa, st->rba->w );

      v3_muls( impulse, -1.0f, impulse );
      m3x3_mulv( st->rbb->iIw, impulse, wb );
      v3_add( st->rbb->w, wb, st->rbb->w );

      float rv2 = v3_dot( st->tangent_axis, st->rbb->w ) - 
                  v3_dot( st->tangent_axis, st->rba->w );
   }
}

VG_STATIC void rb_solve_constr_angle( rigidbody *rba, rigidbody *rbb,
                                      v3f ra, v3f rb )
{
   m3x3f ssra, ssrb, ssrat, ssrbt;
   m3x3f cma, cmb;

   m3x3_skew_symetric( ssrat, ra );
   m3x3_skew_symetric( ssrbt, rb );
   m3x3_transpose( ssrat, ssra );
   m3x3_transpose( ssrbt, ssrb );

   m3x3_mul( ssra, rba->iIw, cma );
   m3x3_mul( cma, ssrat, cma );
   m3x3_mul( ssrb, rbb->iIw, cmb );
   m3x3_mul( cmb, ssrbt, cmb );

   m3x3f A, invA;
   m3x3_add( cma, cmb, A );
   m3x3_inv( A, invA );

   v3f b_wa, b_wb, b;
   m3x3_mulv( ssra, rba->w, b_wa );
   m3x3_mulv( ssrb, rbb->w, b_wb );
   v3_add( b_wa, b_wb, b );
   v3_negate( b, b );

   v3f impulse;
   m3x3_mulv( invA, b, impulse );

   v3f delta_wa, delta_wb;
   m3x3f iwa, iwb;
   m3x3_mul( rba->iIw, ssrat, iwa );
   m3x3_mul( rbb->iIw, ssrbt, iwb );
   m3x3_mulv( iwa, impulse, delta_wa );
   m3x3_mulv( iwb, impulse, delta_wb );
   v3_add( rba->w, delta_wa, rba->w );
   v3_sub( rbb->w, delta_wb, rbb->w );
}

/*
 * Correct position constraint drift errors
 * [ 0.0 <= amt <= 1.0 ]: the correction amount
 */
VG_STATIC void rb_correct_position_constraints( rb_constr_pos *buf, int len, 
                                                float amt )
{
   for( int i=0; i<len; i++ )
   {
      rb_constr_pos *constr = &buf[i];
      rigidbody *rba = constr->rba, *rbb = constr->rbb;

      v3f p0, p1, d;
      m3x3_mulv( rba->to_world, constr->lca, p0 );
      m3x3_mulv( rbb->to_world, constr->lcb, p1 );
      v3_add( rba->co, p0, p0 );
      v3_add( rbb->co, p1, p1 );
      v3_sub( p1, p0, d );

      v3_muladds( rbb->co, d, -1.0f * amt, rbb->co );
      rb_update_transform( rbb );
   }
}

VG_STATIC void rb_correct_swingtwist_constraints( rb_constr_swingtwist *buf, 
                                                  int len, float amt )
{
   for( int i=0; i<len; i++ )
   {
      rb_constr_swingtwist *st = &buf[i];

      if( !st->tangent_violation )
         continue;

      v3f va;
      m3x3_mulv( st->rbb->to_world, st->coneva, va );

      float angle = v3_dot( va, st->tangent_target );

      if( fabsf(angle) < 0.9999f )
      {
         v3f axis;
         v3_cross( va, st->tangent_target, axis );

         v4f correction;
         q_axis_angle( correction, axis, acosf(angle) * amt );
         q_mul( correction, st->rbb->q, st->rbb->q );
         rb_update_transform( st->rbb );
      }
   }

   for( int i=0; i<len; i++ )
   {
      rb_constr_swingtwist *st = &buf[i];

      if( !st->axis_violation )
         continue;

      v3f vxb;
      m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );

      float angle = v3_dot( vxb, st->axis_target );

      if( fabsf(angle) < 0.9999f )
      {
         v3f axis;
         v3_cross( vxb, st->axis_target, axis );

         v4f correction;
         q_axis_angle( correction, axis, acosf(angle) * amt );
         q_mul( correction, st->rbb->q, st->rbb->q );
         rb_update_transform( st->rbb );
      }
   }
}

VG_STATIC void rb_correct_contact_constraints( rb_ct *buf, int len, float amt )
{
   for( int i=0; i<len; i++ )
   {
      rb_ct *ct = &buf[i];
      rigidbody *rba = ct->rba,
                *rbb = ct->rbb;

      float mass_total = 1.0f / (rba->inv_mass + rbb->inv_mass);

      v3_muladds( rba->co, ct->n, -mass_total * rba->inv_mass, rba->co );
      v3_muladds( rbb->co, ct->n,  mass_total * rbb->inv_mass, rbb->co );
   }
}


/* 
 * Effectors
 */

VG_STATIC void rb_effect_simple_bouyency( rigidbody *ra, v4f plane, 
                                          float amt, float drag )
{
   /* float */
   float depth  = v3_dot( plane, ra->co ) - plane[3],
         lambda = vg_clampf( -depth, 0.0f, 1.0f ) * amt;

   v3_muladds( ra->v, plane, lambda * k_rb_delta, ra->v );

   if( depth < 0.0f )
      v3_muls( ra->v, 1.0f-(drag*k_rb_delta), ra->v );
}

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

VG_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 );
}

VG_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;
}

VG_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;
}

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

VG_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 */