func (poly *PolygonShape) valueOnAxis(n vect.Vect, d float64) float64 { verts := poly.TVerts min := vect.Dot(n, verts[0]) for i := 1; i < poly.NumVerts; i++ { min = math.Min(min, vect.Dot(n, verts[i])) } return min - d }
func (poly *PolygonShape) ContainsVertPartial(v, n vect.Vect) bool { for _, axis := range poly.TAxes { if vect.Dot(axis.N, n) < 0.0 { continue } dist := vect.Dot(axis.N, v) - axis.D if dist > 0.0 { return false } } return true }
func findPoinsBehindSeg(contacts *[MaxPoints]Contact, num *int, seg *SegmentShape, poly *PolygonShape, pDist, coef float64) { dta := vect.Cross(seg.Tn, seg.Ta) dtb := vect.Cross(seg.Tn, seg.Tb) n := vect.Mult(seg.Tn, coef) for i := 0; i < poly.NumVerts; i++ { v := poly.TVerts[i] if vect.Dot(v, n) < vect.Dot(seg.Tn, seg.Ta)*coef+seg.Radius { dt := vect.Cross(seg.Tn, v) if dta >= dt && dt >= dtb { nextContact(contacts, num).reset(v, n, pDist) } } } }
func segmentEncapQuery(p1, p2 vect.Vect, r1, r2 float64, con *Contact, tangent vect.Vect) int { count := circle2circleQuery(p1, p2, r1, r2, con) if vect.Dot(con.Normal, tangent) >= 0.0 { return count } else { return 0 } panic("Never reached") }
func (poly *PolygonShape) ContainsVert(v vect.Vect) bool { for _, axis := range poly.TAxes { dist := vect.Dot(axis.N, v) - axis.D if dist > 0.0 { return false } } return true }
func circle2segmentFunc(contacts *[MaxPoints]Contact, circle *CircleShape, segment *SegmentShape) int { rsum := circle.Radius + segment.Radius //Calculate normal distance from segment dn := vect.Dot(segment.Tn, circle.Tc) - vect.Dot(segment.Ta, segment.Tn) dist := math.Abs(dn) - rsum if dist > 0.0 { return 0 } //Calculate tangential distance along segment dt := -vect.Cross(segment.Tn, circle.Tc) dtMin := -vect.Cross(segment.Tn, segment.Ta) dtMax := -vect.Cross(segment.Tn, segment.Tb) // Decision tree to decide which feature of the segment to collide with. if dt < dtMin { if dt < (dtMin - rsum) { return 0 } else { return segmentEncapQuery(circle.Tc, segment.Ta, circle.Radius, segment.Radius, &contacts[0], segment.A_tangent) } } else { if dt < dtMax { n := segment.Tn if dn >= 0.0 { n.Mult(-1) } con := &contacts[0] pos := vect.Add(circle.Tc, vect.Mult(n, circle.Radius+dist*0.5)) con.reset(pos, n, dist) return 1 } else { if dt < (dtMax + rsum) { return segmentEncapQuery(circle.Tc, segment.Tb, circle.Radius, segment.Radius, &contacts[0], segment.B_tangent) } else { return 0 } } } panic("Never reached") }
func (arb *Arbiter) preStep(inv_dt float64) { const allowedPenetration = 0.01 biasFactor := 0.0 if Settings.PositionCorrection { biasFactor = 0.2 } b1 := arb.ShapeA.Body b2 := arb.ShapeB.Body for i := 0; i < arb.NumContacts; i++ { c := &arb.Contacts[i] c.R1 = vect.Sub(c.Position, b1.Transform.Position) c.R2 = vect.Sub(c.Position, b2.Transform.Position) r1 := c.R1 r2 := c.R2 //Precompute normal mass, tangent mass, and bias rn1 := vect.Dot(r1, c.Normal) rn2 := vect.Dot(r2, c.Normal) kNormal := b1.invMass + b2.invMass kNormal += b1.invI*(vect.Dot(r1, r1)-rn1*rn1) + b2.invI*(vect.Dot(r2, r2)-rn2*rn2) c.MassNormal = 1.0 / kNormal tangent := vect.CrossVF(c.Normal, 1.0) rt1 := vect.Dot(r1, tangent) rt2 := vect.Dot(r2, tangent) kTangent := b1.invMass + b2.invMass kTangent += b1.invI*(vect.Dot(r1, r1)-rt1*rt1) + b2.invI*(vect.Dot(r2, r2)-rt2*rt2) c.MassTangent = 1.0 / kTangent c.Bias = -biasFactor * inv_dt * math.Min(0.0, c.Separation+allowedPenetration) if Settings.AccumulateImpulses { //Apply normal + friction impulse P := vect.Add(vect.Mult(c.Normal, c.Pn), vect.Mult(tangent, c.Pt)) b1.Velocity.Sub(vect.Mult(P, b1.invMass)) b1.AngularVelocity -= b1.invI * vect.Cross(r1, P) b2.Velocity.Add(vect.Mult(P, b2.invMass)) b2.AngularVelocity += b2.invI * vect.Cross(r2, P) } } }
func circle2polyFunc(contacts *[MaxPoints]Contact, circle *CircleShape, poly *PolygonShape) int { axes := poly.TAxes mini := 0 min := vect.Dot(axes[0].N, circle.Tc) - axes[0].D - circle.Radius for i, axis := range axes { dist := vect.Dot(axis.N, circle.Tc) - axis.D - circle.Radius if dist > 0.0 { return 0 } else if dist > min { min = dist mini = i } } n := axes[mini].N a := poly.TVerts[mini] b := poly.TVerts[(mini+1)%poly.NumVerts] dta := vect.Cross(n, a) dtb := vect.Cross(n, b) dt := vect.Cross(n, circle.Tc) if dt < dtb { return circle2circleQuery(circle.Tc, b, circle.Radius, 0.0, &contacts[0]) } else if dt < dta { contacts[0].reset( vect.Sub(circle.Tc, vect.Mult(n, circle.Radius+min/2.0)), vect.Mult(n, -1), min, ) return 1 } else { return circle2circleQuery(circle.Tc, a, circle.Radius, 0.0, &contacts[0]) } panic("Never reached") }
// Sets the vertices offset by the offset and calculates the PolygonAxes. func (poly *PolygonShape) SetVerts(verts Vertices, offset vect.Vect) { if verts == nil { log.Printf("Error: no vertices passed!") return } if verts.ValidatePolygon() == false { log.Printf("Warning: vertices not valid") } numVerts := len(verts) oldnumVerts := len(poly.Verts) poly.NumVerts = numVerts if oldnumVerts < numVerts { //create new slices poly.Verts = make(Vertices, numVerts) poly.TVerts = make(Vertices, numVerts) poly.Axes = make([]PolygonAxis, numVerts) poly.TAxes = make([]PolygonAxis, numVerts) } else { //reuse old slices poly.Verts = poly.Verts[:numVerts] poly.TVerts = poly.TVerts[:numVerts] poly.Axes = poly.Axes[:numVerts] poly.TAxes = poly.TAxes[:numVerts] } for i := 0; i < numVerts; i++ { a := vect.Add(offset, verts[i]) b := vect.Add(offset, verts[(i+1)%numVerts]) n := vect.Normalize(vect.Perp(vect.Sub(b, a))) poly.Verts[i] = a poly.Axes[i].N = n poly.Axes[i].D = vect.Dot(n, a) } }
// Calculates the transformed vertices and axes and the bounding box. func (poly *PolygonShape) update(xf transform.Transform) aabb.AABB { //transform axes { src := poly.Axes dst := poly.TAxes for i := 0; i < poly.NumVerts; i++ { n := xf.RotateVect(src[i].N) dst[i].N = n dst[i].D = vect.Dot(xf.Position, n) + src[i].D } } //transform verts { inf := math.Inf(1) aabb := aabb.AABB{ Lower: vect.Vect{inf, inf}, Upper: vect.Vect{-inf, -inf}, } src := poly.Verts dst := poly.TVerts for i := 0; i < poly.NumVerts; i++ { v := xf.TransformVect(src[i]) dst[i] = v aabb.Lower.X = math.Min(aabb.Lower.X, v.X) aabb.Upper.X = math.Max(aabb.Upper.X, v.X) aabb.Lower.Y = math.Min(aabb.Lower.Y, v.Y) aabb.Upper.Y = math.Max(aabb.Upper.Y, v.Y) } return aabb } }
func seg2polyFunc(contacts *[MaxPoints]Contact, seg *SegmentShape, poly *PolygonShape) int { axes := poly.TAxes segD := vect.Dot(seg.Tn, seg.Ta) minNorm := poly.ValueOnAxis(seg.Tn, segD) - seg.Radius minNeg := poly.ValueOnAxis(vect.Mult(seg.Tn, -1), -segD) - seg.Radius if minNeg > 0.0 || minNorm > 0.0 { return 0 } mini := 0 poly_min := segValueOnAxis(seg, axes[0].N, axes[0].D) if poly_min > 0.0 { return 0 } for i := 0; i < poly.NumVerts; i++ { dist := segValueOnAxis(seg, axes[i].N, axes[i].D) if dist > 0.0 { return 0 } else if dist > poly_min { poly_min = dist mini = i } } num := 0 poly_n := vect.Mult(axes[mini].N, -1) va := vect.Add(seg.Ta, vect.Mult(poly_n, seg.Radius)) vb := vect.Add(seg.Tb, vect.Mult(poly_n, seg.Radius)) if poly.ContainsVert(va) { nextContact(contacts, &num).reset(va, poly_n, poly_min) } if poly.ContainsVert(vb) { nextContact(contacts, &num).reset(vb, poly_n, poly_min) } if minNorm >= poly_min || minNeg >= poly_min { if minNorm > minNeg { findPoinsBehindSeg(contacts, &num, seg, poly, minNorm, 1.0) } else { findPoinsBehindSeg(contacts, &num, seg, poly, minNeg, -1.0) } } // If no other collision points are found, try colliding endpoints. if num == 0 { poly_a := poly.TVerts[mini] poly_b := poly.TVerts[(mini+1)%poly.NumVerts] if segmentEncapQuery(seg.Ta, poly_a, seg.Radius, 0.0, &contacts[0], vect.Mult(seg.A_tangent, -1)) != 0 { return 1 } if segmentEncapQuery(seg.Tb, poly_a, seg.Radius, 0.0, &contacts[0], vect.Mult(seg.B_tangent, -1)) != 0 { return 1 } if segmentEncapQuery(seg.Ta, poly_b, seg.Radius, 0.0, &contacts[0], vect.Mult(seg.A_tangent, -1)) != 0 { return 1 } if segmentEncapQuery(seg.Tb, poly_b, seg.Radius, 0.0, &contacts[0], vect.Mult(seg.B_tangent, -1)) != 0 { return 1 } } return num }
func segValueOnAxis(seg *SegmentShape, n vect.Vect, d float64) float64 { a := vect.Dot(n, seg.Ta) - seg.Radius b := vect.Dot(n, seg.Tb) - seg.Radius return math.Min(a, b) - d }
// Returns true if the given point is located inside the circle. func (circle *CircleShape) TestPoint(point vect.Vect) bool { d := vect.Sub(point, circle.Tc) return vect.Dot(d, d) <= circle.Radius*circle.Radius }
func (arb *Arbiter) applyImpulse() { sA := arb.ShapeA sB := arb.ShapeB b1 := sA.Body b2 := sB.Body //xfA := b1.Transform //xfB := b2.Transform for i := 0; i < arb.NumContacts; i++ { c := &arb.Contacts[i] // Relative velocity at contact dv := vect.Vect{} { t1 := vect.Add(b2.Velocity, vect.CrossFV(b2.AngularVelocity, c.R2)) t2 := vect.Sub(b1.Velocity, vect.CrossFV(b1.AngularVelocity, c.R1)) dv = vect.Sub(t1, t2) } // Compute normal impulse vn := vect.Dot(dv, c.Normal) dPn := c.MassNormal * (-vn + c.Bias) if Settings.AccumulateImpulses { // Clamp the accumulated impulse Pn0 := c.Pn c.Pn = math.Max(Pn0+dPn, 0.0) dPn = c.Pn - Pn0 } else { dPn = math.Max(dPn, 0.0) } //Apply contact impulse Pn := vect.Mult(c.Normal, dPn) b1.Velocity.Sub(vect.Mult(Pn, b1.invMass)) b1.AngularVelocity -= b1.invI * vect.Cross(c.R1, Pn) b2.Velocity.Add(vect.Mult(Pn, b2.invMass)) b2.AngularVelocity += b2.invI * vect.Cross(c.R2, Pn) //Relative velocity at contact { t1 := vect.Add(b2.Velocity, vect.CrossFV(b2.AngularVelocity, c.R2)) t2 := vect.Sub(b1.Velocity, vect.CrossFV(b1.AngularVelocity, c.R1)) dv = vect.Sub(t1, t2) } tangent := vect.CrossVF(c.Normal, 1.0) vt := vect.Dot(dv, tangent) dPt := c.MassTangent * (-vt) if Settings.AccumulateImpulses { //Compute friction impulse maxPt := arb.Friction * c.Pn //Clamp Friction oldTangentImpulse := c.Pt c.Pt = clamp(oldTangentImpulse+dPt, -maxPt, maxPt) dPt = c.Pt - oldTangentImpulse } else { maxPt := arb.Friction * dPn dPt = clamp(dPt, -maxPt, maxPt) } // Apply contact impulse Pt := vect.Mult(tangent, dPt) b1.Velocity.Sub(vect.Mult(Pt, b1.invMass)) b1.AngularVelocity -= b1.invI * vect.Cross(c.R1, Pt) b2.Velocity.Add(vect.Mult(Pt, b2.invMass)) b2.AngularVelocity += b2.invI * vect.Cross(c.R2, Pt) } }