public final void getSearchDirection(final Vec2 out) { switch (m_count) { case 1: out.set(m_v1.w).negateLocal(); return; case 2: e12.set(m_v2.w).subLocal(m_v1.w); // use out for a temp variable real quick out.set(m_v1.w).negateLocal(); float sgn = Vec2.cross(e12, out); if (sgn > 0f) { // Origin is left of e12. Vec2.crossToOutUnsafe(1f, e12, out); return; } else { // Origin is right of e12. Vec2.crossToOutUnsafe(e12, 1f, out); return; } default: assert (false); out.setZero(); return; } }
public void set(SimplexVertex sv) { wA.set(sv.wA); wB.set(sv.wB); w.set(sv.w); a = sv.a; indexA = sv.indexA; indexB = sv.indexB; }
protected PulleyJoint(IWorldPool argWorldPool, PulleyJointDef def) { super(argWorldPool, def); m_groundAnchorA.set(def.groundAnchorA); m_groundAnchorB.set(def.groundAnchorB); m_localAnchorA.set(def.localAnchorA); m_localAnchorB.set(def.localAnchorB); assert (def.ratio != 0.0f); m_ratio = def.ratio; m_lengthA = def.lengthA; m_lengthB = def.lengthB; m_constant = def.lengthA + m_ratio * def.lengthB; m_impulse = 0.0f; }
/** Solve a line segment using barycentric coordinates. */ public void solve2() { // Solve a line segment using barycentric coordinates. // // p = a1 * w1 + a2 * w2 // a1 + a2 = 1 // // The vector from the origin to the closest point on the line is // perpendicular to the line. // e12 = w2 - w1 // dot(p, e) = 0 // a1 * dot(w1, e) + a2 * dot(w2, e) = 0 // // 2-by-2 linear system // [1 1 ][a1] = [1] // [w1.e12 w2.e12][a2] = [0] // // Define // d12_1 = dot(w2, e12) // d12_2 = -dot(w1, e12) // d12 = d12_1 + d12_2 // // Solution // a1 = d12_1 / d12 // a2 = d12_2 / d12 final Vec2 w1 = m_v1.w; final Vec2 w2 = m_v2.w; e12.set(w2).subLocal(w1); // w1 region float d12_2 = -Vec2.dot(w1, e12); if (d12_2 <= 0.0f) { // a2 <= 0, so we clamp it to 0 m_v1.a = 1.0f; m_count = 1; return; } // w2 region float d12_1 = Vec2.dot(w2, e12); if (d12_1 <= 0.0f) { // a1 <= 0, so we clamp it to 0 m_v2.a = 1.0f; m_count = 1; m_v1.set(m_v2); return; } // Must be in e12 region. float inv_d12 = 1.0f / (d12_1 + d12_2); m_v1.a = d12_1 * inv_d12; m_v2.a = d12_2 * inv_d12; m_count = 2; }
// djm pooled, from above public float getMetric() { switch (m_count) { case 0: assert (false); return 0.0f; case 1: return 0.0f; case 2: return MathUtils.distance(m_v1.w, m_v2.w); case 3: case3.set(m_v2.w).subLocal(m_v1.w); case33.set(m_v3.w).subLocal(m_v1.w); // return Vec2.cross(m_v2.w - m_v1.w, m_v3.w - m_v1.w); return Vec2.cross(case3, case33); default: assert (false); return 0.0f; } }
/** * this returns pooled objects. don't keep or modify them * * @return */ public void getClosestPoint(final Vec2 out) { switch (m_count) { case 0: assert (false); out.setZero(); return; case 1: out.set(m_v1.w); return; case 2: case22.set(m_v2.w).mulLocal(m_v2.a); case2.set(m_v1.w).mulLocal(m_v1.a).addLocal(case22); out.set(case2); return; case 3: out.setZero(); return; default: assert (false); out.setZero(); return; } }
@Override public void solveVelocityConstraints(final SolverData data) { Vec2 vA = data.velocities[m_indexA].v; float wA = data.velocities[m_indexA].w; Vec2 vB = data.velocities[m_indexB].v; float wB = data.velocities[m_indexB].w; final Vec2 vpA = pool.popVec2(); final Vec2 vpB = pool.popVec2(); final Vec2 PA = pool.popVec2(); final Vec2 PB = pool.popVec2(); Vec2.crossToOutUnsafe(wA, m_rA, vpA); vpA.addLocal(vA); Vec2.crossToOutUnsafe(wB, m_rB, vpB); vpB.addLocal(vB); float Cdot = -Vec2.dot(m_uA, vpA) - m_ratio * Vec2.dot(m_uB, vpB); float impulse = -m_mass * Cdot; m_impulse += impulse; PA.set(m_uA).mulLocal(-impulse); PB.set(m_uB).mulLocal(-m_ratio * impulse); vA.x += m_invMassA * PA.x; vA.y += m_invMassA * PA.y; wA += m_invIA * Vec2.cross(m_rA, PA); vB.x += m_invMassB * PB.x; vB.y += m_invMassB * PB.y; wB += m_invIB * Vec2.cross(m_rB, PB); // data.velocities[m_indexA].v.set(vA); data.velocities[m_indexA].w = wA; // data.velocities[m_indexB].v.set(vB); data.velocities[m_indexB].w = wB; pool.pushVec2(4); }
public void getWitnessPoints(Vec2 pA, Vec2 pB) { switch (m_count) { case 0: assert (false); break; case 1: pA.set(m_v1.wA); pB.set(m_v1.wB); break; case 2: case2.set(m_v1.wA).mulLocal(m_v1.a); pA.set(m_v2.wA).mulLocal(m_v2.a).addLocal(case2); // m_v1.a * m_v1.wA + m_v2.a * m_v2.wA; // *pB = m_v1.a * m_v1.wB + m_v2.a * m_v2.wB; case2.set(m_v1.wB).mulLocal(m_v1.a); pB.set(m_v2.wB).mulLocal(m_v2.a).addLocal(case2); break; case 3: pA.set(m_v1.wA).mulLocal(m_v1.a); case3.set(m_v2.wA).mulLocal(m_v2.a); case33.set(m_v3.wA).mulLocal(m_v3.a); pA.addLocal(case3).addLocal(case33); pB.set(pA); // *pA = m_v1.a * m_v1.wA + m_v2.a * m_v2.wA + m_v3.a * m_v3.wA; // *pB = *pA; break; default: assert (false); break; } }
@Override public boolean solvePositionConstraints(final SolverData data) { final Rot qA = pool.popRot(); final Rot qB = pool.popRot(); final Vec2 rA = pool.popVec2(); final Vec2 rB = pool.popVec2(); final Vec2 uA = pool.popVec2(); final Vec2 uB = pool.popVec2(); final Vec2 temp = pool.popVec2(); final Vec2 PA = pool.popVec2(); final Vec2 PB = pool.popVec2(); Vec2 cA = data.positions[m_indexA].c; float aA = data.positions[m_indexA].a; Vec2 cB = data.positions[m_indexB].c; float aB = data.positions[m_indexB].a; qA.set(aA); qB.set(aB); Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), rA); Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), rB); uA.set(cA).addLocal(rA).subLocal(m_groundAnchorA); uB.set(cB).addLocal(rB).subLocal(m_groundAnchorB); float lengthA = uA.length(); float lengthB = uB.length(); if (lengthA > 10.0f * Settings.linearSlop) { uA.mulLocal(1.0f / lengthA); } else { uA.setZero(); } if (lengthB > 10.0f * Settings.linearSlop) { uB.mulLocal(1.0f / lengthB); } else { uB.setZero(); } // Compute effective mass. float ruA = Vec2.cross(rA, uA); float ruB = Vec2.cross(rB, uB); float mA = m_invMassA + m_invIA * ruA * ruA; float mB = m_invMassB + m_invIB * ruB * ruB; float mass = mA + m_ratio * m_ratio * mB; if (mass > 0.0f) { mass = 1.0f / mass; } float C = m_constant - lengthA - m_ratio * lengthB; float linearError = MathUtils.abs(C); float impulse = -mass * C; PA.set(uA).mulLocal(-impulse); PB.set(uB).mulLocal(-m_ratio * impulse); cA.x += m_invMassA * PA.x; cA.y += m_invMassA * PA.y; aA += m_invIA * Vec2.cross(rA, PA); cB.x += m_invMassB * PB.x; cB.y += m_invMassB * PB.y; aB += m_invIB * Vec2.cross(rB, PB); // data.positions[m_indexA].c.set(cA); data.positions[m_indexA].a = aA; // data.positions[m_indexB].c.set(cB); data.positions[m_indexB].a = aB; pool.pushRot(2); pool.pushVec2(7); return linearError < Settings.linearSlop; }
@Override public void initVelocityConstraints(final SolverData data) { m_indexA = m_bodyA.m_islandIndex; m_indexB = m_bodyB.m_islandIndex; m_localCenterA.set(m_bodyA.m_sweep.localCenter); m_localCenterB.set(m_bodyB.m_sweep.localCenter); m_invMassA = m_bodyA.m_invMass; m_invMassB = m_bodyB.m_invMass; m_invIA = m_bodyA.m_invI; m_invIB = m_bodyB.m_invI; Vec2 cA = data.positions[m_indexA].c; float aA = data.positions[m_indexA].a; Vec2 vA = data.velocities[m_indexA].v; float wA = data.velocities[m_indexA].w; Vec2 cB = data.positions[m_indexB].c; float aB = data.positions[m_indexB].a; Vec2 vB = data.velocities[m_indexB].v; float wB = data.velocities[m_indexB].w; final Rot qA = pool.popRot(); final Rot qB = pool.popRot(); final Vec2 temp = pool.popVec2(); qA.set(aA); qB.set(aB); // Compute the effective masses. Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), m_rA); Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), m_rB); m_uA.set(cA).addLocal(m_rA).subLocal(m_groundAnchorA); m_uB.set(cB).addLocal(m_rB).subLocal(m_groundAnchorB); float lengthA = m_uA.length(); float lengthB = m_uB.length(); if (lengthA > 10f * Settings.linearSlop) { m_uA.mulLocal(1.0f / lengthA); } else { m_uA.setZero(); } if (lengthB > 10f * Settings.linearSlop) { m_uB.mulLocal(1.0f / lengthB); } else { m_uB.setZero(); } // Compute effective mass. float ruA = Vec2.cross(m_rA, m_uA); float ruB = Vec2.cross(m_rB, m_uB); float mA = m_invMassA + m_invIA * ruA * ruA; float mB = m_invMassB + m_invIB * ruB * ruB; m_mass = mA + m_ratio * m_ratio * mB; if (m_mass > 0.0f) { m_mass = 1.0f / m_mass; } if (data.step.warmStarting) { // Scale impulses to support variable time steps. m_impulse *= data.step.dtRatio; // Warm starting. final Vec2 PA = pool.popVec2(); final Vec2 PB = pool.popVec2(); PA.set(m_uA).mulLocal(-m_impulse); PB.set(m_uB).mulLocal(-m_ratio * m_impulse); vA.x += m_invMassA * PA.x; vA.y += m_invMassA * PA.y; wA += m_invIA * Vec2.cross(m_rA, PA); vB.x += m_invMassB * PB.x; vB.y += m_invMassB * PB.y; wB += m_invIB * Vec2.cross(m_rB, PB); pool.pushVec2(2); } else { m_impulse = 0.0f; } // data.velocities[m_indexA].v.set(vA); data.velocities[m_indexA].w = wA; // data.velocities[m_indexB].v.set(vB); data.velocities[m_indexB].w = wB; pool.pushVec2(1); pool.pushRot(2); }
@Override public void getReactionForce(float inv_dt, Vec2 argOut) { argOut.set(m_uB).mulLocal(m_impulse).mulLocal(inv_dt); }
/** * Compute the closest points between two shapes. Supports any combination of: CircleShape and * PolygonShape. The simplex cache is input/output. On the first call set SimplexCache.count to * zero. * * @param output * @param cache * @param input */ public final void distance( final DistanceOutput output, final SimplexCache cache, final DistanceInput input) { GJK_CALLS++; final DistanceProxy proxyA = input.proxyA; final DistanceProxy proxyB = input.proxyB; Transform transformA = input.transformA; Transform transformB = input.transformB; // Initialize the simplex. simplex.readCache(cache, proxyA, transformA, proxyB, transformB); // Get simplex vertices as an array. SimplexVertex[] vertices = simplex.vertices; // These store the vertices of the last simplex so that we // can check for duplicates and prevent cycling. // (pooled above) int saveCount = 0; simplex.getClosestPoint(closestPoint); float distanceSqr1 = closestPoint.lengthSquared(); float distanceSqr2 = distanceSqr1; // Main iteration loop int iter = 0; while (iter < MAX_ITERS) { // Copy simplex so we can identify duplicates. saveCount = simplex.m_count; for (int i = 0; i < saveCount; i++) { saveA[i] = vertices[i].indexA; saveB[i] = vertices[i].indexB; } switch (simplex.m_count) { case 1: break; case 2: simplex.solve2(); break; case 3: simplex.solve3(); break; default: assert (false); } // If we have 3 points, then the origin is in the corresponding triangle. if (simplex.m_count == 3) { break; } // Compute closest point. simplex.getClosestPoint(closestPoint); distanceSqr2 = closestPoint.lengthSquared(); // ensure progress if (distanceSqr2 >= distanceSqr1) { // break; } distanceSqr1 = distanceSqr2; // get search direction; simplex.getSearchDirection(d); // Ensure the search direction is numerically fit. if (d.lengthSquared() < Settings.EPSILON * Settings.EPSILON) { // The origin is probably contained by a line segment // or triangle. Thus the shapes are overlapped. // We can't return zero here even though there may be overlap. // In case the simplex is a point, segment, or triangle it is difficult // to determine if the origin is contained in the CSO or very close to it. break; } /* * SimplexVertex* vertex = vertices + simplex.m_count; vertex.indexA = * proxyA.GetSupport(MulT(transformA.R, -d)); vertex.wA = Mul(transformA, * proxyA.GetVertex(vertex.indexA)); Vec2 wBLocal; vertex.indexB = * proxyB.GetSupport(MulT(transformB.R, d)); vertex.wB = Mul(transformB, * proxyB.GetVertex(vertex.indexB)); vertex.w = vertex.wB - vertex.wA; */ // Compute a tentative new simplex vertex using support points. SimplexVertex vertex = vertices[simplex.m_count]; Rot.mulTransUnsafe(transformA.q, d.negateLocal(), temp); vertex.indexA = proxyA.getSupport(temp); Transform.mulToOutUnsafe(transformA, proxyA.getVertex(vertex.indexA), vertex.wA); // Vec2 wBLocal; Rot.mulTransUnsafe(transformB.q, d.negateLocal(), temp); vertex.indexB = proxyB.getSupport(temp); Transform.mulToOutUnsafe(transformB, proxyB.getVertex(vertex.indexB), vertex.wB); vertex.w.set(vertex.wB).subLocal(vertex.wA); // Iteration count is equated to the number of support point calls. ++iter; ++GJK_ITERS; // Check for duplicate support points. This is the main termination criteria. boolean duplicate = false; for (int i = 0; i < saveCount; ++i) { if (vertex.indexA == saveA[i] && vertex.indexB == saveB[i]) { duplicate = true; break; } } // If we found a duplicate support point we must exit to avoid cycling. if (duplicate) { break; } // New vertex is ok and needed. ++simplex.m_count; } GJK_MAX_ITERS = MathUtils.max(GJK_MAX_ITERS, iter); // Prepare output. simplex.getWitnessPoints(output.pointA, output.pointB); output.distance = MathUtils.distance(output.pointA, output.pointB); output.iterations = iter; // Cache the simplex. simplex.writeCache(cache); // Apply radii if requested. if (input.useRadii) { float rA = proxyA.m_radius; float rB = proxyB.m_radius; if (output.distance > rA + rB && output.distance > Settings.EPSILON) { // Shapes are still no overlapped. // Move the witness points to the outer surface. output.distance -= rA + rB; normal.set(output.pointB).subLocal(output.pointA); normal.normalize(); temp.set(normal).mulLocal(rA); output.pointA.addLocal(temp); temp.set(normal).mulLocal(rB); output.pointB.subLocal(temp); } else { // Shapes are overlapped when radii are considered. // Move the witness points to the middle. // Vec2 p = 0.5f * (output.pointA + output.pointB); output.pointA.addLocal(output.pointB).mulLocal(.5f); output.pointB.set(output.pointA); output.distance = 0.0f; } } }
/** * Solve a line segment using barycentric coordinates.<br> * Possible regions:<br> * - points[2]<br> * - edge points[0]-points[2]<br> * - edge points[1]-points[2]<br> * - inside the triangle */ public void solve3() { w1.set(m_v1.w); w2.set(m_v2.w); w3.set(m_v3.w); // Edge12 // [1 1 ][a1] = [1] // [w1.e12 w2.e12][a2] = [0] // a3 = 0 e12.set(w2).subLocal(w1); float w1e12 = Vec2.dot(w1, e12); float w2e12 = Vec2.dot(w2, e12); float d12_1 = w2e12; float d12_2 = -w1e12; // Edge13 // [1 1 ][a1] = [1] // [w1.e13 w3.e13][a3] = [0] // a2 = 0 e13.set(w3).subLocal(w1); float w1e13 = Vec2.dot(w1, e13); float w3e13 = Vec2.dot(w3, e13); float d13_1 = w3e13; float d13_2 = -w1e13; // Edge23 // [1 1 ][a2] = [1] // [w2.e23 w3.e23][a3] = [0] // a1 = 0 e23.set(w3).subLocal(w2); float w2e23 = Vec2.dot(w2, e23); float w3e23 = Vec2.dot(w3, e23); float d23_1 = w3e23; float d23_2 = -w2e23; // Triangle123 float n123 = Vec2.cross(e12, e13); float d123_1 = n123 * Vec2.cross(w2, w3); float d123_2 = n123 * Vec2.cross(w3, w1); float d123_3 = n123 * Vec2.cross(w1, w2); // w1 region if (d12_2 <= 0.0f && d13_2 <= 0.0f) { m_v1.a = 1.0f; m_count = 1; return; } // e12 if (d12_1 > 0.0f && d12_2 > 0.0f && d123_3 <= 0.0f) { float inv_d12 = 1.0f / (d12_1 + d12_2); m_v1.a = d12_1 * inv_d12; m_v2.a = d12_2 * inv_d12; m_count = 2; return; } // e13 if (d13_1 > 0.0f && d13_2 > 0.0f && d123_2 <= 0.0f) { float inv_d13 = 1.0f / (d13_1 + d13_2); m_v1.a = d13_1 * inv_d13; m_v3.a = d13_2 * inv_d13; m_count = 2; m_v2.set(m_v3); return; } // w2 region if (d12_1 <= 0.0f && d23_2 <= 0.0f) { m_v2.a = 1.0f; m_count = 1; m_v1.set(m_v2); return; } // w3 region if (d13_1 <= 0.0f && d23_1 <= 0.0f) { m_v3.a = 1.0f; m_count = 1; m_v1.set(m_v3); return; } // e23 if (d23_1 > 0.0f && d23_2 > 0.0f && d123_1 <= 0.0f) { float inv_d23 = 1.0f / (d23_1 + d23_2); m_v2.a = d23_1 * inv_d23; m_v3.a = d23_2 * inv_d23; m_count = 2; m_v1.set(m_v3); return; } // Must be in triangle123 float inv_d123 = 1.0f / (d123_1 + d123_2 + d123_3); m_v1.a = d123_1 * inv_d123; m_v2.a = d123_2 * inv_d123; m_v3.a = d123_3 * inv_d123; m_count = 3; }