func circle2circleQuery(p1, p2 vect.Vect, r1, r2 float64, con *Contact) int {
minDist := r1 + r2
delta := vect.Sub(p2, p1)
distSqr := delta.LengthSqr()
if distSqr >= minDist*minDist {
return 0
}
dist := math.Sqrt(distSqr)
pDist := dist
if dist == 0.0 {
pDist = math.Inf(1)
}
pos := vect.Add(p1, vect.Mult(delta, 0.5+(r1-0.5*minDist)/pDist))
norm := vect.Vect{1, 0}
if dist != 0.0 {
norm = vect.Mult(delta, 1.0/dist)
}
con.reset(pos, norm, dist-minDist)
return 1
}
func DrawDebugData(space *collision.Space) {
//Draw shapes
for _, b := range space.Bodies {
if b.Enabled == false {
//Inactive
gl.Color3f(.5, .8, .5)
} else if b.IsStatic() {
//Static
gl.Color3f(1, 1, 1)
} else {
//Normal
gl.Color3f(1, 0, 0)
}
for _, s := range b.Shapes {
DrawShape(s)
}
}
gl.Color3f(0, 1, 0.5)
for _, b := range space.Bodies {
DrawTransform(&b.Transform, 0.2)
}
if Settings.DrawAABBs {
for _, b := range space.Bodies {
gl.Color3f(.3, .7, .7)
for _, s := range b.Shapes {
DrawQuad(s.AABB.Lower, s.AABB.Upper, false)
}
}
}
const contactRadius = 0.2
const contactNormalScale = 0.5
for arb := space.ContactManager.ArbiterList.Arbiter; arb != nil; arb = arb.Next {
for i := 0; i < arb.NumContacts; i++ {
con := arb.Contacts[i]
gl.Color3f(0, 0, 1)
p1 := con.Position
p2 := vect.Add(p1, vect.Mult(con.Normal, contactNormalScale))
//p2 := vect.Add(p1, vect.Mult(con.Normal, con.Separation))
DrawLine(p1, p2)
gl.Color3f(0, 1, 0)
DrawCircle(con.Position, contactRadius, false)
}
}
if Settings.DrawTreeNodes {
for _, node := range space.GetDynamicTreeNodes() {
gl.Color3f(0.0, .7, .7)
DrawQuad(node.AABB().Lower, node.AABB().Upper, false)
}
}
}
// Recalculates the global center of the circle and the the bounding box.
func (circle *CircleShape) update(xf transform.Transform) aabb.AABB {
//global center of the circle
center := xf.TransformVect(circle.Position)
circle.Tc = center
rv := vect.Vect{circle.Radius, circle.Radius}
return aabb.AABB{
vect.Sub(center, rv),
vect.Add(center, rv),
}
}
// 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)
}
}
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 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 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 (xf *Transform) TransformVectInv(v vect.Vect) vect.Vect {
return vect.Add(vect.Mult(xf.Position, -1), xf.RotateVectInv(v))
}
//moves and roates the input vector.
func (xf *Transform) TransformVect(v vect.Vect) vect.Vect {
return vect.Add(xf.Position, xf.RotateVect(v))
}
func DrawShape(shape *collision.Shape) {
switch shape.ShapeType() {
case collision.ShapeType_Circle:
circle := shape.ShapeClass.(*collision.CircleShape)
DrawCircle(circle.Tc, circle.Radius, false)
const circleMarkerSize = 0.08
{
p1 := vect.Add(circle.Tc, vect.Vect{0, circleMarkerSize})
p2 := vect.Sub(circle.Tc, vect.Vect{0, circleMarkerSize})
DrawLine(p1, p2)
}
{
p1 := vect.Add(circle.Tc, vect.Vect{circleMarkerSize, 0})
p2 := vect.Sub(circle.Tc, vect.Vect{circleMarkerSize, 0})
DrawLine(p1, p2)
}
break
case collision.ShapeType_Segment:
segment := shape.ShapeClass.(*collision.SegmentShape)
a := segment.Ta
b := segment.Tb
r := segment.Radius
DrawLine(a, b)
if segment.Radius > 0.0 {
DrawCircle(a, r, false)
DrawCircle(b, r, false)
verts := [4]vect.Vect{
vect.Add(a, vect.Vect{0, r}),
vect.Add(a, vect.Vect{0, -r}),
vect.Add(b, vect.Vect{0, -r}),
vect.Add(b, vect.Vect{0, r}),
}
DrawPoly(verts[:], 4, false)
}
if Settings.DrawNormals {
n := segment.Tn
DrawLine(a, vect.Add(a, n))
DrawLine(b, vect.Add(b, n))
}
case collision.ShapeType_Polygon:
poly := shape.ShapeClass.(*collision.PolygonShape)
verts := poly.TVerts
DrawPoly(verts, poly.NumVerts, false)
if Settings.DrawNormals {
axes := poly.TAxes
for i, v := range verts {
a := axes[i]
v1 := v
v2 := verts[(i+1)%len(verts)]
DrawLine(v1, vect.Add(v1, a.N))
DrawLine(v2, vect.Add(v2, a.N))
}
}
case collision.ShapeType_Box:
poly := shape.ShapeClass.(*collision.BoxShape).Polygon
verts := poly.TVerts
DrawPoly(verts, poly.NumVerts, false)
}
}
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)
}
}
//returns the center of the aabb
func (aabb *AABB) Center() vect.Vect {
return vect.Mult(vect.Add(aabb.Lower, aabb.Upper), 0.5)
}