* 5.d Raycast & Spherecasts
* 5.e Curves
* 5.f Volumes
+ * 5.g Inertia tensors
* 6. Statistics
* 6.a Random numbers
- **/
+ */
#ifndef VG_M_H
#define VG_M_H
* -----------------------------------------------------------------------------
*/
-static float vg_sphere_volume( float radius ){
- float r3 = radius*radius*radius;
- return (4.0f/3.0f) * VG_PIf * r3;
+static f32 vg_sphere_volume( f32 r ){
+ return (4.0f/3.0f) * VG_PIf * r*r*r;
+}
+
+static f32 vg_box_volume( boxf box ){
+ v3f e;
+ v3_sub( box[1], box[0], e );
+ return e[0]*e[1]*e[2];
+}
+
+static f32 vg_cylinder_volume( f32 r, f32 h ){
+ return VG_PIf * r*r * h;
+}
+
+static f32 vg_capsule_volume( f32 r, f32 h ){
+ return vg_sphere_volume( r ) + vg_cylinder_volume( r, h-r*2.0f );
+}
+
+static void vg_sphere_bound( f32 r, boxf out_box ){
+ v3_fill( out_box[0], -r );
+ v3_fill( out_box[1], r );
+}
+
+static void vg_capsule_bound( f32 r, f32 h, boxf out_box ){
+ v3_copy( (v3f){-r,-h*0.5f,r}, out_box[0] );
+ v3_copy( (v3f){-r, h*0.5f,r}, out_box[1] );
+}
+
+
+/*
+ * -----------------------------------------------------------------------------
+ * Section 5.g Inertia Tensors
+ * -----------------------------------------------------------------------------
+ */
+
+/*
+ * Translate existing inertia tensor
+ */
+static void vg_translate_inertia( m3x3f inout_inertia, f32 mass, v3f d ){
+ /*
+ * I = I_0 + m*[(d.d)E_3 - d(X)d]
+ *
+ * I: updated tensor
+ * I_0: original tensor
+ * m: scalar mass
+ * d: translation vector
+ * (X): outer product
+ * E_3: identity matrix
+ */
+ m3x3f t, outer, scale;
+ m3x3_diagonal( t, v3_dot(d,d) );
+ m3x3_outer_product( outer, d, d );
+ m3x3_sub( t, outer, t );
+ m3x3_diagonal( scale, mass );
+ m3x3_mul( scale, t, t );
+ m3x3_add( inout_inertia, t, inout_inertia );
+}
+
+/*
+ * Rotate existing inertia tensor
+ */
+static void vg_rotate_inertia( m3x3f inout_inertia, m3x3f rotation ){
+ /*
+ * I = R I_0 R^T
+ *
+ * I: updated tensor
+ * I_0: original tensor
+ * R: rotation matrix
+ * R^T: tranposed rotation matrix
+ */
+
+ m3x3f Rt;
+ m3x3_transpose( rotation, Rt );
+ m3x3_mul( rotation, inout_inertia, inout_inertia );
+ m3x3_mul( inout_inertia, Rt, inout_inertia );
+}
+/*
+ * Create inertia tensor for box
+ */
+static void vg_box_inertia( boxf box, f32 mass, m3x3f out_inertia ){
+ v3f e, com;
+ v3_sub( box[1], box[0], e );
+ v3_muladds( box[0], e, 0.5f, com );
+
+ f32 ex2 = e[0]*e[0],
+ ey2 = e[1]*e[1],
+ ez2 = e[2]*e[2],
+ ix = (ey2+ez2) * mass * (1.0f/12.0f),
+ iy = (ex2+ez2) * mass * (1.0f/12.0f),
+ iz = (ex2+ey2) * mass * (1.0f/12.0f);
+
+ m3x3_identity( out_inertia );
+ m3x3_setdiagonalv3( out_inertia, (v3f){ ix, iy, iz } );
+ vg_translate_inertia( out_inertia, mass, com );
+}
+
+/*
+ * Create inertia tensor for sphere
+ */
+static void vg_sphere_inertia( f32 r, f32 mass, m3x3f out_inertia ){
+ f32 ixyz = r*r * mass * (2.0f/5.0f);
+
+ m3x3_identity( out_inertia );
+ m3x3_setdiagonalv3( out_inertia, (v3f){ ixyz, ixyz, ixyz } );
+}
+
+/*
+ * Create inertia tensor for capsule
+ */
+static void vg_capsule_inertia( f32 r, f32 h, f32 mass, m3x3f out_inertia ){
+ f32 density = mass / vg_capsule_volume( r, h ),
+ ch = h-r*2.0f, /* cylinder height */
+ cm = VG_PIf * ch*r*r * density, /* cylinder mass */
+ hm = VG_TAUf * (1.0f/3.0f) * r*r*r * density, /* hemisphere mass */
+
+ iy = r*r*cm * 0.5f,
+ ixz = iy * 0.5f + cm*ch*ch*(1.0f/12.0f),
+
+ aux0= (hm*2.0f*r*r)/5.0f;
+
+ iy += aux0 * 2.0f;
+
+ f32 aux1= ch*0.5f,
+ aux2= aux0 + hm*(aux1*aux1 + 3.0f*(1.0f/8.0f)*ch*r);
+
+ ixz += aux2*2.0f;
+
+ m3x3_identity( out_inertia );
+ m3x3_setdiagonalv3( out_inertia, (v3f){ ixz, iy, ixz } );
}
/*
--- /dev/null
+#pragma once
+
+/*
+ * Copyright (C) 2021-2024 Mt.ZERO Software - All Rights Reserved
+ *
+ * Rigidbody main file, related:
+ * vg_rigidbody_collision.h
+ * vg_rigidbody_constraints.h
+ */
+
+#include "vg_console.h"
+#include <math.h>
+
+/*
+ * -----------------------------------------------------------------------------
+ * (K)onstants
+ * -----------------------------------------------------------------------------
+ */
+
+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 = 4.0f,
+ k_phys_baumgarte = 0.2f,
+ k_gravity = 9.6f,
+ k_rb_density = 8.0f;
+
+static float
+ k_limit_bias = 0.02f,
+ k_joint_correction = 0.01f,
+ k_joint_impulse = 1.0f,
+ k_joint_bias = 0.08f; /* positional joints */
+
+static void rb_register_cvar(void){
+ VG_VAR_F32( k_limit_bias, flags=VG_VAR_CHEAT );
+ VG_VAR_F32( k_joint_bias, flags=VG_VAR_CHEAT );
+ VG_VAR_F32( k_joint_correction, flags=VG_VAR_CHEAT );
+ VG_VAR_F32( k_joint_impulse, flags=VG_VAR_CHEAT );
+}
+
+enum rb_shape {
+ k_rb_shape_none = 0,
+ k_rb_shape_box = 1,
+ k_rb_shape_sphere = 2,
+ k_rb_shape_capsule = 3,
+};
+
+/*
+ * -----------------------------------------------------------------------------
+ * structure definitions
+ * -----------------------------------------------------------------------------
+ */
+
+typedef struct rigidbody rigidbody;
+typedef struct rb_capsule rb_capsule;
+
+struct rb_capsule{
+ f32 h, r;
+};
+
+struct rigidbody{
+ v3f co, v, w;
+ v4f q;
+
+ f32 inv_mass;
+
+ m3x3f iI, iIw; /* inertia model and inverse world tensor */
+ m4x3f to_world, to_local;
+};
+
+/*
+ * Initialize rigidbody inverse mass and inertia tensor with some common shapes
+ */
+static void rb_setbody_capsule( rigidbody *rb, f32 r, f32 h,
+ f32 density, f32 inertia_scale ){
+ f32 vol = vg_capsule_volume( r, h ),
+ mass = vol*density;
+
+ rb->inv_mass = 1.0f/mass;
+
+ m3x3f I;
+ vg_capsule_inertia( r, h, mass * inertia_scale, I );
+ m3x3_inv( I, rb->iI );
+}
+
+static void rb_setbody_box( rigidbody *rb, boxf box,
+ f32 density, f32 inertia_scale ){
+ f32 vol = vg_box_volume( box ),
+ mass = vol*density;
+
+ rb->inv_mass = 1.0f/mass;
+
+ m3x3f I;
+ vg_box_inertia( box, mass * inertia_scale, I );
+ m3x3_inv( I, rb->iI );
+}
+
+static void rb_setbody_sphere( rigidbody *rb, f32 r,
+ f32 density, f32 inertia_scale ){
+ f32 vol = vg_sphere_volume( r ),
+ mass = vol*density;
+
+ rb->inv_mass = 1.0f/mass;
+ m3x3f I;
+ vg_sphere_inertia( r, mass * inertia_scale, I );
+ m3x3_inv( I, rb->iI );
+}
+
+/*
+ * Update ALL matrices and tensors on rigidbody
+ */
+static void rb_update_matrices( 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 );
+
+ /* I = R I_0 R^T */
+ m3x3_mul( rb->to_world, rb->iI, rb->iIw );
+ m3x3_mul( rb->iIw, rb->to_local, rb->iIw );
+}
+
+/*
+ * Extrapolate rigidbody into a transform based on vg accumulator.
+ * Useful for rendering
+ */
+static void rb_extrapolate( rigidbody *rb, v3f co, v4f q ){
+ float substep = vg.time_fixed_extrapolate;
+ 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 );
+ }
+}
+
+static void rb_iter( rigidbody *rb ){
+ if( !vg_validf( rb->v[0] ) ||
+ !vg_validf( rb->v[1] ) ||
+ !vg_validf( rb->v[2] ) )
+ {
+ vg_fatal_error( "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 );
+ q_normalize( rb->q );
+ }
+}
+
+/*
+ * Creates relative contact velocity vector
+ */
+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
+ */
+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 );
+}
+
+/*
+ * Effectors
+ */
+
+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 );
+}
+
+/* apply a spring&dampener force to match ra(worldspace) on rigidbody, to
+ * rt(worldspace)
+ */
+static void rb_effect_spring_target_vector( rigidbody *rba, v3f ra, v3f rt,
+ float spring, float dampening,
+ float timestep ){
+ float d = v3_dot( rt, ra );
+ float a = acosf( vg_clampf( d, -1.0f, 1.0f ) );
+
+ v3f axis;
+ v3_cross( rt, ra, axis );
+
+ float Fs = -a * spring,
+ Fd = -v3_dot( rba->w, axis ) * dampening;
+
+ v3_muladds( rba->w, axis, (Fs+Fd) * timestep, rba->w );
+}
--- /dev/null
+#pragma once
+#include "vg_rigidbody.h"
+
+typedef struct rb_ct rb_ct;
+static struct rb_ct{
+ 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];
+static int rb_contact_count = 0;
+
+/*
+ * 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{
+ f32 t0, t1;
+ f32 r0, r1;
+ v3f d0, d1;
+};
+
+/*
+ * Expand a line manifold with a new pair. t value is the time along segment
+ * on the oriented object which created this pair.
+ */
+static void rb_capsule_manifold( v3f pa, v3f pb, f32 t, f32 r,
+ capsule_manifold *manifold ){
+ v3f delta;
+ v3_sub( pa, pb, delta );
+
+ if( v3_length2(delta) < r*r ){
+ if( t < manifold->t0 ){
+ v3_copy( delta, manifold->d0 );
+ manifold->t0 = t;
+ manifold->r0 = r;
+ }
+
+ if( t > manifold->t1 ){
+ v3_copy( delta, manifold->d1 );
+ manifold->t1 = t;
+ manifold->r1 = r;
+ }
+ }
+}
+
+static void rb_capsule_manifold_init( capsule_manifold *manifold ){
+ manifold->t0 = INFINITY;
+ manifold->t1 = -INFINITY;
+}
+
+static int rb_capsule__manifold_done( m4x3f mtx, rb_capsule *c,
+ capsule_manifold *manifold,
+ rb_ct *buf ){
+ v3f p0, p1;
+ v3_muladds( mtx[3], mtx[1], -c->h*0.5f+c->r, p0 );
+ v3_muladds( mtx[3], mtx[1], c->h*0.5f-c->r, 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 );
+
+ f32 d = v3_length( manifold->d0 );
+ v3_muls( manifold->d0, 1.0f/d, ct->n );
+ v3_muladds( pa, ct->n, -c->r, 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 );
+
+ f32 d = v3_length( manifold->d1 );
+ v3_muls( manifold->d1, 1.0f/d, ct->n );
+ v3_muladds( pa, ct->n, -c->r, 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;
+}
+
+#if 0
+static int rb_capsule_sphere( rb_object *obja, rb_object *objb, rb_ct *buf ){
+ rigidbody *rba = &obja->rb, *rbb = &objb->rb;
+ f32 h = obja->inf.capsule.h,
+ ra = obja->inf.capsule.r,
+ rb = objb->inf.sphere.r;
+
+ v3f p0, p1;
+ v3_muladds( rba->co, rba->to_world[1], -h*0.5f+ra, p0 );
+ v3_muladds( rba->co, rba->to_world[1], h*0.5f-ra, p1 );
+
+ v3f c, delta;
+ closest_point_segment( p0, p1, rbb->co, c );
+ v3_sub( c, rbb->co, delta );
+
+ f32 d2 = v3_length2(delta),
+ r = ra + rb;
+
+ if( d2 < r*r ){
+ f32 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;
+}
+#endif
+
+static int rb_capsule__capsule( m4x3f mtxA, rb_capsule *ca,
+ m4x3f mtxB, rb_capsule *cb, rb_ct *buf ){
+ f32 ha = ca->h,
+ hb = cb->h,
+ ra = ca->r,
+ rb = cb->r,
+ r = ra+rb;
+
+ v3f p0, p1, p2, p3;
+ v3_muladds( mtxA[3], mtxA[1], -ha*0.5f+ra, p0 );
+ v3_muladds( mtxA[3], mtxA[1], ha*0.5f-ra, p1 );
+ v3_muladds( mtxB[3], mtxB[1], -hb*0.5f+rb, p2 );
+ v3_muladds( mtxB[3], mtxB[1], hb*0.5f-rb, p3 );
+
+ capsule_manifold manifold;
+ rb_capsule_manifold_init( &manifold );
+
+ v3f pa, pb;
+ f32 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( mtxA, ca, &manifold, buf );
+}
+
+#if 0
+static int rb_sphere_box( rb_object *obja, rb_object *objb, rb_ct *buf ){
+ v3f co, delta;
+ rigidbody *rba = &obja->rb, *rbb = &objb->rb;
+
+ closest_point_obb( rba->co, rbb->bbx, rbb->to_world, rbb->to_local, co );
+ v3_sub( rba->co, co, delta );
+
+ f32 d2 = v3_length2(delta),
+ r = obja->inf.sphere.radius;
+
+ if( d2 <= r*r ){
+ f32 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.
+ */
+ f32 lx = v3_dot( rbb->to_world[0], delta ),
+ ly = v3_dot( rbb->to_world[1], delta ),
+ lz = v3_dot( rbb->to_world[2], 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->to_world[0], vg_signf(lx), ct->n );
+ else if( py < pz )
+ v3_muls( rbb->to_world[1], vg_signf(ly), ct->n );
+ else
+ v3_muls( rbb->to_world[2], 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;
+}
+#endif
+
+#if 0
+static int rb_sphere_sphere( rb_object *obja, rb_object *objb, rb_ct *buf ){
+ rigidbody *rba = &obja->rb, *rbb = &objb->rb;
+ v3f delta;
+ v3_sub( rba->co, rbb->co, delta );
+
+ f32 d2 = v3_length2(delta),
+ r = obja->inf.sphere.radius + objb->inf.sphere.radius;
+
+ if( d2 < r*r ){
+ f32 d = sqrtf(d2);
+
+ rb_ct *ct = buf;
+ v3_muls( delta, 1.0f/d, ct->n );
+
+ v3f p0, p1;
+ v3_muladds( rba->co, ct->n,-obja->inf.sphere.radius, p0 );
+ v3_muladds( rbb->co, ct->n, objb->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;
+}
+#endif
+
+static int rb_sphere__triangle( m4x3f mtxA, f32 r,
+ 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 );
+ f32 d2 = v3_length2( delta );
+
+ 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 ){
+#ifdef RIGIDBODY_CRY_ABOUT_EVERYTHING
+ vg_error( "Zero area triangle!\n" );
+#endif
+ return 0;
+ }
+
+ v3_normalize( ct->n );
+
+ f32 d = sqrtf(d2);
+
+ v3_copy( co, ct->co );
+ ct->type = type;
+ ct->p = r-d;
+ return 1;
+ }
+
+ return 0;
+}
+
+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->h*0.5f+c->r, p0w );
+ v3_muladds( mtxA[3], mtxA[1], c->h*0.5f-c->r, p1w );
+
+ capsule_manifold manifold;
+ rb_capsule_manifold_init( &manifold );
+
+ v3f v0, v1, n;
+ v3_sub( tri[1], tri[0], v0 );
+ v3_sub( tri[2], tri[0], v1 );
+ v3_cross( v0, v1, n );
+
+ if( v3_length2( n ) <= 0.00001f ){
+#ifdef RIGIDBODY_CRY_ABOUT_EVERYTHING
+ vg_error( "Zero area triangle!\n" );
+#endif
+ return 0;
+ }
+
+ v3_normalize( n );
+
+#if 1
+ /* deep penetration recovery. for when we clip through the triangles. so its
+ * not very 'correct' */
+ f32 dist;
+ if( ray_tri( tri, p0w, mtxA[1], &dist, 1 ) ){
+ f32 l = c->h - c->r*2.0f;
+ if( (dist >= 0.0f) && (dist < l) ){
+ v3f co;
+ v3_muladds( p0w, mtxA[1], dist, co );
+ vg_line_point( co, 0.02f, 0xffffff00 );
+
+ v3f d0, d1;
+ v3_sub( p0w, co, d0 );
+ v3_sub( p1w, co, d1 );
+
+ f32 p = vg_minf( v3_dot( n, d0 ), v3_dot( n, d1 ) ) - c->r;
+
+ rb_ct *ct = buf;
+ ct->p = -p;
+ ct->type = k_contact_type_default;
+ v3_copy( n, ct->n );
+ v3_muladds( co, n, p, ct->co );
+
+ return 1;
+ }
+ }
+#endif
+
+ 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);
+
+ /* the two balls at the ends */
+ if( v3_dot( da, d0 ) <= 0.01f )
+ rb_capsule_manifold( p0w, c0, 0.0f, c->r, &manifold );
+ if( v3_dot( da, d1 ) >= -0.01f )
+ rb_capsule_manifold( p1w, c1, 1.0f, c->r, &manifold );
+
+ /* the edges to edges */
+ for( int i=0; i<3; i++ ){
+ int i0 = i,
+ i1 = (i+1)%3;
+
+ v3f ca, cb;
+ f32 ta, tb;
+ closest_segment_segment( p0w, p1w, tri[i0], tri[i1], &ta, &tb, ca, cb );
+ rb_capsule_manifold( ca, cb, ta, c->r, &manifold );
+ }
+
+ 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;
+}
+
+static int rb_global_has_space( void ){
+ if( rb_contact_count + 16 > vg_list_size(rb_contact_buffer) )
+ return 0;
+
+ return 1;
+}
+
+static rb_ct *rb_global_buffer( void ){
+ return &rb_contact_buffer[ rb_contact_count ];
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Boolean shape overlap functions
+ * -----------------------------------------------------------------------------
+ */
+
+/*
+ * Project AABB, and triangle interval onto axis to check if they overlap
+ */
+static int rb_box_triangle_interval( v3f extent, v3f axis, v3f tri[3] ){
+ float
+
+ r = extent[0] * fabsf(axis[0]) +
+ extent[1] * fabsf(axis[1]) +
+ extent[2] * fabsf(axis[2]),
+
+ p0 = v3_dot( axis, tri[0] ),
+ p1 = v3_dot( axis, tri[1] ),
+ p2 = v3_dot( axis, tri[2] ),
+
+ e = vg_maxf(-vg_maxf(p0,vg_maxf(p1,p2)), vg_minf(p0,vg_minf(p1,p2)));
+
+ if( e > r ) return 0;
+ else return 1;
+}
+
+/*
+ * Seperating axis test box vs triangle
+ */
+static int rb_box_triangle_sat( v3f extent, v3f center,
+ m4x3f to_local, v3f tri_src[3] ){
+ v3f tri[3];
+
+ for( int i=0; i<3; i++ ){
+ m4x3_mulv( to_local, tri_src[i], tri[i] );
+ v3_sub( tri[i], center, tri[i] );
+ }
+
+ v3f f0,f1,f2,n;
+ v3_sub( tri[1], tri[0], f0 );
+ v3_sub( tri[2], tri[1], f1 );
+ v3_sub( tri[0], tri[2], f2 );
+
+
+ v3f axis[9];
+ v3_cross( (v3f){1.0f,0.0f,0.0f}, f0, axis[0] );
+ v3_cross( (v3f){1.0f,0.0f,0.0f}, f1, axis[1] );
+ v3_cross( (v3f){1.0f,0.0f,0.0f}, f2, axis[2] );
+ v3_cross( (v3f){0.0f,1.0f,0.0f}, f0, axis[3] );
+ v3_cross( (v3f){0.0f,1.0f,0.0f}, f1, axis[4] );
+ v3_cross( (v3f){0.0f,1.0f,0.0f}, f2, axis[5] );
+ v3_cross( (v3f){0.0f,0.0f,1.0f}, f0, axis[6] );
+ v3_cross( (v3f){0.0f,0.0f,1.0f}, f1, axis[7] );
+ v3_cross( (v3f){0.0f,0.0f,1.0f}, f2, axis[8] );
+
+ for( int i=0; i<9; i++ )
+ if(!rb_box_triangle_interval( extent, axis[i], tri )) return 0;
+
+ /* 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;
+
+ /* normal */
+ v3_cross( f0, f1, n );
+ if(!rb_box_triangle_interval( extent, n, tri )) return 0;
+
+ return 1;
+}
+
+/*
+ * -----------------------------------------------------------------------------
+ * Manifold
+ * -----------------------------------------------------------------------------
+ */
+
+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
+ */
+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 );
+ }
+ }
+}
+
+/*
+ *
+ */
+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
+ */
+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
+ */
+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.
+ */
+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;
+ }
+ }
+ }
+}
+
+static void rb_debug_contact( rb_ct *ct ){
+ v3f p1;
+ v3_muladds( ct->co, ct->n, 0.05f, p1 );
+
+ if( ct->type == k_contact_type_default ){
+ vg_line_point( ct->co, 0.0125f, 0xff0000ff );
+ vg_line( ct->co, p1, 0xffffffff );
+ }
+ else if( ct->type == k_contact_type_edge ){
+ vg_line_point( ct->co, 0.0125f, 0xff00ffc0 );
+ vg_line( ct->co, p1, 0xffffffff );
+ }
+}
+
+static void rb_solver_reset(void){
+ rb_contact_count = 0;
+}
+
+static rb_ct *rb_global_ct(void){
+ return rb_contact_buffer + rb_contact_count;
+}
+
+static void rb_prepare_contact( rb_ct *ct, float timestep ){
+ ct->bias = -k_phys_baumgarte * (timestep*3600.0f)
+ * vg_minf( 0.0f, -ct->p+k_penetration_slop );
+
+ v3_tangent_basis( ct->n, ct->t[0], ct->t[1] );
+ ct->norm_impulse = 0.0f;
+ ct->tangent_impulse[0] = 0.0f;
+ ct->tangent_impulse[1] = 0.0f;
+}
+
+/*
+ * calculate total move to depenetrate object from contacts.
+ * manifold should belong to ONE object only
+ */
+static void rb_depenetrate( rb_ct *manifold, int len, v3f dt ){
+ v3_zero( dt );
+
+ for( int j=0; j<7; j++ ){
+ for( int i=0; i<len; i++ ){
+ rb_ct *ct = &manifold[i];
+
+ float resolved_amt = v3_dot( ct->n, dt ),
+ remaining = (ct->p-k_penetration_slop) - resolved_amt,
+ apply = vg_maxf( remaining, 0.0f ) * 0.4f;
+
+ v3_muladds( dt, ct->n, apply, dt );
+ }
+ }
+}
+
+/*
+ * Initializing things like tangent vectors
+ */
+static void rb_presolve_contacts( rb_ct *buffer, int len ){
+ for( int i=0; i<len; i++ ){
+ rb_ct *ct = &buffer[i];
+ rb_prepare_contact( ct, k_rb_delta );
+
+ 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 );
+ }
+}
+
+static void rb_contact_restitution( rb_ct *ct, float cr ){
+ 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 );
+
+ float v = v3_dot( rv, ct->n );
+
+ if( v < -1.0f ){
+ ct->bias += -cr * v;
+ }
+}
+
+/*
+ * One iteration to solve the contact constraint
+ */
+static void rb_solve_contacts( rb_ct *buf, int len ){
+ for( int i=0; i<len; i++ ){
+ rb_ct *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 );
+ }
+}
+
--- /dev/null
+#pragma once
+#include "vg_rigidbody.h"
+
+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;
+
+ f32 conv_tangent, conv_axis;
+};
+
+/*
+ * -----------------------------------------------------------------------------
+ * Constraints
+ * -----------------------------------------------------------------------------
+ */
+
+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_point( p0, 0.0025f, 0xff000000 );
+ vg_line_point( p1, 0.0025f, 0xffffffff );
+ vg_line2( p0, p1, 0xff000000, 0xffffffff );
+ }
+}
+
+static void rb_presolve_swingtwist_constraints( rb_constr_swingtwist *buf,
+ int len ){
+ 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 ));
+ }
+ }
+}
+
+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_point( p1, 0.00025f, 0xffffffff );
+
+ if( st->tangent_violation ){
+ v3_muladds( center, st->tangent_target, size, p0 );
+
+ vg_line( center, p0, 0xff00ff00 );
+ vg_line_point( 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_point( 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
+ */
+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 );
+ }
+}
+
+static void rb_solve_swingtwist_constraints( rb_constr_swingtwist *buf,
+ int len ){
+ 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 );
+ }
+}
+
+/* debugging */
+static void rb_postsolve_swingtwist_constraints( rb_constr_swingtwist *buf,
+ u32 len ){
+ for( int i=0; i<len; i++ ){
+ rb_constr_swingtwist *st = &buf[ i ];
+
+ if( !st->axis_violation ){
+ st->conv_axis = 0.0f;
+ continue;
+ }
+
+ f32 rv = v3_dot( st->axis, st->rbb->w ) -
+ v3_dot( st->axis, st->rba->w );
+
+ if( rv * (f32)st->axis_violation > 0.0f )
+ st->conv_axis = 0.0f;
+ else
+ st->conv_axis = rv;
+ }
+
+ for( int i=0; i<len; i++ ){
+ rb_constr_swingtwist *st = &buf[ i ];
+
+ if( !st->tangent_violation ){
+ st->conv_tangent = 0.0f;
+ continue;
+ }
+
+ f32 rv = v3_dot( st->tangent_axis, st->rbb->w ) -
+ v3_dot( st->tangent_axis, st->rba->w );
+
+ if( rv > 0.0f )
+ st->conv_tangent = 0.0f;
+ else
+ st->conv_tangent = rv;
+ }
+}
+
+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
+ */
+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 );
+
+#if 1
+ v3_muladds( rbb->co, d, -1.0f * amt, rbb->co );
+ rb_update_matrices( rbb );
+#else
+ f32 mt = 1.0f/(rba->inv_mass+rbb->inv_mass),
+ a = mt * (k_phys_baumgarte/k_rb_delta);
+
+ v3_muladds( rba->v, d, a* rba->inv_mass, rba->v );
+ v3_muladds( rbb->v, d, a*-rbb->inv_mass, rbb->v );
+#endif
+ }
+}
+
+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 );
+
+ f32 angle = v3_dot( va, st->tangent_target );
+
+ if( fabsf(angle) < 0.9999f ){
+ v3f axis;
+ v3_cross( va, st->tangent_target, axis );
+#if 1
+ angle = acosf(angle) * amt;
+ v4f correction;
+ q_axis_angle( correction, axis, angle );
+ q_mul( correction, st->rbb->q, st->rbb->q );
+ q_normalize( st->rbb->q );
+ rb_update_matrices( st->rbb );
+#else
+ f32 mt = 1.0f/(st->rba->inv_mass+st->rbb->inv_mass),
+ wa = mt * acosf(angle) * (k_phys_baumgarte/k_rb_delta);
+ //v3_muladds( st->rba->w, axis, wa*-st->rba->inv_mass, st->rba->w );
+ v3_muladds( st->rbb->w, axis, wa* st->rbb->inv_mass, st->rbb->w );
+#endif
+ }
+ }
+
+ 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 );
+
+ f32 angle = v3_dot( vxb, st->axis_target );
+
+ if( fabsf(angle) < 0.9999f ){
+ v3f axis;
+ v3_cross( vxb, st->axis_target, axis );
+
+#if 1
+ angle = acosf(angle) * amt;
+ v4f correction;
+ q_axis_angle( correction, axis, angle );
+ q_mul( correction, st->rbb->q, st->rbb->q );
+ q_normalize( st->rbb->q );
+ rb_update_matrices( st->rbb );
+#else
+ f32 mt = 1.0f/(st->rba->inv_mass+st->rbb->inv_mass),
+ wa = mt * acosf(angle) * (k_phys_baumgarte/k_rb_delta);
+ //v3_muladds( st->rba->w, axis, wa*-0.5f, st->rba->w );
+ v3_muladds( st->rbb->w, axis, wa* st->rbb->inv_mass, st->rbb->w );
+#endif
+ }
+ }
+}
projects / vg.git / commitdiff