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)
}
}
