void
cpDampedSpring(cpBody *a, cpBody *b, cpVect anchr1, cpVect anchr2, cpFloat rlen, cpFloat k, cpFloat dmp, cpFloat dt)
{
// Calculate the world space anchor coordinates.
cpVect r1 = cpvrotate(anchr1, a->rot);
cpVect r2 = cpvrotate(anchr2, b->rot);
cpVect delta = cpvsub(cpvadd(b->p, r2), cpvadd(a->p, r1));
cpFloat dist = cpvlength(delta);
cpVect n = dist ? cpvmult(delta, 1.0f/dist) : cpvzero;
cpFloat f_spring = (dist - rlen)*k;
// Calculate the world relative velocities of the anchor points.
cpVect v1 = cpvadd(a->v, cpvmult(cpvperp(r1), a->w));
cpVect v2 = cpvadd(b->v, cpvmult(cpvperp(r2), b->w));
// Calculate the damping force.
// This really should be in the impulse solver and can produce problems when using large damping values.
cpFloat vrn = cpvdot(cpvsub(v2, v1), n);
cpFloat f_damp = vrn*cpfmin(dmp, 1.0f/(dt*(a->m_inv + b->m_inv)));
// Apply!
cpVect f = cpvmult(n, f_spring + f_damp);
cpBodyApplyForce(a, f, r1);
cpBodyApplyForce(b, cpvneg(f), r2);
}
void
cpArbiterApplyImpulse(cpArbiter *arb)
{
cpBody *a = arb->a->body;
cpBody *b = arb->b->body;
for(int i=0; i<arb->numContacts; i++){
cpContact *con = &arb->contacts[i];
cpVect n = con->n;
cpVect r1 = con->r1;
cpVect r2 = con->r2;
// Calculate the relative bias velocities.
cpVect vb1 = cpvadd(a->v_bias, cpvmult(cpvperp(r1), a->w_bias));
cpVect vb2 = cpvadd(b->v_bias, cpvmult(cpvperp(r2), b->w_bias));
cpFloat vbn = cpvdot(cpvsub(vb2, vb1), n);
// Calculate and clamp the bias impulse.
cpFloat jbn = (con->bias - vbn)*con->nMass;
cpFloat jbnOld = con->jBias;
con->jBias = cpfmax(jbnOld + jbn, 0.0f);
jbn = con->jBias - jbnOld;
// Apply the bias impulse.
cpVect jb = cpvmult(n, jbn);
cpBodyApplyBiasImpulse(a, cpvneg(jb), r1);
cpBodyApplyBiasImpulse(b, jb, r2);
// Calculate the relative velocity.
cpVect v1 = cpvadd(a->v, cpvmult(cpvperp(r1), a->w));
cpVect v2 = cpvadd(b->v, cpvmult(cpvperp(r2), b->w));
cpVect vr = cpvsub(v2, v1);
cpFloat vrn = cpvdot(vr, n);
// Calculate and clamp the normal impulse.
cpFloat jn = -(con->bounce + vrn)*con->nMass;
cpFloat jnOld = con->jnAcc;
con->jnAcc = cpfmax(jnOld + jn, 0.0f);
jn = con->jnAcc - jnOld;
// Calculate the relative tangent velocity.
cpVect t = cpvperp(n);
cpFloat vrt = cpvdot(cpvadd(vr, arb->target_v), t);
// Calculate and clamp the friction impulse.
cpFloat jtMax = arb->u*con->jnAcc;
cpFloat jt = -vrt*con->tMass;
cpFloat jtOld = con->jtAcc;
con->jtAcc = cpfmin(cpfmax(jtOld + jt, -jtMax), jtMax);
jt = con->jtAcc - jtOld;
// Apply the final impulse.
cpVect j = cpvadd(cpvmult(n, jn), cpvmult(t, jt));
cpBodyApplyImpulse(a, cpvneg(j), r1);
cpBodyApplyImpulse(b, j, r2);
}
}
void
cpArbiterPreStep(cpArbiter *arb, cpFloat dt_inv)
{
cpShape *shapea = arb->a;
cpShape *shapeb = arb->b;
arb->e = shapea->e * shapeb->e;
arb->u = shapea->u * shapeb->u;
arb->target_v = cpvsub(shapeb->surface_v, shapea->surface_v);
cpBody *a = shapea->body;
cpBody *b = shapeb->body;
for(int i=0; i<arb->numContacts; i++){
cpContact *con = &arb->contacts[i];
// Calculate the offsets.
con->r1 = cpvsub(con->p, a->p);
con->r2 = cpvsub(con->p, b->p);
// Calculate the mass normal.
cpFloat mass_sum = a->m_inv + b->m_inv;
cpFloat r1cn = cpvcross(con->r1, con->n);
cpFloat r2cn = cpvcross(con->r2, con->n);
cpFloat kn = mass_sum + a->i_inv*r1cn*r1cn + b->i_inv*r2cn*r2cn;
con->nMass = 1.0f/kn;
// Calculate the mass tangent.
cpVect t = cpvperp(con->n);
cpFloat r1ct = cpvcross(con->r1, t);
cpFloat r2ct = cpvcross(con->r2, t);
cpFloat kt = mass_sum + a->i_inv*r1ct*r1ct + b->i_inv*r2ct*r2ct;
con->tMass = 1.0f/kt;
// Calculate the target bias velocity.
con->bias = -cp_bias_coef*dt_inv*cpfmin(0.0f, con->dist + cp_collision_slop);
con->jBias = 0.0f;
// Calculate the target bounce velocity.
cpVect v1 = cpvadd(a->v, cpvmult(cpvperp(con->r1), a->w));
cpVect v2 = cpvadd(b->v, cpvmult(cpvperp(con->r2), b->w));
con->bounce = cpvdot(con->n, cpvsub(v2, v1))*arb->e;
// Apply the previous accumulated impulse.
cpVect j = cpvadd(cpvmult(con->n, con->jnAcc), cpvmult(t, con->jtAcc));
cpBodyApplyImpulse(a, cpvneg(j), con->r1);
cpBodyApplyImpulse(b, j, con->r2);
}
}
void
cpArbiterApplyImpulse(cpArbiter *arb, cpFloat eCoef)
{
cpBody *a = arb->a->body;
cpBody *b = arb->b->body;
for(int i=0; i<arb->numContacts; i++){
cpContact *con = &arb->contacts[i];
cpVect n = con->n;
cpVect r1 = con->r1;
cpVect r2 = con->r2;
// Calculate the relative bias velocities.
cpVect vb1 = cpvadd(a->v_bias, cpvmult(cpvperp(r1), a->w_bias));
cpVect vb2 = cpvadd(b->v_bias, cpvmult(cpvperp(r2), b->w_bias));
cpFloat vbn = cpvdot(cpvsub(vb2, vb1), n);
// Calculate and clamp the bias impulse.
cpFloat jbn = (con->bias - vbn)*con->nMass;
cpFloat jbnOld = con->jBias;
con->jBias = cpfmax(jbnOld + jbn, 0.0f);
jbn = con->jBias - jbnOld;
// Apply the bias impulse.
apply_bias_impulses(a, b, r1, r2, cpvmult(n, jbn));
// Calculate the relative velocity.
cpVect vr = relative_velocity(a, b, r1, r2);
cpFloat vrn = cpvdot(vr, n);
// Calculate and clamp the normal impulse.
cpFloat jn = -(con->bounce*eCoef + vrn)*con->nMass;
cpFloat jnOld = con->jnAcc;
con->jnAcc = cpfmax(jnOld + jn, 0.0f);
jn = con->jnAcc - jnOld;
// Calculate the relative tangent velocity.
cpFloat vrt = cpvdot(cpvadd(vr, arb->surface_vr), cpvperp(n));
// Calculate and clamp the friction impulse.
cpFloat jtMax = arb->u*con->jnAcc;
cpFloat jt = -vrt*con->tMass;
cpFloat jtOld = con->jtAcc;
con->jtAcc = cpfclamp(jtOld + jt, -jtMax, jtMax);
jt = con->jtAcc - jtOld;
// Apply the final impulse.
apply_impulses(a, b, r1, r2, cpvrotate(n, cpv(jn, jt)));
}
}
static void
setUpVerts(cpPolyShape *poly, int numVerts, const cpVect *verts, cpVect offset)
{
// Fail if the user attempts to pass a concave poly, or a bad winding.
cpAssertHard(cpPolyValidate(verts, numVerts), "Polygon is concave or has a reversed winding. Consider using cpConvexHull() or CP_CONVEX_HULL().");
poly->numVerts = numVerts;
poly->verts = (cpVect *)cpcalloc(2*numVerts, sizeof(cpVect));
poly->planes = (cpSplittingPlane *)cpcalloc(2*numVerts, sizeof(cpSplittingPlane));
poly->tVerts = poly->verts + numVerts;
poly->tPlanes = poly->planes + numVerts;
for(int i=0; i<numVerts; i++){
cpVect a = cpvadd(offset, verts[i]);
cpVect b = cpvadd(offset, verts[(i+1)%numVerts]);
cpVect n = cpvnormalize(cpvperp(cpvsub(b, a)));
poly->verts[i] = a;
poly->planes[i].n = n;
poly->planes[i].d = cpvdot(n, a);
}
// TODO: Why did I add this? It duplicates work from above.
for(int i=0; i<numVerts; i++){
poly->planes[i] = cpSplittingPlaneNew(poly->verts[(i - 1 + numVerts)%numVerts], poly->verts[i]);
}
}
static inline struct ClosestPoints
ClosestPointsNew(const struct MinkowskiPoint v0, const struct MinkowskiPoint v1)
{
cpFloat t = ClosestT(v0.ab, v1.ab);
cpVect p = LerpT(v0.ab, v1.ab, t);
cpVect pa = LerpT(v0.a, v1.a, t);
cpVect pb = LerpT(v0.b, v1.b, t);
cpCollisionID id = (v0.id & 0xFFFF)<<16 | (v1.id & 0xFFFF);
cpVect delta = cpvsub(v1.ab, v0.ab);
cpVect n = cpvnormalize(cpvperp(delta));
cpFloat d = -cpvdot(n, p);
if(d <= 0.0f || (0.0f < t && t < 1.0f)){
struct ClosestPoints points = {pa, pb, cpvneg(n), d, id};
return points;
} else {
cpFloat d2 = cpvlength(p);
cpVect n = cpvmult(p, 1.0f/(d2 + CPFLOAT_MIN));
struct ClosestPoints points = {pa, pb, n, d2, id};
return points;
}
}
void
cpArbiterPreStep(cpArbiter *arb, cpFloat dt, cpFloat slop, cpFloat bias)
{
cpBody *a = arb->body_a;
cpBody *b = arb->body_b;
for(int i=0; i<arb->numContacts; i++){
cpContact *con = &arb->contacts[i];
// Calculate the offsets.
con->r1 = cpvsub(con->p, a->p);
con->r2 = cpvsub(con->p, b->p);
// Calculate the mass normal and mass tangent.
con->nMass = 1.0f/k_scalar(a, b, con->r1, con->r2, con->n);
con->tMass = 1.0f/k_scalar(a, b, con->r1, con->r2, cpvperp(con->n));
// Calculate the target bias velocity.
con->bias = -bias*cpfmin(0.0f, con->dist + slop)/dt;
con->jBias = 0.0f;
// Calculate the target bounce velocity.
con->bounce = normal_relative_velocity(a, b, con->r1, con->r2, con->n)*arb->e;
}
}
static void
add_box(cpSpace *space)
{
const cpFloat size = 10.0f;
const cpFloat mass = 1.0f;
cpVect verts[] = {
cpv(-size,-size),
cpv(-size, size),
cpv( size, size),
cpv( size,-size),
};
cpFloat radius = cpvlength(cpv(size, size));
cpVect pos = rand_pos(radius);
cpBody *body = cpSpaceAddBody(space, cpBodyNew(mass, cpMomentForPoly(mass, 4, verts, cpvzero, 0.0f)));
body->velocity_func = planetGravityVelocityFunc;
cpBodySetPosition(body, pos);
// Set the box's velocity to put it into a circular orbit from its
// starting position.
cpFloat r = cpvlength(pos);
cpFloat v = cpfsqrt(gravityStrength / r) / r;
cpBodySetVelocity(body, cpvmult(cpvperp(pos), v));
// Set the box's angular velocity to match its orbital period and
// align its initial angle with its position.
cpBodySetAngularVelocity(body, v);
cpBodySetAngle(body, cpfatan2(pos.y, pos.x));
cpShape *shape = cpSpaceAddShape(space, cpPolyShapeNew(body, 4, verts, cpTransformIdentity, 0.0));
cpShapeSetElasticity(shape, 0.0f);
cpShapeSetFriction(shape, 0.7f);
}
void
cpArbiterPreStep(cpArbiter *arb, cpFloat dt_inv)
{
cpBody *a = arb->a->body;
cpBody *b = arb->b->body;
for(int i=0; i<arb->numContacts; i++){
cpContact *con = &arb->contacts[i];
// Calculate the offsets.
con->r1 = cpvsub(con->p, a->p);
con->r2 = cpvsub(con->p, b->p);
// Calculate the mass normal and mass tangent.
con->nMass = 1.0f/k_scalar(a, b, con->r1, con->r2, con->n);
con->tMass = 1.0f/k_scalar(a, b, con->r1, con->r2, cpvperp(con->n));
// Calculate the target bias velocity.
con->bias = -cp_bias_coef*dt_inv*cpfmin(0.0f, con->dist + cp_collision_slop);
con->jBias = 0.0f;
// Calculate the target bounce velocity.
con->bounce = normal_relative_velocity(a, b, con->r1, con->r2, con->n)*arb->e;//cpvdot(con->n, cpvsub(v2, v1))*e;
}
}
void update_drive()
{
const cpFloat max_forward_speed = 150;
const cpFloat max_backward_speed = -20;
const cpFloat max_drive_force = 100;
int i;
for(i=0; i<1; i++) {
cpFloat desired_speed = 0;
// find desired speed
if(controls.forward)
desired_speed = max_forward_speed;
else if(controls.back)
desired_speed = max_backward_speed;
// find speed
cpVect forward_normal = cpvperp(cpvforangle(cpBodyGetAngle(tire[i])));
cpFloat speed = cpvdot(forward_velocity(i), forward_normal);
// apply force
cpFloat force = 0;
if(desired_speed > speed)
force = max_drive_force;
else if(desired_speed < speed)
force = -max_drive_force;
else
return;
cpBodyApplyImpulse(tire[i], cpvmult(forward_normal, force), cpvzero);
}
}
// Recursive implementation of the EPA loop.
// Each recursion adds a point to the convex hull until it's known that we have the closest point on the surface.
static struct ClosestPoints
EPARecurse(const struct SupportContext *ctx, const int count, const struct MinkowskiPoint *hull, const int iteration)
{
int mini = 0;
cpFloat minDist = INFINITY;
// TODO: precalculate this when building the hull and save a step.
// Find the closest segment hull[i] and hull[i + 1] to (0, 0)
for(int j=0, i=count-1; j<count; i=j, j++) {
cpFloat d = ClosestDist(hull[i].ab, hull[j].ab);
if(d < minDist) {
minDist = d;
mini = i;
}
}
struct MinkowskiPoint v0 = hull[mini];
struct MinkowskiPoint v1 = hull[(mini + 1)%count];
cpAssertSoft(!cpveql(v0.ab, v1.ab), "Internal Error: EPA vertexes are the same (%d and %d)", mini, (mini + 1)%count);
// Check if there is a point on the minkowski difference beyond this edge.
struct MinkowskiPoint p = Support(ctx, cpvperp(cpvsub(v1.ab, v0.ab)));
#if DRAW_EPA
cpVect verts[count];
for(int i=0; i<count; i++) verts[i] = hull[i].ab;
ChipmunkDebugDrawPolygon(count, verts, 0.0, RGBAColor(1, 1, 0, 1), RGBAColor(1, 1, 0, 0.25));
ChipmunkDebugDrawSegment(v0.ab, v1.ab, RGBAColor(1, 0, 0, 1));
ChipmunkDebugDrawDot(5, p.ab, LAColor(1, 1));
#endif
if(CheckArea(cpvsub(v1.ab, v0.ab), cpvadd(cpvsub(p.ab, v0.ab), cpvsub(p.ab, v1.ab))) && iteration < MAX_EPA_ITERATIONS) {
// Rebuild the convex hull by inserting p.
struct MinkowskiPoint *hull2 = (struct MinkowskiPoint *)alloca((count + 1)*sizeof(struct MinkowskiPoint));
int count2 = 1;
hull2[0] = p;
for(int i=0; i<count; i++) {
int index = (mini + 1 + i)%count;
cpVect h0 = hull2[count2 - 1].ab;
cpVect h1 = hull[index].ab;
cpVect h2 = (i + 1 < count ? hull[(index + 1)%count] : p).ab;
if(CheckArea(cpvsub(h2, h0), cpvadd(cpvsub(h1, h0), cpvsub(h1, h2)))) {
hull2[count2] = hull[index];
count2++;
}
}
return EPARecurse(ctx, count2, hull2, iteration + 1);
} else {
// Could not find a new point to insert, so we have found the closest edge of the minkowski difference.
cpAssertWarn(iteration < WARN_EPA_ITERATIONS, "High EPA iterations: %d", iteration);
return ClosestPointsNew(v0, v1);
}
}
static struct ClosestPoints
EPARecurse(const struct SupportContext *ctx, const int count, const struct MinkowskiPoint *hull, const int iteration)
{
int mini = 0;
cpFloat minDist = INFINITY;
// TODO: precalculate this when building the hull and save a step.
for(int j=0, i=count-1; j<count; i=j, j++){
cpFloat d = ClosestDist(hull[i].ab, hull[j].ab);
if(d < minDist){
minDist = d;
mini = i;
}
}
struct MinkowskiPoint v0 = hull[mini];
struct MinkowskiPoint v1 = hull[(mini + 1)%count];
cpAssertSoft(!cpveql(v0.ab, v1.ab), "Internal Error: EPA vertexes are the same (%d and %d)", mini, (mini + 1)%count);
struct MinkowskiPoint p = Support(ctx, cpvperp(cpvsub(v1.ab, v0.ab)));
#if DRAW_EPA
cpVect verts[count];
for(int i=0; i<count; i++) verts[i] = hull[i].ab;
ChipmunkDebugDrawPolygon(count, verts, 0.0, RGBAColor(1, 1, 0, 1), RGBAColor(1, 1, 0, 0.25));
ChipmunkDebugDrawSegment(v0.ab, v1.ab, RGBAColor(1, 0, 0, 1));
ChipmunkDebugDrawDot(5, p.ab, LAColor(1, 1));
#endif
cpFloat area2x = cpvcross(cpvsub(v1.ab, v0.ab), cpvadd(cpvsub(p.ab, v0.ab), cpvsub(p.ab, v1.ab)));
if(area2x > 0.0f && iteration < MAX_EPA_ITERATIONS){
int count2 = 1;
struct MinkowskiPoint *hull2 = (struct MinkowskiPoint *)alloca((count + 1)*sizeof(struct MinkowskiPoint));
hull2[0] = p;
for(int i=0; i<count; i++){
int index = (mini + 1 + i)%count;
cpVect h0 = hull2[count2 - 1].ab;
cpVect h1 = hull[index].ab;
cpVect h2 = (i + 1 < count ? hull[(index + 1)%count] : p).ab;
// TODO: Should this be changed to an area2x check?
if(cpvcross(cpvsub(h2, h0), cpvsub(h1, h0)) > 0.0f){
hull2[count2] = hull[index];
count2++;
}
}
return EPARecurse(ctx, count2, hull2, iteration + 1);
} else {
cpAssertWarn(iteration < WARN_EPA_ITERATIONS, "High EPA iterations: %d", iteration);
return ClosestPointsNew(v0, v1);
}
}
void
cpSegmentShapeSetEndpoints(cpShape *shape, cpVect a, cpVect b)
{
cpAssertHard(shape->klass == &cpSegmentShapeClass, "Shape is not a segment shape.");
cpSegmentShape *seg = (cpSegmentShape *)shape;
seg->a = a;
seg->b = b;
seg->n = cpvperp(cpvnormalize(cpvsub(b, a)));
}
void
cpGrooveJointSetGrooveB(cpConstraint *constraint, cpVect value)
{
cpGrooveJoint *g = (cpGrooveJoint *)constraint;
cpConstraintCheckCast(constraint, cpGrooveJoint);
g->grv_b = value;
g->grv_n = cpvperp(cpvnormalize(cpvsub(value, g->grv_a)));
cpConstraintActivateBodies(constraint);
}
void
cpGrooveJointSetGrooveB(cpConstraint *constraint, cpVect value)
{
cpAssertHard(cpConstraintIsGrooveJoint(constraint), "Constraint is not a groove joint.");
cpGrooveJoint *g = (cpGrooveJoint *)constraint;
g->grv_b = value;
g->grv_n = cpvperp(cpvnormalize(cpvsub(value, g->grv_a)));
cpConstraintActivateBodies(constraint);
}
void
cpArbiterApplyImpulse(cpArbiter *arb)
{
cpBody *a = arb->body_a;
cpBody *b = arb->body_b;
cpVect surface_vr = arb->surface_vr;
cpFloat friction = arb->u;
for(int i=0; i<arb->numContacts; i++){
cpContact *con = &arb->contacts[i];
cpFloat nMass = con->nMass;
cpVect n = con->n;
cpVect r1 = con->r1;
cpVect r2 = con->r2;
cpVect vb1 = cpvadd(a->v_bias, cpvmult(cpvperp(r1), a->w_bias));
cpVect vb2 = cpvadd(b->v_bias, cpvmult(cpvperp(r2), b->w_bias));
cpVect vr = relative_velocity(a, b, r1, r2);
cpFloat vbn = cpvdot(cpvsub(vb2, vb1), n);
cpFloat vrn = cpvdot(vr, n);
cpFloat vrt = cpvdot(cpvadd(vr, surface_vr), cpvperp(n));
cpFloat jbn = (con->bias - vbn)*nMass;
cpFloat jbnOld = con->jBias;
con->jBias = cpfmax(jbnOld + jbn, 0.0f);
cpFloat jn = -(con->bounce + vrn)*nMass;
cpFloat jnOld = con->jnAcc;
con->jnAcc = cpfmax(jnOld + jn, 0.0f);
cpFloat jtMax = friction*con->jnAcc;
cpFloat jt = -vrt*con->tMass;
cpFloat jtOld = con->jtAcc;
con->jtAcc = cpfclamp(jtOld + jt, -jtMax, jtMax);
apply_bias_impulses(a, b, r1, r2, cpvmult(n, con->jBias - jbnOld));
apply_impulses(a, b, r1, r2, cpvrotate(n, cpv(con->jnAcc - jnOld, con->jtAcc - jtOld)));
}
}
cpSegmentShape *
cpSegmentShapeInit(cpSegmentShape *seg, cpBody *body, cpVect a, cpVect b, cpFloat r)
{
seg->a = a;
seg->b = b;
seg->n = cpvperp(cpvnormalize(cpvsub(b, a)));
seg->r = r;
cpShapeInit((cpShape *)seg, &cpSegmentShapeClass, body);
return seg;
}
// Recursive implementatino of the GJK loop.
static inline struct ClosestPoints
GJKRecurse(const struct SupportContext *ctx, const struct MinkowskiPoint v0, const struct MinkowskiPoint v1, const int iteration)
{
if(iteration > MAX_GJK_ITERATIONS) {
cpAssertWarn(iteration < WARN_GJK_ITERATIONS, "High GJK iterations: %d", iteration);
return ClosestPointsNew(v0, v1);
}
cpVect delta = cpvsub(v1.ab, v0.ab);
// TODO: should this be an area2x check?
if(cpvcross(delta, cpvadd(v0.ab, v1.ab)) > 0.0f) {
// Origin is behind axis. Flip and try again.
return GJKRecurse(ctx, v1, v0, iteration);
} else {
cpFloat t = ClosestT(v0.ab, v1.ab);
cpVect n = (-1.0f < t && t < 1.0f ? cpvperp(delta) : cpvneg(LerpT(v0.ab, v1.ab, t)));
struct MinkowskiPoint p = Support(ctx, n);
#if DRAW_GJK
ChipmunkDebugDrawSegment(v0.ab, v1.ab, RGBAColor(1, 1, 1, 1));
cpVect c = cpvlerp(v0.ab, v1.ab, 0.5);
ChipmunkDebugDrawSegment(c, cpvadd(c, cpvmult(cpvnormalize(n), 5.0)), RGBAColor(1, 0, 0, 1));
ChipmunkDebugDrawDot(5.0, p.ab, LAColor(1, 1));
#endif
if(
cpvcross(cpvsub(v1.ab, p.ab), cpvadd(v1.ab, p.ab)) > 0.0f &&
cpvcross(cpvsub(v0.ab, p.ab), cpvadd(v0.ab, p.ab)) < 0.0f
) {
// The triangle v0, p, v1 contains the origin. Use EPA to find the MSA.
cpAssertWarn(iteration < WARN_GJK_ITERATIONS, "High GJK->EPA iterations: %d", iteration);
return EPA(ctx, v0, p, v1);
} else {
if(cpvdot(p.ab, n) <= cpfmax(cpvdot(v0.ab, n), cpvdot(v1.ab, n))) {
// The edge v0, v1 that we already have is the closest to (0, 0) since p was not closer.
cpAssertWarn(iteration < WARN_GJK_ITERATIONS, "High GJK iterations: %d", iteration);
return ClosestPointsNew(v0, v1);
} else {
// p was closer to the origin than our existing edge.
// Need to figure out which existing point to drop.
if(ClosestDist(v0.ab, p.ab) < ClosestDist(p.ab, v1.ab)) {
return GJKRecurse(ctx, v0, p, iteration + 1);
} else {
return GJKRecurse(ctx, p, v1, iteration + 1);
}
}
}
}
}
void
cpSegmentShapeSetEndpoints(cpShape *shape, cpVect a, cpVect b)
{
cpAssertHard(shape->klass == &cpSegmentShapeClass, "Shape is not a segment shape.");
cpSegmentShape *seg = (cpSegmentShape *)shape;
seg->a = a;
seg->b = b;
seg->n = cpvperp(cpvnormalize(cpvsub(b, a)));
cpFloat mass = shape->massInfo.m;
shape->massInfo = cpSegmentShapeMassInfo(shape->massInfo.m, seg->a, seg->b, seg->r);
if(mass > 0.0f) cpBodyAccumulateMassFromShapes(shape->body);
}
cpGrooveJoint *
cpGrooveJointInit(cpGrooveJoint *joint, cpBody *a, cpBody *b, cpVect groove_a, cpVect groove_b, cpVect anchorB)
{
cpConstraintInit((cpConstraint *)joint, &klass, a, b);
joint->grv_a = groove_a;
joint->grv_b = groove_b;
joint->grv_n = cpvperp(cpvnormalize(cpvsub(groove_b, groove_a)));
joint->anchorB = anchorB;
joint->jAcc = cpvzero;
return joint;
}
cpVect
cpContactsSumImpulsesWithFriction(cpContact *contacts, int numContacts)
{
cpVect sum = cpvzero;
for(int i=0; i<numContacts; i++){
cpContact *con = &contacts[i];
cpVect t = cpvperp(con->n);
cpVect j = cpvadd(cpvmult(con->n, con->jnAcc), cpvmult(t, con->jtAcc));
sum = cpvadd(sum, j);
}
return sum;
}
static inline struct ClosestPoints
GJKRecurse(const struct SupportContext *ctx, const struct MinkowskiPoint v0, const struct MinkowskiPoint v1, const int iteration)
{
if(iteration > MAX_GJK_ITERATIONS){
cpAssertWarn(iteration < WARN_GJK_ITERATIONS, "High GJK iterations: %d", iteration);
return ClosestPointsNew(v0, v1);
}
cpVect delta = cpvsub(v1.ab, v0.ab);
if(cpvcross(delta, cpvadd(v0.ab, v1.ab)) > 0.0f){
// Origin is behind axis. Flip and try again.
return GJKRecurse(ctx, v1, v0, iteration + 1);
} else {
cpFloat t = ClosestT(v0.ab, v1.ab);
cpVect n = (-1.0f < t && t < 1.0f ? cpvperp(delta) : cpvneg(LerpT(v0.ab, v1.ab, t)));
struct MinkowskiPoint p = Support(ctx, n);
#if DRAW_GJK
ChipmunkDebugDrawSegment(v0.ab, v1.ab, RGBAColor(1, 1, 1, 1));
cpVect c = cpvlerp(v0.ab, v1.ab, 0.5);
ChipmunkDebugDrawSegment(c, cpvadd(c, cpvmult(cpvnormalize(n), 5.0)), RGBAColor(1, 0, 0, 1));
ChipmunkDebugDrawDot(5.0, p.ab, LAColor(1, 1));
#endif
if(
cpvcross(cpvsub(v1.ab, p.ab), cpvadd(v1.ab, p.ab)) > 0.0f &&
cpvcross(cpvsub(v0.ab, p.ab), cpvadd(v0.ab, p.ab)) < 0.0f
){
cpAssertWarn(iteration < WARN_GJK_ITERATIONS, "High GJK->EPA iterations: %d", iteration);
// The triangle v0, p, v1 contains the origin. Use EPA to find the MSA.
return EPA(ctx, v0, p, v1);
} else {
// The new point must be farther along the normal than the existing points.
if(cpvdot(p.ab, n) <= cpfmax(cpvdot(v0.ab, n), cpvdot(v1.ab, n))){
cpAssertWarn(iteration < WARN_GJK_ITERATIONS, "High GJK iterations: %d", iteration);
return ClosestPointsNew(v0, v1);
} else {
if(ClosestDist(v0.ab, p.ab) < ClosestDist(p.ab, v1.ab)){
return GJKRecurse(ctx, v0, p, iteration + 1);
} else {
return GJKRecurse(ctx, p, v1, iteration + 1);
}
}
}
}
}
void Slice::SliceShapePostStep(cpSpace *space, cpShape *shape, struct SliceContext *context)
{
cpVect a = context->a;
cpVect b = context->b;
// Clipping plane normal and distance.
cpVect n = cpvnormalize(cpvperp(cpvsub(b, a)));
cpFloat dist = cpvdot(a, n);
ClipPoly(space, shape, n, dist);
ClipPoly(space, shape, cpvneg(n), -dist);
cpBody *body = cpShapeGetBody(shape);
cpSpaceRemoveShape(space, shape);
cpSpaceRemoveBody(space, body);
cpShapeFree(shape);
cpBodyFree(body);
}
static void
preStep(cpGrooveJoint *joint, cpFloat dt, cpFloat dt_inv)
{
cpBody *a = joint->constraint.a;
cpBody *b = joint->constraint.b;
// calculate endpoints in worldspace
cpVect ta = cpBodyLocal2World(a, joint->grv_a);
cpVect tb = cpBodyLocal2World(a, joint->grv_b);
// calculate axis
cpVect n = cpvrotate(joint->grv_n, a->rot);
cpFloat d = cpvdot(ta, n);
joint->grv_tn = n;
joint->r2 = cpvrotate(joint->anchr2, b->rot);
// calculate tangential distance along the axis of r2
cpFloat td = cpvcross(cpvadd(b->p, joint->r2), n);
// calculate clamping factor and r2
if(td <= cpvcross(ta, n)){
joint->clamp = 1.0f;
joint->r1 = cpvsub(ta, a->p);
} else if(td >= cpvcross(tb, n)){
joint->clamp = -1.0f;
joint->r1 = cpvsub(tb, a->p);
} else {
joint->clamp = 0.0f;
joint->r1 = cpvsub(cpvadd(cpvmult(cpvperp(n), -td), cpvmult(n, d)), a->p);
}
// Calculate mass tensor
k_tensor(a, b, joint->r1, joint->r2, &joint->k1, &joint->k2);
// compute max impulse
joint->jMaxLen = J_MAX(joint, dt);
// calculate bias velocity
cpVect delta = cpvsub(cpvadd(b->p, joint->r2), cpvadd(a->p, joint->r1));
joint->bias = cpvclamp(cpvmult(delta, -joint->constraint.biasCoef*dt_inv), joint->constraint.maxBias);
// apply accumulated impulse
apply_impulses(a, b, joint->r1, joint->r2, joint->jAcc);
}
static void
setUpVerts(cpPolyShape *poly, int numVerts, cpVect *verts, cpVect offset)
{
poly->numVerts = numVerts;
poly->verts = (cpVect *)cpcalloc(numVerts, sizeof(cpVect));
poly->tVerts = (cpVect *)cpcalloc(numVerts, sizeof(cpVect));
poly->axes = (cpPolyShapeAxis *)cpcalloc(numVerts, sizeof(cpPolyShapeAxis));
poly->tAxes = (cpPolyShapeAxis *)cpcalloc(numVerts, sizeof(cpPolyShapeAxis));
for(int i=0; i<numVerts; i++){
cpVect a = cpvadd(offset, verts[i]);
cpVect b = cpvadd(offset, verts[(i+1)%numVerts]);
cpVect n = cpvnormalize(cpvperp(cpvsub(b, a)));
poly->verts[i] = a;
poly->axes[i].n = n;
poly->axes[i].d = cpvdot(n, a);
}
}
void
cpArbiterApplyCachedImpulse(cpArbiter *arb)
{
cpShape *shapea = arb->a;
cpShape *shapeb = arb->b;
arb->u = shapea->u * shapeb->u;
arb->target_v = cpvsub(shapeb->surface_v, shapea->surface_v);
cpBody *a = shapea->body;
cpBody *b = shapeb->body;
for(int i=0; i<arb->numContacts; i++){
cpContact *con = &arb->contacts[i];
cpVect t = cpvperp(con->n);
cpVect j = cpvadd(cpvmult(con->n, con->jnAcc), cpvmult(t, con->jtAcc));
cpBodyApplyImpulse(a, cpvneg(j), con->r1);
cpBodyApplyImpulse(b, j, con->r2);
}
}
// Recursive function used by cpPolylineSimplifyCurves().
static cpPolyline *
DouglasPeucker(
cpVect *verts, cpPolyline *reduced,
int length, int start, int end,
cpFloat min, cpFloat tol
){
// Early exit if the points are adjacent
if((end - start + length)%length < 2) return reduced;
cpVect a = verts[start];
cpVect b = verts[end];
// Check if the length is below the threshold
if(cpvnear(a, b, min) && cpPolylineIsShort(verts, length, start, end, min)) return reduced;
// Find the maximal vertex to split and recurse on
cpFloat max = 0.0;
int maxi = start;
cpVect n = cpvnormalize(cpvperp(cpvsub(b, a)));
cpFloat d = cpvdot(n, a);
for(int i=Next(start, length); i!=end; i=Next(i, length)){
cpFloat dist = fabs(cpvdot(n, verts[i]) - d);
if(dist > max){
max = dist;
maxi = i;
}
}
if(max > tol){
reduced = DouglasPeucker(verts, reduced, length, start, maxi, min, tol);
reduced = cpPolylinePush(reduced, verts[maxi]);
reduced = DouglasPeucker(verts, reduced, length, maxi, end, min, tol);
}
return reduced;
}
static void
preStep(cpGrooveJoint *joint, cpFloat dt)
{
cpBody *a = joint->constraint.a;
cpBody *b = joint->constraint.b;
// calculate endpoints in worldspace
cpVect ta = cpTransformPoint(a->transform, joint->grv_a);
cpVect tb = cpTransformPoint(a->transform, joint->grv_b);
// calculate axis
cpVect n = cpTransformVect(a->transform, joint->grv_n);
cpFloat d = cpvdot(ta, n);
joint->grv_tn = n;
joint->r2 = cpTransformVect(b->transform, cpvsub(joint->anchorB, b->cog));
// calculate tangential distance along the axis of r2
cpFloat td = cpvcross(cpvadd(b->p, joint->r2), n);
// calculate clamping factor and r2
if(td <= cpvcross(ta, n)){
joint->clamp = 1.0f;
joint->r1 = cpvsub(ta, a->p);
} else if(td >= cpvcross(tb, n)){
joint->clamp = -1.0f;
joint->r1 = cpvsub(tb, a->p);
} else {
joint->clamp = 0.0f;
joint->r1 = cpvsub(cpvadd(cpvmult(cpvperp(n), -td), cpvmult(n, d)), a->p);
}
// Calculate mass tensor
joint->k = k_tensor(a, b, joint->r1, joint->r2);
// calculate bias velocity
cpVect delta = cpvsub(cpvadd(b->p, joint->r2), cpvadd(a->p, joint->r1));
joint->bias = cpvclamp(cpvmult(delta, -bias_coef(joint->constraint.errorBias, dt)/dt), joint->constraint.maxBias);
}
static void
update(int ticks)
{
static int lastJumpState = 0;
int jumpState = (arrowDirection.y > 0.0f);
cpVect groundNormal = playerInstance.groundNormal;
if(groundNormal.y > 0.0f){
playerInstance.shape->surface_v = cpvmult(cpvperp(groundNormal), 400.0f*arrowDirection.x);
} else {
playerInstance.shape->surface_v = cpvzero;
}
cpBody *body = playerInstance.shape->body;
// apply jump
if(jumpState && !lastJumpState && cpvlengthsq(groundNormal)){
// body->v = cpvmult(cpvslerp(groundNormal, cpv(0.0f, 1.0f), 0.5f), 500.0f);
body->v = cpvadd(body->v, cpvmult(cpvslerp(groundNormal, cpv(0.0f, 1.0f), 0.75f), 500.0f));
}
if(playerInstance.groundShapes->num == 0){
cpFloat air_accel = body->v.x + arrowDirection.x*(2000.0f);
body->f.x = body->m*air_accel;
// body->v.x = cpflerpconst(body->v.x, 400.0f*arrowDirection.x, 2000.0f/60.0f);
}
int steps = 3;
cpFloat dt = 1.0f/60.0f/(cpFloat)steps;
playerInstance.groundNormal = cpvzero;
for(int i=0; i<steps; i++){
cpSpaceStep(space, dt);
}
lastJumpState = jumpState;
}
void
cpArbiterPreStep(cpArbiter *arb, cpFloat dt, cpFloat slop, cpFloat bias)
{
cpBody *a = arb->body_a;
cpBody *b = arb->body_b;
cpVect n = arb->n;
cpVect body_delta = cpvsub(b->p, a->p);
for(int i=0; i<arb->count; i++){
struct cpContact *con = &arb->contacts[i];
// Calculate the mass normal and mass tangent.
con->nMass = 1.0f/k_scalar(a, b, con->r1, con->r2, n);
con->tMass = 1.0f/k_scalar(a, b, con->r1, con->r2, cpvperp(n));
// Calculate the target bias velocity.
cpFloat dist = cpvdot(cpvadd(cpvsub(con->r2, con->r1), body_delta), n);
con->bias = -bias*cpfmin(0.0f, dist + slop)/dt;
con->jBias = 0.0f;
// Calculate the target bounce velocity.
con->bounce = normal_relative_velocity(a, b, con->r1, con->r2, n)*arb->e;
}
}