cpVect
cpBBClampVect(const cpBB bb, const cpVect v)
{
cpFloat x = cpfmin(cpfmax(bb.l, v.x), bb.r);
cpFloat y = cpfmin(cpfmax(bb.b, v.y), bb.t);
return cpv(x, y);
}
static cpBB
cpPolyShapeCacheData(cpShape *shape, cpVect p, cpVect rot)
{
cpPolyShape *poly = (cpPolyShape *)shape;
cpFloat l, b, r, t;
cpPolyShapeTransformAxes(poly, p, rot);
cpPolyShapeTransformVerts(poly, p, rot);
cpVect *verts = poly->tVerts;
l = r = verts[0].x;
b = t = verts[0].y;
// TODO do as part of cpPolyShapeTransformVerts?
for(int i=1; i<poly->numVerts; i++){
cpVect v = verts[i];
l = cpfmin(l, v.x);
r = cpfmax(r, v.x);
b = cpfmin(b, v.y);
t = cpfmax(t, v.y);
}
return cpBBNew(l, b, r, t);
}
static cpBB
cpPolyShapeCacheData(cpPolyShape *poly, cpTransform transform)
{
int count = poly->count;
struct cpSplittingPlane *dst = poly->planes;
struct cpSplittingPlane *src = dst + count;
cpFloat l = (cpFloat)INFINITY, r = -(cpFloat)INFINITY;
cpFloat b = (cpFloat)INFINITY, t = -(cpFloat)INFINITY;
for(int i=0; i<count; i++){
cpVect v = cpTransformPoint(transform, src[i].v0);
cpVect n = cpTransformVect(transform, src[i].n);
dst[i].v0 = v;
dst[i].n = n;
l = cpfmin(l, v.x);
r = cpfmax(r, v.x);
b = cpfmin(b, v.y);
t = cpfmax(t, v.y);
}
cpFloat radius = poly->r;
return (poly->shape.bb = cpBBNew(l - radius, b - radius, r + radius, t + radius));
}
static void
applyImpulse(cpPulleyJoint *joint)
{
cpBody* b1 = joint->constraint.a;
cpBody* b2 = joint->constraint.b;
cpVect r1 = joint->r1;
cpVect r2 = joint->r2;
// The magic and mystery below
if (joint->state)
{
cpVect v1 = cpvadd(b1->v, cpv(-b1->w * r1.y, b1->w * r1.x));
cpVect v2 = cpvadd(b2->v, cpv(-b2->w * r2.y, b2->w * r2.x));
cpFloat Cdot = -cpvdot(joint->u1, v1) - joint->ratio * cpvdot(joint->u2, v2);
cpFloat impulse = joint->pulleyMass * (-Cdot);
cpFloat oldImpulse = joint->jnAcc;
joint->jnAcc = cpfmax(0.0f, joint->jnAcc + impulse);
impulse = joint->jnAcc - oldImpulse;
cpVect P1 = cpvmult(joint->u1, -impulse);
cpVect P2 = cpvmult(joint->u2, -joint->ratio * impulse);
cpBodyApplyImpulse(b1, P1, r1);
cpBodyApplyImpulse(b2, P2, r2);
}
if (joint->limitState1)
{
cpVect v1 = cpvadd(b1->v, cpv(-b1->w * r1.y, b1->w * r1.x));
cpFloat Cdot = -cpvdot(joint->u1, v1);
cpFloat impulse = -joint->limitMass1 * Cdot;
cpFloat oldImpulse = joint->jnAccLim1;
joint->jnAccLim1 = cpfmax(0.0f, joint->jnAccLim1 + impulse);
impulse = joint->jnAccLim1 - oldImpulse;
cpVect P1 = cpvmult(joint->u1, -impulse);
cpBodyApplyImpulse(b1, P1, r1);
}
if (joint->limitState2)
{
cpVect v2 = cpvadd(b2->v, cpv(-b2->w * r2.y, b2->w * r2.x));
cpFloat Cdot = -cpvdot(joint->u2, v2);
cpFloat impulse = -joint->limitMass2 * Cdot;
cpFloat oldImpulse = joint->jnAccLim2;
joint->jnAccLim2 = cpfmax(0.0f, joint->jnAccLim2 + impulse);
impulse = joint->jnAccLim2 - oldImpulse;
cpVect P2 = cpvmult(joint->u2, -impulse);
cpBodyApplyImpulse(b2, P2, 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
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
NodeRender(Node *node, int depth)
{
if(!NodeIsLeaf(node) && depth <= 10){
NodeRender(node->a, depth + 1);
NodeRender(node->b, depth + 1);
}
cpBB bb = node->bb;
// GLfloat v = depth/2.0f;
// glColor3f(1.0f - v, v, 0.0f);
glLineWidth(cpfmax(5.0f - depth, 1.0f));
glBegin(GL_LINES); {
glVertex2f(bb.l, bb.b);
glVertex2f(bb.l, bb.t);
glVertex2f(bb.l, bb.t);
glVertex2f(bb.r, bb.t);
glVertex2f(bb.r, bb.t);
glVertex2f(bb.r, bb.b);
glVertex2f(bb.r, bb.b);
glVertex2f(bb.l, bb.b);
}; glEnd();
}
static void
playerUpdateVelocity(cpBody *body, cpVect gravity, cpFloat damping, cpFloat dt)
{
cpBodyUpdateVelocity(body, gravity, damping, dt);
body->v.y = cpfmax(body->v.y, -700);
body->v.x = cpfclamp(body->v.x, -400, 400);
}
void
cpSpaceNearestPointQuery(cpSpace *space, cpVect point, cpFloat maxDistance, cpLayers layers, cpGroup group, cpSpaceNearestPointQueryFunc func, void *data)
{
struct NearestPointQueryContext context = {point, maxDistance, layers, group, func};
cpBB bb = cpBBNewForCircle(point, cpfmax(maxDistance, 0.0f));
cpSpaceLock(space); {
cpSpatialIndexQuery(space->activeShapes, &context, bb, (cpSpatialIndexQueryFunc)NearestPointQuery, data);
cpSpatialIndexQuery(space->staticShapes, &context, bb, (cpSpatialIndexQueryFunc)NearestPointQuery, data);
} cpSpaceUnlock(space, cpTrue);
}
static cpBB
cpPolyShapeTransformVerts(cpPolyShape *poly, cpVect p, cpVect rot)
{
cpVect *src = poly->verts;
cpVect *dst = poly->tVerts;
cpFloat l = (cpFloat)INFINITY, r = -(cpFloat)INFINITY;
cpFloat b = (cpFloat)INFINITY, t = -(cpFloat)INFINITY;
for(int i=0; i<poly->numVerts; i++) {
cpVect v = cpvadd(p, cpvrotate(src[i], rot));
dst[i] = v;
l = cpfmin(l, v.x);
r = cpfmax(r, v.x);
b = cpfmin(b, v.y);
t = cpfmax(t, v.y);
}
return cpBBNew(l, b, r, t);
}
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)));
}
}
static void DrawShape(cpShape *shape, DrawNode *renderer)
{
cpBody *body = cpShapeGetBody(shape);
Color4F color = ColorForBody(body);
switch (shape->CP_PRIVATE(klass)->type)
{
case CP_CIRCLE_SHAPE:
{
cpCircleShape *circle = (cpCircleShape *)shape;
cpVect center = circle->tc;
cpFloat radius = circle->r;
renderer->drawDot(cpVert2Point(center), cpfmax(radius, 1.0), color);
renderer->drawSegment(cpVert2Point(center), cpVert2Point(cpvadd(center, cpvmult(cpBodyGetRotation(body), radius))), 1.0, color);
}
break;
case CP_SEGMENT_SHAPE:
{
cpSegmentShape *seg = (cpSegmentShape *)shape;
renderer->drawSegment(cpVert2Point(seg->ta), cpVert2Point(seg->tb), cpfmax(seg->r, 2.0), color);
}
break;
case CP_POLY_SHAPE:
{
cpPolyShape* poly = (cpPolyShape*)shape;
Color4F line = color;
line.a = cpflerp(color.a, 1.0, 0.5);
int num = poly->count;
Vec2* pPoints = new (std::nothrow) Vec2[num];
for(int i=0;i<num;++i)
pPoints[i] = cpVert2Point(poly->planes[i].v0);
renderer->drawPolygon(pPoints, num, color, 1.0, line);
CC_SAFE_DELETE_ARRAY(pPoints);
}
break;
default:
cpAssertHard(false, "Bad assertion in DrawShape()");
}
}
// 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);
}
}
}
}
}
static void DrawShape(cpShape *shape, DrawNode *renderer)
{
cpBody *body = shape->body;
Color4F color = ColorForBody(body);
switch (shape->CP_PRIVATE(klass)->type)
{
case CP_CIRCLE_SHAPE:
{
cpCircleShape *circle = (cpCircleShape *)shape;
cpVect center = circle->tc;
cpFloat radius = circle->r;
renderer->drawDot(cpVert2Point(center), cpfmax(radius, 1.0), color);
renderer->drawSegment(cpVert2Point(center), cpVert2Point(cpvadd(center, cpvmult(body->rot, radius))), 1.0, color);
}
break;
case CP_SEGMENT_SHAPE:
{
cpSegmentShape *seg = (cpSegmentShape *)shape;
renderer->drawSegment(cpVert2Point(seg->ta), cpVert2Point(seg->tb), cpfmax(seg->r, 2.0), color);
}
break;
case CP_POLY_SHAPE:
{
cpPolyShape *poly = (cpPolyShape *)shape;
Color4F line = color;
line.a = cpflerp(color.a, 1.0, 0.5);
Vec2* pPoints = cpVertArray2ccpArrayN(poly->tVerts, poly->numVerts);
renderer->drawPolygon(pPoints, poly->numVerts, color, 1.0, line);
CC_SAFE_DELETE_ARRAY(pPoints);
}
break;
default:
cpAssertHard(false, "Bad assertion in DrawShape()");
}
}
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);
}
}
}
}
}
static void
update(cpSpace *space, double dt)
{
// Set the first anchor point (the one attached to the static body) of the dolly servo to the mouse's x position.
cpPivotJointSetAnchorA(dollyServo, cpv(ChipmunkDemoMouse.x, 100));
// Set the max length of the winch servo to match the mouse's height.
cpSlideJointSetMax(winchServo, cpfmax(100 - ChipmunkDemoMouse.y, 50));
if(hookJoint && ChipmunkDemoRightClick){
cpSpaceRemoveConstraint(space, hookJoint);
cpConstraintFree(hookJoint);
hookJoint = NULL;
}
cpSpaceStep(space, dt);
}
static inline cpBB
GetBB(cpBBTree *tree, void *obj)
{
cpBB bb = tree->spatialIndex.bbfunc(obj);
cpBBTreeVelocityFunc velocityFunc = tree->velocityFunc;
if(velocityFunc){
cpFloat coef = 0.1f;
cpFloat x = (bb.r - bb.l)*coef;
cpFloat y = (bb.t - bb.b)*coef;
cpVect v = cpvmult(velocityFunc(obj), 0.1f);
return cpBBNew(bb.l + cpfmin(-x, v.x), bb.b + cpfmin(-y, v.y), bb.r + cpfmax(x, v.x), bb.t + cpfmax(y, v.y));
} else {
return bb;
}
}
static void
update(int ticks)
{
if(arrowDirection.y){
circleRadius = cpfmax(10.0f, circleRadius + arrowDirection.y);
for(int i=0; i<NUM_CIRCLES; i++){
circles[i]->body->m = cpMomentForCircle(1.0f, 0.0f, circleRadius, cpvzero);
cpCircleShapeSetRadius(circles[i], circleRadius);
}
}
int steps = 1;
cpFloat dt = 1.0f/60.0f/(cpFloat)steps;
for(int i=0; i<steps; i++){
cpSpaceStep(space, dt);
}
}
static void
update(int ticks)
{
int steps = 1;
cpFloat dt = 1.0f/60.0f/(cpFloat)steps;
for(int i=0; i<steps; i++){
// Set the first anchor point (the one attached to the static body) of the dolly servo to the mouse's x position.
cpPivotJointSetAnchr1(dollyServo, cpv(ChipmunkDemoMouse.x, 100));
// Set the max length of the winch servo to match the mouse's height.
cpSlideJointSetMax(winchServo, cpfmax(100 - ChipmunkDemoMouse.y, 50));
if(hookJoint && ChipmunkDemoKeyboard.y < 0){
cpSpaceRemoveConstraint(space, hookJoint);
cpConstraintFree(hookJoint);
hookJoint = NULL;
}
cpSpaceStep(space, dt);
}
}
cpShape *
cpSpaceNearestPointQueryNearest(cpSpace *space, cpVect point, cpFloat maxDistance, cpLayers layers, cpGroup group, cpNearestPointQueryInfo *out)
{
cpNearestPointQueryInfo info = {NULL, cpvzero, maxDistance, cpvzero};
if(out){
(*out) = info;
} else {
out = &info;
}
struct NearestPointQueryContext context = {
point, maxDistance,
layers, group,
NULL
};
cpBB bb = cpBBNewForCircle(point, cpfmax(maxDistance, 0.0f));
cpSpatialIndexQuery(space->activeShapes, &context, bb, (cpSpatialIndexQueryFunc)NearestPointQueryNearest, out);
cpSpatialIndexQuery(space->staticShapes, &context, bb, (cpSpatialIndexQueryFunc)NearestPointQueryNearest, out);
return out->shape;
}
cpBool
cpCheckAxis(cpVect v0, cpVect v1, cpVect p, cpVect n){
return cpvdot(p, n) <= cpfmax(cpvdot(v0, n), cpvdot(v1, n));
}
