2 * Copyright (C) 2021-2022 Mt.ZERO Software, Harry Godden - All Rights Reserved
6 * Resources: Box2D - Erin Catto
14 VG_STATIC
void rb_tangent_basis( v3f n
, v3f tx
, v3f ty
);
15 VG_STATIC bh_system bh_system_rigidbodies
;
21 * -----------------------------------------------------------------------------
23 * -----------------------------------------------------------------------------
27 k_rb_rate
= (1.0/VG_TIMESTEP_FIXED
),
28 k_rb_delta
= (1.0/k_rb_rate
),
30 k_damp_linear
= 0.05f
, /* scale velocity 1/(1+x) */
31 k_damp_angular
= 0.1f
, /* scale angular 1/(1+x) */
33 k_joint_bias
= 0.08f
, /* positional joints */
34 k_joint_correction
= 0.01f
,
35 k_penetration_slop
= 0.01f
,
36 k_inertia_scale
= 4.0f
;
39 * -----------------------------------------------------------------------------
40 * structure definitions
41 * -----------------------------------------------------------------------------
44 typedef struct rigidbody rigidbody
;
45 typedef struct contact rb_ct
;
55 k_rb_shape_sphere
= 1,
56 k_rb_shape_capsule
= 2,
83 v3f right
, up
, forward
;
90 /* inertia model and inverse world tensor */
94 m4x3f to_world
, to_local
;
97 VG_STATIC
struct contact
102 float p
, bias
, norm_impulse
, tangent_impulse
[2],
103 normal_mass
, tangent_mass
[2];
107 rb_contact_buffer
[256];
108 VG_STATIC
int rb_contact_count
= 0;
111 * -----------------------------------------------------------------------------
113 * -----------------------------------------------------------------------------
116 VG_STATIC
float sphere_volume( float radius
)
118 float r3
= radius
*radius
*radius
;
119 return (4.0f
/3.0f
) * VG_PIf
* r3
;
122 VG_STATIC
void rb_tangent_basis( v3f n
, v3f tx
, v3f ty
)
124 /* Compute tangent basis (box2d) */
125 if( fabsf( n
[0] ) >= 0.57735027f
)
139 v3_cross( n
, tx
, ty
);
143 * -----------------------------------------------------------------------------
145 * -----------------------------------------------------------------------------
148 VG_STATIC
void rb_debug_contact( rb_ct
*ct
)
151 v3_muladds( ct
->co
, ct
->n
, 0.1f
, p1
);
152 vg_line_pt3( ct
->co
, 0.025f
, 0xff0000ff );
153 vg_line( ct
->co
, p1
, 0xffffffff );
156 VG_STATIC
void debug_sphere( m4x3f m
, float radius
, u32 colour
)
158 v3f ly
= { 0.0f
, 0.0f
, radius
},
159 lx
= { 0.0f
, radius
, 0.0f
},
160 lz
= { 0.0f
, 0.0f
, radius
};
162 for( int i
=0; i
<16; i
++ )
164 float t
= ((float)(i
+1) * (1.0f
/16.0f
)) * VG_PIf
* 2.0f
,
168 v3f py
= { s
*radius
, 0.0f
, c
*radius
},
169 px
= { s
*radius
, c
*radius
, 0.0f
},
170 pz
= { 0.0f
, s
*radius
, c
*radius
};
172 v3f p0
, p1
, p2
, p3
, p4
, p5
;
173 m4x3_mulv( m
, py
, p0
);
174 m4x3_mulv( m
, ly
, p1
);
175 m4x3_mulv( m
, px
, p2
);
176 m4x3_mulv( m
, lx
, p3
);
177 m4x3_mulv( m
, pz
, p4
);
178 m4x3_mulv( m
, lz
, p5
);
180 vg_line( p0
, p1
, colour
== 0x00? 0xff00ff00: colour
);
181 vg_line( p2
, p3
, colour
== 0x00? 0xff0000ff: colour
);
182 vg_line( p4
, p5
, colour
== 0x00? 0xffff0000: colour
);
190 VG_STATIC
void debug_capsule( m4x3f m
, float radius
, float h
, u32 colour
)
192 v3f ly
= { 0.0f
, 0.0f
, radius
},
193 lx
= { 0.0f
, radius
, 0.0f
},
194 lz
= { 0.0f
, 0.0f
, radius
};
196 float s0
= sinf(0.0f
)*radius
,
197 c0
= cosf(0.0f
)*radius
;
199 v3f p0
, p1
, up
, right
, forward
;
200 m3x3_mulv( m
, (v3f
){0.0f
,1.0f
,0.0f
}, up
);
201 m3x3_mulv( m
, (v3f
){1.0f
,0.0f
,0.0f
}, right
);
202 m3x3_mulv( m
, (v3f
){0.0f
,0.0f
,-1.0f
}, forward
);
203 v3_muladds( m
[3], up
, -h
*0.5f
+radius
, p0
);
204 v3_muladds( m
[3], up
, h
*0.5f
-radius
, p1
);
207 v3_muladds( p0
, right
, radius
, a0
);
208 v3_muladds( p1
, right
, radius
, a1
);
209 v3_muladds( p0
, forward
, radius
, b0
);
210 v3_muladds( p1
, forward
, radius
, b1
);
211 vg_line( a0
, a1
, colour
);
212 vg_line( b0
, b1
, colour
);
214 v3_muladds( p0
, right
, -radius
, a0
);
215 v3_muladds( p1
, right
, -radius
, a1
);
216 v3_muladds( p0
, forward
, -radius
, b0
);
217 v3_muladds( p1
, forward
, -radius
, b1
);
218 vg_line( a0
, a1
, colour
);
219 vg_line( b0
, b1
, colour
);
221 for( int i
=0; i
<16; i
++ )
223 float t
= ((float)(i
+1) * (1.0f
/16.0f
)) * VG_PIf
* 2.0f
,
227 v3f e0
= { s0
, 0.0f
, c0
},
228 e1
= { s1
, 0.0f
, c1
},
229 e2
= { s0
, c0
, 0.0f
},
230 e3
= { s1
, c1
, 0.0f
},
231 e4
= { 0.0f
, c0
, s0
},
232 e5
= { 0.0f
, c1
, s1
};
234 m3x3_mulv( m
, e0
, e0
);
235 m3x3_mulv( m
, e1
, e1
);
236 m3x3_mulv( m
, e2
, e2
);
237 m3x3_mulv( m
, e3
, e3
);
238 m3x3_mulv( m
, e4
, e4
);
239 m3x3_mulv( m
, e5
, e5
);
241 v3_add( p0
, e0
, a0
);
242 v3_add( p0
, e1
, a1
);
243 v3_add( p1
, e0
, b0
);
244 v3_add( p1
, e1
, b1
);
246 vg_line( a0
, a1
, colour
);
247 vg_line( b0
, b1
, colour
);
251 v3_add( p0
, e2
, a0
);
252 v3_add( p0
, e3
, a1
);
253 v3_add( p0
, e4
, b0
);
254 v3_add( p0
, e5
, b1
);
258 v3_add( p1
, e2
, a0
);
259 v3_add( p1
, e3
, a1
);
260 v3_add( p1
, e4
, b0
);
261 v3_add( p1
, e5
, b1
);
264 vg_line( a0
, a1
, colour
);
265 vg_line( b0
, b1
, colour
);
272 VG_STATIC
void rb_debug( rigidbody
*rb
, u32 colour
)
274 if( rb
->type
== k_rb_shape_box
)
277 vg_line_boxf_transformed( rb
->to_world
, rb
->bbx
, colour
);
279 else if( rb
->type
== k_rb_shape_sphere
)
281 debug_sphere( rb
->to_world
, rb
->inf
.sphere
.radius
, colour
);
283 else if( rb
->type
== k_rb_shape_capsule
)
286 float h
= rb
->inf
.capsule
.height
,
287 r
= rb
->inf
.capsule
.radius
;
289 debug_capsule( rb
->to_world
, r
, h
, colour
);
291 else if( rb
->type
== k_rb_shape_scene
)
293 vg_line_boxf( rb
->bbx
, colour
);
298 * -----------------------------------------------------------------------------
300 * -----------------------------------------------------------------------------
304 * Update world space bounding box based on local one
306 VG_STATIC
void rb_update_bounds( rigidbody
*rb
)
308 box_copy( rb
->bbx
, rb
->bbx_world
);
309 m4x3_transform_aabb( rb
->to_world
, rb
->bbx_world
);
313 * Commit transform to rigidbody. Updates matrices
315 VG_STATIC
void rb_update_transform( rigidbody
*rb
)
317 q_normalize( rb
->q
);
318 q_m3x3( rb
->q
, rb
->to_world
);
319 v3_copy( rb
->co
, rb
->to_world
[3] );
321 m4x3_invert_affine( rb
->to_world
, rb
->to_local
);
323 m3x3_mulv( rb
->to_world
, (v3f
){1.0f
,0.0f
, 0.0f
}, rb
->right
);
324 m3x3_mulv( rb
->to_world
, (v3f
){0.0f
,1.0f
, 0.0f
}, rb
->up
);
325 m3x3_mulv( rb
->to_world
, (v3f
){0.0f
,0.0f
,-1.0f
}, rb
->forward
);
327 m3x3_mul( rb
->iI
, rb
->to_local
, rb
->iIw
);
328 m3x3_mul( rb
->to_world
, rb
->iIw
, rb
->iIw
);
330 rb_update_bounds( rb
);
334 * Extrapolate rigidbody into a transform based on vg accumulator.
335 * Useful for rendering
337 VG_STATIC
void rb_extrapolate_transform( rigidbody
*rb
, m4x3f transform
)
339 float substep
= vg_clampf( vg
.accumulator
/ k_rb_delta
, 0.0f
, 1.0f
);
344 v3_muladds( rb
->co
, rb
->v
, k_rb_delta
*substep
, co
);
346 if( v3_length2( rb
->w
) > 0.0f
)
350 v3_copy( rb
->w
, axis
);
352 float mag
= v3_length( axis
);
353 v3_divs( axis
, mag
, axis
);
354 q_axis_angle( rotation
, axis
, mag
*k_rb_delta
*substep
);
355 q_mul( rotation
, rb
->q
, q
);
363 q_m3x3( q
, transform
);
364 v3_copy( co
, transform
[3] );
368 * Initialize rigidbody and calculate masses, inertia
370 VG_STATIC
void rb_init( rigidbody
*rb
)
374 if( rb
->type
== k_rb_shape_box
)
377 v3_sub( rb
->bbx
[1], rb
->bbx
[0], dims
);
378 volume
= dims
[0]*dims
[1]*dims
[2];
380 else if( rb
->type
== k_rb_shape_sphere
)
382 volume
= sphere_volume( rb
->inf
.sphere
.radius
);
383 v3_fill( rb
->bbx
[0], -rb
->inf
.sphere
.radius
);
384 v3_fill( rb
->bbx
[1], rb
->inf
.sphere
.radius
);
386 else if( rb
->type
== k_rb_shape_capsule
)
388 float r
= rb
->inf
.capsule
.radius
,
389 h
= rb
->inf
.capsule
.height
;
390 volume
= sphere_volume( r
) + VG_PIf
* r
*r
* (h
- r
*2.0f
);
392 v3_fill( rb
->bbx
[0], -rb
->inf
.sphere
.radius
);
393 v3_fill( rb
->bbx
[1], rb
->inf
.sphere
.radius
);
397 else if( rb
->type
== k_rb_shape_scene
)
400 box_copy( rb
->inf
.scene
.bh_scene
->nodes
[0].bbx
, rb
->bbx
);
411 float mass
= 2.0f
*volume
;
412 rb
->inv_mass
= 1.0f
/mass
;
415 v3_sub( rb
->bbx
[1], rb
->bbx
[0], extent
);
416 v3_muls( extent
, 0.5f
, extent
);
418 /* local intertia tensor */
419 float scale
= k_inertia_scale
;
420 float ex2
= scale
*extent
[0]*extent
[0],
421 ey2
= scale
*extent
[1]*extent
[1],
422 ez2
= scale
*extent
[2]*extent
[2];
424 rb
->I
[0] = ((1.0f
/12.0f
) * mass
* (ey2
+ez2
));
425 rb
->I
[1] = ((1.0f
/12.0f
) * mass
* (ex2
+ez2
));
426 rb
->I
[2] = ((1.0f
/12.0f
) * mass
* (ex2
+ey2
));
428 m3x3_identity( rb
->iI
);
429 rb
->iI
[0][0] = rb
->I
[0];
430 rb
->iI
[1][1] = rb
->I
[1];
431 rb
->iI
[2][2] = rb
->I
[2];
432 m3x3_inv( rb
->iI
, rb
->iI
);
438 rb_update_transform( rb
);
441 VG_STATIC
void rb_iter( rigidbody
*rb
)
443 v3f gravity
= { 0.0f
, -9.8f
, 0.0f
};
444 v3_muladds( rb
->v
, gravity
, k_rb_delta
, rb
->v
);
446 /* intergrate velocity */
447 v3_muladds( rb
->co
, rb
->v
, k_rb_delta
, rb
->co
);
448 v3_lerp( rb
->w
, (v3f
){0.0f
,0.0f
,0.0f
}, 0.0025f
, rb
->w
);
450 /* inegrate inertia */
451 if( v3_length2( rb
->w
) > 0.0f
)
455 v3_copy( rb
->w
, axis
);
457 float mag
= v3_length( axis
);
458 v3_divs( axis
, mag
, axis
);
459 q_axis_angle( rotation
, axis
, mag
*k_rb_delta
);
460 q_mul( rotation
, rb
->q
, rb
->q
);
464 v3_muls( rb
->v
, 1.0f
/(1.0f
+k_rb_delta
*k_damp_linear
), rb
->v
);
465 v3_muls( rb
->w
, 1.0f
/(1.0f
+k_rb_delta
*k_damp_angular
), rb
->w
);
469 * -----------------------------------------------------------------------------
470 * Closest point functions
471 * -----------------------------------------------------------------------------
475 * These closest point tests were learned from Real-Time Collision Detection by
478 VG_STATIC
float closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
479 float *s
, float *t
, v3f c1
, v3f c2
)
482 v3_sub( q1
, p1
, d1
);
483 v3_sub( q2
, p2
, d2
);
486 float a
= v3_length2( d1
),
487 e
= v3_length2( d2
),
490 const float kEpsilon
= 0.0001f
;
492 if( a
<= kEpsilon
&& e
<= kEpsilon
)
500 v3_sub( c1
, c2
, v0
);
502 return v3_length2( v0
);
508 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
512 float c
= v3_dot( d1
, r
);
516 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
520 float b
= v3_dot(d1
,d2
),
525 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
537 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
542 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
547 v3_muladds( p1
, d1
, *s
, c1
);
548 v3_muladds( p2
, d2
, *t
, c2
);
551 v3_sub( c1
, c2
, v0
);
552 return v3_length2( v0
);
555 VG_STATIC
void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
557 v3_maxv( p
, box
[0], dest
);
558 v3_minv( dest
, box
[1], dest
);
561 VG_STATIC
void closest_point_obb( v3f p
, rigidbody
*rb
, v3f dest
)
564 m4x3_mulv( rb
->to_local
, p
, local
);
565 closest_point_aabb( local
, rb
->bbx
, local
);
566 m4x3_mulv( rb
->to_world
, local
, dest
);
569 VG_STATIC
float closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
573 v3_sub( point
, a
, v1
);
575 float t
= v3_dot( v1
, v0
) / v3_length2(v0
);
576 t
= vg_clampf(t
,0.0f
,1.0f
);
577 v3_muladds( a
, v0
, t
, dest
);
581 VG_STATIC
void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
586 /* Region outside A */
587 v3_sub( tri
[1], tri
[0], ab
);
588 v3_sub( tri
[2], tri
[0], ac
);
589 v3_sub( p
, tri
[0], ap
);
593 if( d1
<= 0.0f
&& d2
<= 0.0f
)
595 v3_copy( tri
[0], dest
);
596 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
600 /* Region outside B */
604 v3_sub( p
, tri
[1], bp
);
605 d3
= v3_dot( ab
, bp
);
606 d4
= v3_dot( ac
, bp
);
608 if( d3
>= 0.0f
&& d4
<= d3
)
610 v3_copy( tri
[1], dest
);
611 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
615 /* Edge region of AB */
616 float vc
= d1
*d4
- d3
*d2
;
617 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
619 float v
= d1
/ (d1
-d3
);
620 v3_muladds( tri
[0], ab
, v
, dest
);
621 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
625 /* Region outside C */
628 v3_sub( p
, tri
[2], cp
);
632 if( d6
>= 0.0f
&& d5
<= d6
)
634 v3_copy( tri
[2], dest
);
635 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
640 float vb
= d5
*d2
- d1
*d6
;
641 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
643 float w
= d2
/ (d2
-d6
);
644 v3_muladds( tri
[0], ac
, w
, dest
);
645 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
650 float va
= d3
*d6
- d5
*d4
;
651 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
653 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
655 v3_sub( tri
[2], tri
[1], bc
);
656 v3_muladds( tri
[1], bc
, w
, dest
);
657 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
661 /* P inside region, Q via barycentric coordinates uvw */
662 float d
= 1.0f
/(va
+vb
+vc
),
666 v3_muladds( tri
[0], ab
, v
, dest
);
667 v3_muladds( dest
, ac
, w
, dest
);
670 VG_STATIC
void closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
675 /* Region outside A */
676 v3_sub( tri
[1], tri
[0], ab
);
677 v3_sub( tri
[2], tri
[0], ac
);
678 v3_sub( p
, tri
[0], ap
);
682 if( d1
<= 0.0f
&& d2
<= 0.0f
)
684 v3_copy( tri
[0], dest
);
688 /* Region outside B */
692 v3_sub( p
, tri
[1], bp
);
693 d3
= v3_dot( ab
, bp
);
694 d4
= v3_dot( ac
, bp
);
696 if( d3
>= 0.0f
&& d4
<= d3
)
698 v3_copy( tri
[1], dest
);
702 /* Edge region of AB */
703 float vc
= d1
*d4
- d3
*d2
;
704 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
706 float v
= d1
/ (d1
-d3
);
707 v3_muladds( tri
[0], ab
, v
, dest
);
711 /* Region outside C */
714 v3_sub( p
, tri
[2], cp
);
718 if( d6
>= 0.0f
&& d5
<= d6
)
720 v3_copy( tri
[2], dest
);
725 float vb
= d5
*d2
- d1
*d6
;
726 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
728 float w
= d2
/ (d2
-d6
);
729 v3_muladds( tri
[0], ac
, w
, dest
);
734 float va
= d3
*d6
- d5
*d4
;
735 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
737 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
739 v3_sub( tri
[2], tri
[1], bc
);
740 v3_muladds( tri
[1], bc
, w
, dest
);
744 /* P inside region, Q via barycentric coordinates uvw */
745 float d
= 1.0f
/(va
+vb
+vc
),
749 v3_muladds( tri
[0], ab
, v
, dest
);
750 v3_muladds( dest
, ac
, w
, dest
);
754 * -----------------------------------------------------------------------------
755 * Boolean shape overlap functions
756 * -----------------------------------------------------------------------------
760 * Project AABB, and triangle interval onto axis to check if they overlap
762 VG_STATIC
int rb_box_triangle_interval( v3f extent
, v3f axis
, v3f tri
[3] )
766 r
= extent
[0] * fabsf(axis
[0]) +
767 extent
[1] * fabsf(axis
[1]) +
768 extent
[2] * fabsf(axis
[2]),
770 p0
= v3_dot( axis
, tri
[0] ),
771 p1
= v3_dot( axis
, tri
[1] ),
772 p2
= v3_dot( axis
, tri
[2] ),
774 e
= vg_maxf(-vg_maxf(p0
,vg_maxf(p1
,p2
)), vg_minf(p0
,vg_minf(p1
,p2
)));
776 if( e
> r
) return 0;
781 * Seperating axis test box vs triangle
783 VG_STATIC
int rb_box_triangle_sat( rigidbody
*rba
, v3f tri_src
[3] )
788 v3_sub( rba
->bbx
[1], rba
->bbx
[0], extent
);
789 v3_muls( extent
, 0.5f
, extent
);
790 v3_add( rba
->bbx
[0], extent
, c
);
792 for( int i
=0; i
<3; i
++ )
794 m4x3_mulv( rba
->to_local
, tri_src
[i
], tri
[i
] );
795 v3_sub( tri
[i
], c
, tri
[i
] );
799 if(!rb_box_triangle_interval( extent
, (v3f
){1.0f
,0.0f
,0.0f
}, tri
)) return 0;
800 if(!rb_box_triangle_interval( extent
, (v3f
){0.0f
,1.0f
,0.0f
}, tri
)) return 0;
801 if(!rb_box_triangle_interval( extent
, (v3f
){0.0f
,0.0f
,1.0f
}, tri
)) return 0;
803 v3f v0
,v1
,v2
,n
, e0
,e1
,e2
;
804 v3_sub( tri
[1], tri
[0], v0
);
805 v3_sub( tri
[2], tri
[0], v1
);
806 v3_sub( tri
[2], tri
[1], v2
);
810 v3_cross( v0
, v1
, n
);
811 v3_cross( v0
, n
, e0
);
812 v3_cross( n
, v1
, e1
);
813 v3_cross( v2
, n
, e2
);
816 if(!rb_box_triangle_interval( extent
, n
, tri
)) return 0;
819 v3_cross( e0
, (v3f
){1.0f
,0.0f
,0.0f
}, axis
[0] );
820 v3_cross( e0
, (v3f
){0.0f
,1.0f
,0.0f
}, axis
[1] );
821 v3_cross( e0
, (v3f
){0.0f
,0.0f
,1.0f
}, axis
[2] );
822 v3_cross( e1
, (v3f
){1.0f
,0.0f
,0.0f
}, axis
[3] );
823 v3_cross( e1
, (v3f
){0.0f
,1.0f
,0.0f
}, axis
[4] );
824 v3_cross( e1
, (v3f
){0.0f
,0.0f
,1.0f
}, axis
[5] );
825 v3_cross( e2
, (v3f
){1.0f
,0.0f
,0.0f
}, axis
[6] );
826 v3_cross( e2
, (v3f
){0.0f
,1.0f
,0.0f
}, axis
[7] );
827 v3_cross( e2
, (v3f
){0.0f
,0.0f
,1.0f
}, axis
[8] );
829 for( int i
=0; i
<9; i
++ )
830 if(!rb_box_triangle_interval( extent
, axis
[i
], tri
)) return 0;
836 * -----------------------------------------------------------------------------
838 * -----------------------------------------------------------------------------
844 * These do not automatically allocate contacts, an appropriately sized
845 * buffer must be supplied. The function returns the size of the manifold
846 * which was generated.
848 * The values set on the contacts are: n, co, p, rba, rbb
852 * By collecting the minimum(time) and maximum(time) pairs of points, we
853 * build a reduced and stable exact manifold.
856 * rx: minimum distance of these points
857 * dx: the delta between the two points
859 * pairs will only ammend these if they are creating a collision
861 typedef struct capsule_manifold capsule_manifold
;
862 struct capsule_manifold
870 * Expand a line manifold with a new pair. t value is the time along segment
871 * on the oriented object which created this pair.
873 VG_STATIC
void rb_capsule_manifold( v3f pa
, v3f pb
, float t
, float r
,
874 capsule_manifold
*manifold
)
877 v3_sub( pa
, pb
, delta
);
879 if( v3_length2(delta
) < r
*r
)
881 if( t
< manifold
->t0
)
883 v3_copy( delta
, manifold
->d0
);
888 if( t
> manifold
->t1
)
890 v3_copy( delta
, manifold
->d1
);
897 VG_STATIC
void rb_capsule_manifold_init( capsule_manifold
*manifold
)
899 manifold
->t0
= INFINITY
;
900 manifold
->t1
= -INFINITY
;
903 VG_STATIC
int rb_capsule_manifold_done( rigidbody
*rba
, rigidbody
*rbb
,
904 capsule_manifold
*manifold
, rb_ct
*buf
)
906 float h
= rba
->inf
.capsule
.height
,
907 ra
= rba
->inf
.capsule
.radius
;
910 v3_muladds( rba
->co
, rba
->up
, -h
*0.5f
+ra
, p0
);
911 v3_muladds( rba
->co
, rba
->up
, h
*0.5f
-ra
, p1
);
914 if( manifold
->t0
<= 1.0f
)
919 v3_muls( p0
, 1.0f
-manifold
->t0
, pa
);
920 v3_muladds( pa
, p1
, manifold
->t0
, pa
);
922 float d
= v3_length( manifold
->d0
);
923 v3_muls( manifold
->d0
, 1.0f
/d
, ct
->n
);
924 v3_muladds( pa
, ct
->n
, -ra
, ct
->co
);
926 ct
->p
= manifold
->r0
- d
;
933 if( (manifold
->t1
>= 0.0f
) && (manifold
->t0
!= manifold
->t1
) )
935 rb_ct
*ct
= buf
+count
;
938 v3_muls( p0
, 1.0f
-manifold
->t1
, pa
);
939 v3_muladds( pa
, p1
, manifold
->t1
, pa
);
941 float d
= v3_length( manifold
->d1
);
942 v3_muls( manifold
->d1
, 1.0f
/d
, ct
->n
);
943 v3_muladds( pa
, ct
->n
, -ra
, ct
->co
);
945 ct
->p
= manifold
->r1
- d
;
957 vg_line( buf
[0].co
, buf
[1].co
, 0xff0000ff );
962 VG_STATIC
int rb_capsule_sphere( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
964 float h
= rba
->inf
.capsule
.height
,
965 ra
= rba
->inf
.capsule
.radius
,
966 rb
= rbb
->inf
.sphere
.radius
;
969 v3_muladds( rba
->co
, rba
->up
, -h
*0.5f
+ra
, p0
);
970 v3_muladds( rba
->co
, rba
->up
, h
*0.5f
-ra
, p1
);
973 closest_point_segment( p0
, p1
, rbb
->co
, c
);
974 v3_sub( c
, rbb
->co
, delta
);
976 float d2
= v3_length2(delta
),
984 v3_muls( delta
, 1.0f
/d
, ct
->n
);
988 v3_muladds( c
, ct
->n
, -ra
, p0
);
989 v3_muladds( rbb
->co
, ct
->n
, rb
, p1
);
990 v3_add( p0
, p1
, ct
->co
);
991 v3_muls( ct
->co
, 0.5f
, ct
->co
);
1002 VG_STATIC
int rb_capsule_capsule( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1004 float ha
= rba
->inf
.capsule
.height
,
1005 hb
= rbb
->inf
.capsule
.height
,
1006 ra
= rba
->inf
.capsule
.radius
,
1007 rb
= rbb
->inf
.capsule
.radius
,
1011 v3_muladds( rba
->co
, rba
->up
, -ha
*0.5f
+ra
, p0
);
1012 v3_muladds( rba
->co
, rba
->up
, ha
*0.5f
-ra
, p1
);
1013 v3_muladds( rbb
->co
, rbb
->up
, -hb
*0.5f
+rb
, p2
);
1014 v3_muladds( rbb
->co
, rbb
->up
, hb
*0.5f
-rb
, p3
);
1016 capsule_manifold manifold
;
1017 rb_capsule_manifold_init( &manifold
);
1021 closest_segment_segment( p0
, p1
, p2
, p3
, &ta
, &tb
, pa
, pb
);
1022 rb_capsule_manifold( pa
, pb
, ta
, r
, &manifold
);
1024 ta
= closest_point_segment( p0
, p1
, p2
, pa
);
1025 tb
= closest_point_segment( p0
, p1
, p3
, pb
);
1026 rb_capsule_manifold( pa
, p2
, ta
, r
, &manifold
);
1027 rb_capsule_manifold( pb
, p3
, tb
, r
, &manifold
);
1029 closest_point_segment( p2
, p3
, p0
, pa
);
1030 closest_point_segment( p2
, p3
, p1
, pb
);
1031 rb_capsule_manifold( p0
, pa
, 0.0f
, r
, &manifold
);
1032 rb_capsule_manifold( p1
, pb
, 1.0f
, r
, &manifold
);
1034 return rb_capsule_manifold_done( rba
, rbb
, &manifold
, buf
);
1038 * Generates up to two contacts; optimised for the most stable manifold
1040 VG_STATIC
int rb_capsule_box( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1042 float h
= rba
->inf
.capsule
.height
,
1043 r
= rba
->inf
.capsule
.radius
;
1046 * Solving this in symetric local space of the cube saves us some time and a
1047 * couple branches when it comes to the quad stage.
1050 v3_add( rbb
->bbx
[0], rbb
->bbx
[1], centroid
);
1051 v3_muls( centroid
, 0.5f
, centroid
);
1054 v3_sub( rbb
->bbx
[0], centroid
, bbx
[0] );
1055 v3_sub( rbb
->bbx
[1], centroid
, bbx
[1] );
1057 v3f pc
, p0w
, p1w
, p0
, p1
;
1058 v3_muladds( rba
->co
, rba
->up
, -h
*0.5f
+r
, p0w
);
1059 v3_muladds( rba
->co
, rba
->up
, h
*0.5f
-r
, p1w
);
1061 m4x3_mulv( rbb
->to_local
, p0w
, p0
);
1062 m4x3_mulv( rbb
->to_local
, p1w
, p1
);
1063 v3_sub( p0
, centroid
, p0
);
1064 v3_sub( p1
, centroid
, p1
);
1065 v3_add( p0
, p1
, pc
);
1066 v3_muls( pc
, 0.5f
, pc
);
1069 * Finding an appropriate quad to collide lines with
1072 v3_div( pc
, bbx
[1], region
);
1075 if( (fabsf(region
[0]) > fabsf(region
[1])) &&
1076 (fabsf(region
[0]) > fabsf(region
[2])) )
1078 float px
= vg_signf(region
[0]) * bbx
[1][0];
1079 v3_copy( (v3f
){ px
, bbx
[0][1], bbx
[0][2] }, quad
[0] );
1080 v3_copy( (v3f
){ px
, bbx
[1][1], bbx
[0][2] }, quad
[1] );
1081 v3_copy( (v3f
){ px
, bbx
[1][1], bbx
[1][2] }, quad
[2] );
1082 v3_copy( (v3f
){ px
, bbx
[0][1], bbx
[1][2] }, quad
[3] );
1084 else if( fabsf(region
[1]) > fabsf(region
[2]) )
1086 float py
= vg_signf(region
[1]) * bbx
[1][1];
1087 v3_copy( (v3f
){ bbx
[0][0], py
, bbx
[0][2] }, quad
[0] );
1088 v3_copy( (v3f
){ bbx
[1][0], py
, bbx
[0][2] }, quad
[1] );
1089 v3_copy( (v3f
){ bbx
[1][0], py
, bbx
[1][2] }, quad
[2] );
1090 v3_copy( (v3f
){ bbx
[0][0], py
, bbx
[1][2] }, quad
[3] );
1094 float pz
= vg_signf(region
[2]) * bbx
[1][2];
1095 v3_copy( (v3f
){ bbx
[0][0], bbx
[0][1], pz
}, quad
[0] );
1096 v3_copy( (v3f
){ bbx
[1][0], bbx
[0][1], pz
}, quad
[1] );
1097 v3_copy( (v3f
){ bbx
[1][0], bbx
[1][1], pz
}, quad
[2] );
1098 v3_copy( (v3f
){ bbx
[0][0], bbx
[1][1], pz
}, quad
[3] );
1101 capsule_manifold manifold
;
1102 rb_capsule_manifold_init( &manifold
);
1105 closest_point_aabb( p0
, bbx
, c0
);
1106 closest_point_aabb( p1
, bbx
, c1
);
1109 v3_sub( c0
, p0
, d0
);
1110 v3_sub( c1
, p1
, d1
);
1111 v3_sub( p1
, p0
, da
);
1117 if( v3_dot( da
, d0
) <= 0.01f
)
1118 rb_capsule_manifold( p0
, c0
, 0.0f
, r
, &manifold
);
1120 if( v3_dot( da
, d1
) >= -0.01f
)
1121 rb_capsule_manifold( p1
, c1
, 1.0f
, r
, &manifold
);
1123 for( int i
=0; i
<4; i
++ )
1130 closest_segment_segment( p0
, p1
, quad
[i0
], quad
[i1
], &ta
, &tb
, ca
, cb
);
1131 rb_capsule_manifold( ca
, cb
, ta
, r
, &manifold
);
1135 * Create final contacts based on line manifold
1137 m3x3_mulv( rbb
->to_world
, manifold
.d0
, manifold
.d0
);
1138 m3x3_mulv( rbb
->to_world
, manifold
.d1
, manifold
.d1
);
1145 for( int i
=0; i
<4; i
++ )
1151 v3_add( quad
[i0
], centroid
, q0
);
1152 v3_add( quad
[i1
], centroid
, q1
);
1154 m4x3_mulv( rbb
->to_world
, q0
, q0
);
1155 m4x3_mulv( rbb
->to_world
, q1
, q1
);
1157 vg_line( q0
, q1
, 0xffffffff );
1161 return rb_capsule_manifold_done( rba
, rbb
, &manifold
, buf
);
1164 VG_STATIC
int rb_sphere_box( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1168 closest_point_obb( rba
->co
, rbb
, co
);
1169 v3_sub( rba
->co
, co
, delta
);
1171 float d2
= v3_length2(delta
),
1172 r
= rba
->inf
.sphere
.radius
;
1181 v3_sub( rba
->co
, rbb
->co
, delta
);
1184 * some extra testing is required to find the best axis to push the
1185 * object back outside the box. Since there isnt a clear seperating
1186 * vector already, especially on really high aspect boxes.
1188 float lx
= v3_dot( rbb
->right
, delta
),
1189 ly
= v3_dot( rbb
->up
, delta
),
1190 lz
= v3_dot( rbb
->forward
, delta
),
1191 px
= rbb
->bbx
[1][0] - fabsf(lx
),
1192 py
= rbb
->bbx
[1][1] - fabsf(ly
),
1193 pz
= rbb
->bbx
[1][2] - fabsf(lz
);
1195 if( px
< py
&& px
< pz
)
1196 v3_muls( rbb
->right
, vg_signf(lx
), ct
->n
);
1198 v3_muls( rbb
->up
, vg_signf(ly
), ct
->n
);
1200 v3_muls( rbb
->forward
, vg_signf(lz
), ct
->n
);
1202 v3_muladds( rba
->co
, ct
->n
, -r
, ct
->co
);
1208 v3_muls( delta
, 1.0f
/d
, ct
->n
);
1210 v3_copy( co
, ct
->co
);
1221 VG_STATIC
int rb_sphere_sphere( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1224 v3_sub( rba
->co
, rbb
->co
, delta
);
1226 float d2
= v3_length2(delta
),
1227 r
= rba
->inf
.sphere
.radius
+ rbb
->inf
.sphere
.radius
;
1231 float d
= sqrtf(d2
);
1234 v3_muls( delta
, 1.0f
/d
, ct
->n
);
1237 v3_muladds( rba
->co
, ct
->n
,-rba
->inf
.sphere
.radius
, p0
);
1238 v3_muladds( rbb
->co
, ct
->n
, rbb
->inf
.sphere
.radius
, p1
);
1239 v3_add( p0
, p1
, ct
->co
);
1240 v3_muls( ct
->co
, 0.5f
, ct
->co
);
1250 VG_STATIC
int rb_sphere_triangle( rigidbody
*rba
, rigidbody
*rbb
,
1251 v3f tri
[3], rb_ct
*buf
)
1255 closest_on_triangle_1( rba
->co
, tri
, co
);
1256 v3_sub( rba
->co
, co
, delta
);
1258 vg_line( rba
->co
, co
, 0xffff0000 );
1259 vg_line_pt3( rba
->co
, 0.1f
, 0xff00ffff );
1261 float d2
= v3_length2( delta
),
1262 r
= rba
->inf
.sphere
.radius
;
1269 v3_sub( tri
[2], tri
[0], ab
);
1270 v3_sub( tri
[1], tri
[0], ac
);
1271 v3_cross( ac
, ab
, tn
);
1272 v3_copy( tn
, ct
->n
);
1273 v3_normalize( ct
->n
);
1275 float d
= sqrtf(d2
);
1277 v3_copy( co
, ct
->co
);
1287 VG_STATIC
int rb_sphere_scene( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1289 scene
*sc
= rbb
->inf
.scene
.bh_scene
->user
;
1293 int len
= bh_select( rbb
->inf
.scene
.bh_scene
, rba
->bbx_world
, geo
, 128 );
1297 for( int i
=0; i
<len
; i
++ )
1299 u32
*ptri
= &sc
->arrindices
[ geo
[i
]*3 ];
1301 for( int j
=0; j
<3; j
++ )
1302 v3_copy( sc
->arrvertices
[ptri
[j
]].co
, tri
[j
] );
1304 vg_line(tri
[0],tri
[1],0xff00ff00 );
1305 vg_line(tri
[1],tri
[2],0xff00ff00 );
1306 vg_line(tri
[2],tri
[0],0xff00ff00 );
1308 buf
[count
].element_id
= ptri
[0];
1309 count
+= rb_sphere_triangle( rba
, rbb
, tri
, buf
+count
);
1313 vg_warn( "Exceeding sphere_vs_scene capacity. Geometry too dense!\n" );
1321 VG_STATIC
int rb_box_scene( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1323 scene
*sc
= rbb
->inf
.scene
.bh_scene
->user
;
1327 int len
= bh_select( rbb
->inf
.scene
.bh_scene
, rba
->bbx_world
, geo
, 128 );
1331 for( int i
=0; i
<len
; i
++ )
1333 u32
*ptri
= &sc
->arrindices
[ geo
[i
]*3 ];
1335 for( int j
=0; j
<3; j
++ )
1336 v3_copy( sc
->arrvertices
[ptri
[j
]].co
, tri
[j
] );
1338 if( rb_box_triangle_sat( rba
, tri
) )
1340 vg_line(tri
[0],tri
[1],0xff50ff00 );
1341 vg_line(tri
[1],tri
[2],0xff50ff00 );
1342 vg_line(tri
[2],tri
[0],0xff50ff00 );
1346 vg_line(tri
[0],tri
[1],0xff0000ff );
1347 vg_line(tri
[1],tri
[2],0xff0000ff );
1348 vg_line(tri
[2],tri
[0],0xff0000ff );
1354 v3_sub( tri
[1], tri
[0], v0
);
1355 v3_sub( tri
[2], tri
[0], v1
);
1356 v3_cross( v0
, v1
, n
);
1359 /* find best feature */
1360 float best
= v3_dot( rba
->right
, n
);
1363 float cy
= v3_dot( rba
->up
, n
);
1364 if( fabsf(cy
) > fabsf(best
) )
1370 float cz
= -v3_dot( rba
->forward
, n
);
1371 if( fabsf(cz
) > fabsf(best
) )
1381 float px
= best
> 0.0f
? rba
->bbx
[0][0]: rba
->bbx
[1][0];
1382 manifold
[0][0] = px
;
1383 manifold
[0][1] = rba
->bbx
[0][1];
1384 manifold
[0][2] = rba
->bbx
[0][2];
1385 manifold
[1][0] = px
;
1386 manifold
[1][1] = rba
->bbx
[1][1];
1387 manifold
[1][2] = rba
->bbx
[0][2];
1388 manifold
[2][0] = px
;
1389 manifold
[2][1] = rba
->bbx
[1][1];
1390 manifold
[2][2] = rba
->bbx
[1][2];
1391 manifold
[3][0] = px
;
1392 manifold
[3][1] = rba
->bbx
[0][1];
1393 manifold
[3][2] = rba
->bbx
[1][2];
1395 else if( axis
== 1 )
1397 float py
= best
> 0.0f
? rba
->bbx
[0][1]: rba
->bbx
[1][1];
1398 manifold
[0][0] = rba
->bbx
[0][0];
1399 manifold
[0][1] = py
;
1400 manifold
[0][2] = rba
->bbx
[0][2];
1401 manifold
[1][0] = rba
->bbx
[1][0];
1402 manifold
[1][1] = py
;
1403 manifold
[1][2] = rba
->bbx
[0][2];
1404 manifold
[2][0] = rba
->bbx
[1][0];
1405 manifold
[2][1] = py
;
1406 manifold
[2][2] = rba
->bbx
[1][2];
1407 manifold
[3][0] = rba
->bbx
[0][0];
1408 manifold
[3][1] = py
;
1409 manifold
[3][2] = rba
->bbx
[1][2];
1413 float pz
= best
> 0.0f
? rba
->bbx
[0][2]: rba
->bbx
[1][2];
1414 manifold
[0][0] = rba
->bbx
[0][0];
1415 manifold
[0][1] = rba
->bbx
[0][1];
1416 manifold
[0][2] = pz
;
1417 manifold
[1][0] = rba
->bbx
[1][0];
1418 manifold
[1][1] = rba
->bbx
[0][1];
1419 manifold
[1][2] = pz
;
1420 manifold
[2][0] = rba
->bbx
[1][0];
1421 manifold
[2][1] = rba
->bbx
[1][1];
1422 manifold
[2][2] = pz
;
1423 manifold
[3][0] = rba
->bbx
[0][0];
1424 manifold
[3][1] = rba
->bbx
[1][1];
1425 manifold
[3][2] = pz
;
1428 for( int j
=0; j
<4; j
++ )
1429 m4x3_mulv( rba
->to_world
, manifold
[j
], manifold
[j
] );
1431 vg_line( manifold
[0], manifold
[1], 0xffffffff );
1432 vg_line( manifold
[1], manifold
[2], 0xffffffff );
1433 vg_line( manifold
[2], manifold
[3], 0xffffffff );
1434 vg_line( manifold
[3], manifold
[0], 0xffffffff );
1436 for( int j
=0; j
<4; j
++ )
1438 rb_ct
*ct
= buf
+count
;
1440 v3_copy( manifold
[j
], ct
->co
);
1441 v3_copy( n
, ct
->n
);
1443 float l0
= v3_dot( tri
[0], n
),
1444 l1
= v3_dot( manifold
[j
], n
);
1446 ct
->p
= (l0
-l1
)*0.5f
;
1461 VG_STATIC
int RB_MATRIX_ERROR( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1463 vg_error( "Collision type is unimplemented between types %d and %d\n",
1464 rba
->type
, rbb
->type
);
1469 VG_STATIC
int rb_sphere_capsule( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1471 return rb_capsule_sphere( rbb
, rba
, buf
);
1474 VG_STATIC
int rb_box_capsule( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1476 return rb_capsule_box( rbb
, rba
, buf
);
1479 VG_STATIC
int rb_box_sphere( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1481 return rb_sphere_box( rbb
, rba
, buf
);
1484 VG_STATIC
int rb_scene_box( rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1486 return rb_box_scene( rbb
, rba
, buf
);
1489 VG_STATIC
int (*rb_jump_table
[4][4])( rigidbody
*a
, rigidbody
*b
, rb_ct
*buf
) =
1491 /* box */ /* Sphere */ /* Capsule */ /* Mesh */
1492 { RB_MATRIX_ERROR
, rb_box_sphere
, rb_box_capsule
, rb_box_scene
},
1493 { rb_sphere_box
, rb_sphere_sphere
, rb_sphere_capsule
, rb_sphere_scene
},
1494 { rb_capsule_box
, rb_capsule_sphere
, rb_capsule_capsule
, RB_MATRIX_ERROR
},
1495 { rb_scene_box
, RB_MATRIX_ERROR
, RB_MATRIX_ERROR
, RB_MATRIX_ERROR
}
1498 VG_STATIC
int rb_collide( rigidbody
*rba
, rigidbody
*rbb
)
1500 int (*collider_jump
)(rigidbody
*rba
, rigidbody
*rbb
, rb_ct
*buf
)
1501 = rb_jump_table
[rba
->type
][rbb
->type
];
1504 * 12 is the maximum manifold size we can generate, so we are forced to abort
1505 * potentially checking any more.
1507 if( rb_contact_count
+ 12 > vg_list_size(rb_contact_buffer
) )
1509 vg_warn( "Too many contacts made in global collider buffer (%d of %d\n)",
1510 rb_contact_count
, vg_list_size(rb_contact_buffer
) );
1515 * FUTURE: Replace this with a more dedicated broad phase pass
1517 if( box_overlap( rba
->bbx_world
, rbb
->bbx_world
) )
1519 int count
= collider_jump( rba
, rbb
, rb_contact_buffer
+rb_contact_count
);
1520 rb_contact_count
+= count
;
1528 * -----------------------------------------------------------------------------
1530 * -----------------------------------------------------------------------------
1533 VG_STATIC
void rb_solver_reset(void)
1535 rb_contact_count
= 0;
1538 VG_STATIC rb_ct
*rb_global_ct(void)
1540 return rb_contact_buffer
+ rb_contact_count
;
1544 * Initializing things like tangent vectors
1546 VG_STATIC
void rb_presolve_contacts( rb_ct
*buffer
, int len
)
1548 for( int i
=0; i
<len
; i
++ )
1550 rb_ct
*ct
= &buffer
[i
];
1551 ct
->bias
= -0.2f
* k_rb_rate
* vg_minf( 0.0f
, -ct
->p
+k_penetration_slop
);
1552 rb_tangent_basis( ct
->n
, ct
->t
[0], ct
->t
[1] );
1554 ct
->norm_impulse
= 0.0f
;
1555 ct
->tangent_impulse
[0] = 0.0f
;
1556 ct
->tangent_impulse
[1] = 0.0f
;
1558 v3f ra
, rb
, raCn
, rbCn
, raCt
, rbCt
;
1559 v3_sub( ct
->co
, ct
->rba
->co
, ra
);
1560 v3_sub( ct
->co
, ct
->rbb
->co
, rb
);
1561 v3_cross( ra
, ct
->n
, raCn
);
1562 v3_cross( rb
, ct
->n
, rbCn
);
1564 /* orient inverse inertia tensors */
1566 m3x3_mulv( ct
->rba
->iIw
, raCn
, raCnI
);
1567 m3x3_mulv( ct
->rbb
->iIw
, rbCn
, rbCnI
);
1569 ct
->normal_mass
= ct
->rba
->inv_mass
+ ct
->rbb
->inv_mass
;
1570 ct
->normal_mass
+= v3_dot( raCn
, raCnI
);
1571 ct
->normal_mass
+= v3_dot( rbCn
, rbCnI
);
1572 ct
->normal_mass
= 1.0f
/ct
->normal_mass
;
1574 for( int j
=0; j
<2; j
++ )
1577 v3_cross( ct
->t
[j
], ra
, raCt
);
1578 v3_cross( ct
->t
[j
], rb
, rbCt
);
1579 m3x3_mulv( ct
->rba
->iIw
, raCt
, raCtI
);
1580 m3x3_mulv( ct
->rbb
->iIw
, rbCt
, rbCtI
);
1582 ct
->tangent_mass
[j
] = ct
->rba
->inv_mass
+ ct
->rbb
->inv_mass
;
1583 ct
->tangent_mass
[j
] += v3_dot( raCt
, raCtI
);
1584 ct
->tangent_mass
[j
] += v3_dot( rbCt
, rbCtI
);
1585 ct
->tangent_mass
[j
] = 1.0f
/ct
->tangent_mass
[j
];
1588 rb_debug_contact( ct
);
1593 * Creates relative contact velocity vector, and offsets between each body
1595 VG_STATIC
void rb_rcv( rb_ct
*ct
, v3f rv
, v3f da
, v3f db
)
1597 rigidbody
*rba
= ct
->rba
,
1600 v3_sub( ct
->co
, rba
->co
, da
);
1601 v3_sub( ct
->co
, rbb
->co
, db
);
1604 v3_cross( rba
->w
, da
, rva
);
1605 v3_add( rba
->v
, rva
, rva
);
1606 v3_cross( rbb
->w
, db
, rvb
);
1607 v3_add( rbb
->v
, rvb
, rvb
);
1609 v3_sub( rva
, rvb
, rv
);
1613 * Apply impulse to object
1615 VG_STATIC
void rb_linear_impulse( rigidbody
*rb
, v3f delta
, v3f impulse
)
1618 v3_muladds( rb
->v
, impulse
, rb
->inv_mass
, rb
->v
);
1620 /* Angular velocity */
1622 v3_cross( delta
, impulse
, wa
);
1624 m3x3_mulv( rb
->iIw
, wa
, wa
);
1625 v3_add( rb
->w
, wa
, rb
->w
);
1629 * One iteration to solve the contact constraint
1631 VG_STATIC
void rb_solve_contacts( rb_ct
*buf
, int len
)
1633 for( int i
=0; i
<len
; i
++ )
1635 struct contact
*ct
= &buf
[i
];
1636 rigidbody
*rb
= ct
->rba
;
1639 rb_rcv( ct
, rv
, da
, db
);
1642 for( int j
=0; j
<2; j
++ )
1644 float f
= k_friction
* ct
->norm_impulse
,
1645 vt
= v3_dot( rv
, ct
->t
[j
] ),
1646 lambda
= ct
->tangent_mass
[j
] * -vt
;
1648 float temp
= ct
->tangent_impulse
[j
];
1649 ct
->tangent_impulse
[j
] = vg_clampf( temp
+ lambda
, -f
, f
);
1650 lambda
= ct
->tangent_impulse
[j
] - temp
;
1653 v3_muls( ct
->t
[j
], lambda
, impulse
);
1654 rb_linear_impulse( ct
->rba
, da
, impulse
);
1656 v3_muls( ct
->t
[j
], -lambda
, impulse
);
1657 rb_linear_impulse( ct
->rbb
, db
, impulse
);
1661 rb_rcv( ct
, rv
, da
, db
);
1662 float vn
= v3_dot( rv
, ct
->n
),
1663 lambda
= ct
->normal_mass
* (-vn
+ ct
->bias
);
1665 float temp
= ct
->norm_impulse
;
1666 ct
->norm_impulse
= vg_maxf( temp
+ lambda
, 0.0f
);
1667 lambda
= ct
->norm_impulse
- temp
;
1670 v3_muls( ct
->n
, lambda
, impulse
);
1671 rb_linear_impulse( ct
->rba
, da
, impulse
);
1673 v3_muls( ct
->n
, -lambda
, impulse
);
1674 rb_linear_impulse( ct
->rbb
, db
, impulse
);
1679 * -----------------------------------------------------------------------------
1681 * -----------------------------------------------------------------------------
1684 VG_STATIC
void draw_angle_limit( v3f c
, v3f major
, v3f minor
,
1685 float amin
, float amax
, float measured
,
1690 v3_muls( major
, f
, ay
);
1691 v3_muls( minor
, f
, ax
);
1693 for( int x
=0; x
<16; x
++ )
1695 float t0
= (float)x
/ 16.0f
,
1696 t1
= (float)(x
+1) / 16.0f
,
1697 a0
= vg_lerpf( amin
, amax
, t0
),
1698 a1
= vg_lerpf( amin
, amax
, t1
);
1701 v3_muladds( c
, ay
, cosf(a0
), p0
);
1702 v3_muladds( p0
, ax
, sinf(a0
), p0
);
1703 v3_muladds( c
, ay
, cosf(a1
), p1
);
1704 v3_muladds( p1
, ax
, sinf(a1
), p1
);
1706 vg_line( p0
, p1
, colour
);
1709 vg_line( c
, p0
, colour
);
1711 vg_line( c
, p1
, colour
);
1715 v3_muladds( c
, ay
, cosf(measured
)*1.2f
, p2
);
1716 v3_muladds( p2
, ax
, sinf(measured
)*1.2f
, p2
);
1717 vg_line( c
, p2
, colour
);
1720 VG_STATIC
void rb_debug_constraint_limits( rigidbody
*ra
, rigidbody
*rb
, v3f lca
,
1723 v3f ax
, ay
, az
, bx
, by
, bz
;
1724 m3x3_mulv( ra
->to_world
, (v3f
){1.0f
,0.0f
,0.0f
}, ax
);
1725 m3x3_mulv( ra
->to_world
, (v3f
){0.0f
,1.0f
,0.0f
}, ay
);
1726 m3x3_mulv( ra
->to_world
, (v3f
){0.0f
,0.0f
,1.0f
}, az
);
1727 m3x3_mulv( rb
->to_world
, (v3f
){1.0f
,0.0f
,0.0f
}, bx
);
1728 m3x3_mulv( rb
->to_world
, (v3f
){0.0f
,1.0f
,0.0f
}, by
);
1729 m3x3_mulv( rb
->to_world
, (v3f
){0.0f
,0.0f
,1.0f
}, bz
);
1732 px
[0] = v3_dot( ay
, by
);
1733 px
[1] = v3_dot( az
, by
);
1735 py
[0] = v3_dot( az
, bz
);
1736 py
[1] = v3_dot( ax
, bz
);
1738 pz
[0] = v3_dot( ax
, bx
);
1739 pz
[1] = v3_dot( ay
, bx
);
1741 float r0
= atan2f( px
[1], px
[0] ),
1742 r1
= atan2f( py
[1], py
[0] ),
1743 r2
= atan2f( pz
[1], pz
[0] );
1746 m4x3_mulv( ra
->to_world
, lca
, c
);
1747 draw_angle_limit( c
, ay
, az
, limits
[0][0], limits
[1][0], r0
, 0xff0000ff );
1748 draw_angle_limit( c
, az
, ax
, limits
[0][1], limits
[1][1], r1
, 0xff00ff00 );
1749 draw_angle_limit( c
, ax
, ay
, limits
[0][2], limits
[1][2], r2
, 0xffff0000 );
1752 VG_STATIC
void rb_limit_cure( rigidbody
*ra
, rigidbody
*rb
, v3f axis
, float d
)
1756 float avx
= v3_dot( ra
->w
, axis
) - v3_dot( rb
->w
, axis
);
1757 float joint_mass
= rb
->inv_mass
+ ra
->inv_mass
;
1758 joint_mass
= 1.0f
/joint_mass
;
1760 float bias
= (k_limit_bias
* k_rb_rate
) * d
,
1761 lambda
= -(avx
+ bias
) * joint_mass
;
1763 /* Angular velocity */
1765 v3_muls( axis
, lambda
* ra
->inv_mass
, wa
);
1766 v3_muls( axis
, -lambda
* rb
->inv_mass
, wb
);
1768 v3_add( ra
->w
, wa
, ra
->w
);
1769 v3_add( rb
->w
, wb
, rb
->w
);
1773 VG_STATIC
void rb_constraint_limits( rigidbody
*ra
, v3f lca
,
1774 rigidbody
*rb
, v3f lcb
, v3f limits
[2] )
1776 v3f ax
, ay
, az
, bx
, by
, bz
;
1777 m3x3_mulv( ra
->to_world
, (v3f
){1.0f
,0.0f
,0.0f
}, ax
);
1778 m3x3_mulv( ra
->to_world
, (v3f
){0.0f
,1.0f
,0.0f
}, ay
);
1779 m3x3_mulv( ra
->to_world
, (v3f
){0.0f
,0.0f
,1.0f
}, az
);
1780 m3x3_mulv( rb
->to_world
, (v3f
){1.0f
,0.0f
,0.0f
}, bx
);
1781 m3x3_mulv( rb
->to_world
, (v3f
){0.0f
,1.0f
,0.0f
}, by
);
1782 m3x3_mulv( rb
->to_world
, (v3f
){0.0f
,0.0f
,1.0f
}, bz
);
1785 px
[0] = v3_dot( ay
, by
);
1786 px
[1] = v3_dot( az
, by
);
1788 py
[0] = v3_dot( az
, bz
);
1789 py
[1] = v3_dot( ax
, bz
);
1791 pz
[0] = v3_dot( ax
, bx
);
1792 pz
[1] = v3_dot( ay
, bx
);
1794 float r0
= atan2f( px
[1], px
[0] ),
1795 r1
= atan2f( py
[1], py
[0] ),
1796 r2
= atan2f( pz
[1], pz
[0] );
1798 /* calculate angle deltas */
1799 float dx
= 0.0f
, dy
= 0.0f
, dz
= 0.0f
;
1801 if( r0
< limits
[0][0] ) dx
= limits
[0][0] - r0
;
1802 if( r0
> limits
[1][0] ) dx
= limits
[1][0] - r0
;
1803 if( r1
< limits
[0][1] ) dy
= limits
[0][1] - r1
;
1804 if( r1
> limits
[1][1] ) dy
= limits
[1][1] - r1
;
1805 if( r2
< limits
[0][2] ) dz
= limits
[0][2] - r2
;
1806 if( r2
> limits
[1][2] ) dz
= limits
[1][2] - r2
;
1809 m3x3_mulv( ra
->to_world
, lca
, wca
);
1810 m3x3_mulv( rb
->to_world
, lcb
, wcb
);
1812 rb_limit_cure( ra
, rb
, ax
, dx
);
1813 rb_limit_cure( ra
, rb
, ay
, dy
);
1814 rb_limit_cure( ra
, rb
, az
, dz
);
1817 VG_STATIC
void rb_debug_constraint_position( rigidbody
*ra
, v3f lca
,
1818 rigidbody
*rb
, v3f lcb
)
1821 m3x3_mulv( ra
->to_world
, lca
, wca
);
1822 m3x3_mulv( rb
->to_world
, lcb
, wcb
);
1825 v3_add( wca
, ra
->co
, p0
);
1826 v3_add( wcb
, rb
->co
, p1
);
1827 vg_line_pt3( p0
, 0.005f
, 0xffffff00 );
1828 vg_line_pt3( p1
, 0.005f
, 0xffffff00 );
1829 vg_line( p0
, p1
, 0xffffff00 );
1832 VG_STATIC
void rb_constraint_position( rigidbody
*ra
, v3f lca
,
1833 rigidbody
*rb
, v3f lcb
)
1835 /* C = (COa + Ra*LCa) - (COb + Rb*LCb) = 0 */
1837 m3x3_mulv( ra
->to_world
, lca
, wca
);
1838 m3x3_mulv( rb
->to_world
, lcb
, wcb
);
1841 v3_sub( ra
->v
, rb
->v
, rcv
);
1844 v3_cross( ra
->w
, wca
, rcv_Ra
);
1845 v3_cross( rb
->w
, wcb
, rcv_Rb
);
1846 v3_add( rcv_Ra
, rcv
, rcv
);
1847 v3_sub( rcv
, rcv_Rb
, rcv
);
1851 v3_add( wca
, ra
->co
, p0
);
1852 v3_add( wcb
, rb
->co
, p1
);
1853 v3_sub( p1
, p0
, delta
);
1855 float dist2
= v3_length2( delta
);
1857 if( dist2
> 0.00001f
)
1859 float dist
= sqrtf(dist2
);
1860 v3_muls( delta
, 1.0f
/dist
, delta
);
1862 float joint_mass
= rb
->inv_mass
+ ra
->inv_mass
;
1864 v3f raCn
, rbCn
, raCt
, rbCt
;
1865 v3_cross( wca
, delta
, raCn
);
1866 v3_cross( wcb
, delta
, rbCn
);
1868 /* orient inverse inertia tensors */
1870 m3x3_mulv( ra
->iIw
, raCn
, raCnI
);
1871 m3x3_mulv( rb
->iIw
, rbCn
, rbCnI
);
1872 joint_mass
+= v3_dot( raCn
, raCnI
);
1873 joint_mass
+= v3_dot( rbCn
, rbCnI
);
1874 joint_mass
= 1.0f
/joint_mass
;
1876 float vd
= v3_dot( rcv
, delta
),
1877 bias
= -(k_joint_bias
* k_rb_rate
) * dist
,
1878 lambda
= -(vd
+ bias
) * joint_mass
;
1881 v3_muls( delta
, lambda
, impulse
);
1882 rb_linear_impulse( ra
, wca
, impulse
);
1883 v3_muls( delta
, -lambda
, impulse
);
1884 rb_linear_impulse( rb
, wcb
, impulse
);
1887 v3_muladds( ra
->co
, delta
, dist
* k_joint_correction
, ra
->co
);
1888 v3_muladds( rb
->co
, delta
, -dist
* k_joint_correction
, rb
->co
);
1896 VG_STATIC
void rb_effect_simple_bouyency( rigidbody
*ra
, v4f plane
,
1897 float amt
, float drag
)
1900 float depth
= v3_dot( plane
, ra
->co
) - plane
[3],
1901 lambda
= vg_clampf( -depth
, 0.0f
, 1.0f
) * amt
;
1903 v3_muladds( ra
->v
, plane
, lambda
* k_rb_delta
, ra
->v
);
1906 v3_muls( ra
->v
, 1.0f
-(drag
*k_rb_delta
), ra
->v
);
1910 * -----------------------------------------------------------------------------
1911 * BVH implementation, this is ONLY for VG_STATIC rigidbodies, its to slow for
1913 * -----------------------------------------------------------------------------
1916 VG_STATIC
void rb_bh_expand_bound( void *user
, boxf bound
, u32 item_index
)
1918 rigidbody
*rb
= &((rigidbody
*)user
)[ item_index
];
1919 box_concat( bound
, rb
->bbx_world
);
1922 VG_STATIC
float rb_bh_centroid( void *user
, u32 item_index
, int axis
)
1924 rigidbody
*rb
= &((rigidbody
*)user
)[ item_index
];
1925 return (rb
->bbx_world
[axis
][0] + rb
->bbx_world
[1][axis
]) * 0.5f
;
1928 VG_STATIC
void rb_bh_swap( void *user
, u32 ia
, u32 ib
)
1930 rigidbody temp
, *rba
, *rbb
;
1931 rba
= &((rigidbody
*)user
)[ ia
];
1932 rbb
= &((rigidbody
*)user
)[ ib
];
1939 VG_STATIC
void rb_bh_debug( void *user
, u32 item_index
)
1941 rigidbody
*rb
= &((rigidbody
*)user
)[ item_index
];
1942 rb_debug( rb
, 0xff00ffff );
1945 VG_STATIC bh_system bh_system_rigidbodies
=
1947 .expand_bound
= rb_bh_expand_bound
,
1948 .item_centroid
= rb_bh_centroid
,
1949 .item_swap
= rb_bh_swap
,
1950 .item_debug
= rb_bh_debug
,
1954 #endif /* RIGIDBODY_H */