func (body *Body) UpdatePosition(dt float32) {
if body.UpdatePositionFunc != nil {
body.UpdatePositionFunc(body, dt)
return
}
body.p = vect.Add(body.p, vect.Mult(vect.Add(body.v, body.v_bias), dt))
body.setAngle(body.a + (body.w+body.w_bias)*dt)
body.v_bias = vect.Vector_Zero
body.w_bias = 0.0
}
func (body *Body) UpdateVelocity(gravity vect.Vect, ldamping, adamping, dt float32) {
if body.UpdateVelocityFunc != nil {
body.UpdateVelocityFunc(body, gravity, ldamping, dt)
return
}
body.v = vect.Add(vect.Mult(body.v, ldamping), vect.Mult(vect.Add(gravity, vect.Mult(body.f, body.m_inv)), dt))
body.w = (body.w * adamping) + (body.t * body.i_inv * dt)
body.f = vect.Vector_Zero
body.t = 0.0
}
func RayAgainstPolygon(c *RayCast, poly *PolygonShape, outT *float32) bool {
for i, axis := range poly.TAxes {
cosAngle := vect.Dot(c.dir, axis.N)
if cosAngle < EPS && cosAngle >= -EPS {
return false
}
t := -(vect.Dot(c.begin, axis.N) - axis.D) / cosAngle
if t > 1.0 || t < 0.0 {
return false
}
//check if point belongs to polygon line
point := vect.Add(c.begin, vect.Mult(c.dir, t))
v1 := poly.TVerts[i]
v2 := poly.TVerts[(i+1)%poly.NumVerts]
polyDir := vect.Sub(v2, v1)
polyT := float32(-1.0)
if polyDir.X < EPS || polyDir.X > -EPS {
polyT = (point.Y - v1.Y) / polyDir.Y
} else {
polyT = (point.Y - v1.Y) / polyDir.Y
}
if polyT >= 0.0 && polyT <= 1.0 {
*outT = t
return true
}
}
return false
}
func circle2circleQuery(p1, p2 vect.Vect, r1, r2 float32, con *Contact) int {
minDist := r1 + r2
delta := vect.Sub(p2, p1)
distSqr := delta.LengthSqr()
if distSqr >= minDist*minDist {
return 0
}
dist := float32(math.Sqrt(float64(distSqr)))
pDist := dist
if dist == 0.0 {
pDist = float32(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, 0)
return 1
}
func (this *PivotJoint) PreStep(dt float32) {
a, b := this.BodyA, this.BodyB
this.r1 = transform.RotateVect(this.Anchor1, transform.Rotation{a.rot.X, a.rot.Y})
this.r2 = transform.RotateVect(this.Anchor2, transform.Rotation{b.rot.X, b.rot.Y})
// Calculate mass tensor
k_tensor(a, b, this.r1, this.r2, &this.k1, &this.k2)
// compute max impulse
this.jMaxLen = this.MaxForce * dt
// calculate bias velocity
delta := vect.Sub(vect.Add(b.p, this.r2), vect.Add(a.p, this.r1))
this.bias = vect.Clamp(vect.Mult(delta, -bias_coef(this.ErrorBias, dt)/dt), this.MaxBias)
}
func (arb *Arbiter) applyImpulse3() {
a := arb.ShapeA.Body
b := arb.ShapeB.Body
for i := 0; i < arb.NumContacts; i++ {
con := arb.Contacts[i]
n := con.n
r1 := con.r1
r2 := con.r2
// Calculate the relative bias velocities.
vb1 := vect.Add(a.v_bias, vect.Mult(vect.Perp(r1), a.w_bias))
vb2 := vect.Add(b.v_bias, vect.Mult(vect.Perp(r2), b.w_bias))
vbn := vect.Dot(vect.Sub(vb2, vb1), n)
// Calculate the relative velocity.
vr := relative_velocity(a, b, r1, r2)
vrn := vect.Dot(vr, n)
// Calculate the relative tangent velocity.
vrt := vect.Dot(vect.Add(vr, arb.Surface_vr), vect.Perp(n))
// Calculate and clamp the bias impulse.
jbn := (con.bias - vbn) * con.nMass
jbnOld := con.jBias
con.jBias = vect.FMax(jbnOld+jbn, 0.0)
// Calculate and clamp the normal impulse.
jn := -(con.bounce + vrn) * con.nMass
jnOld := con.jnAcc
con.jnAcc = vect.FMax(jnOld+jn, 0.0)
// Calculate and clamp the friction impulse.
jtMax := arb.u * con.jnAcc
jt := -vrt * con.tMass
jtOld := con.jtAcc
con.jtAcc = vect.FClamp(jtOld+jt, -jtMax, jtMax)
// Apply the bias impulse.
apply_bias_impulses(a, b, r1, r2, vect.Mult(n, con.jBias-jbnOld))
// Apply the final impulse.
apply_impulses(a, b, r1, r2, transform.RotateVect(n, transform.Rotation{con.jnAcc - jnOld, con.jtAcc - jtOld}))
}
}
// Recalculates the global center of the circle and the the bounding box.
func (circle *CircleShape) update(xf transform.Transform) AABB {
//global center of the circle
center := xf.TransformVect(circle.Position)
circle.Tc = center
rv := vect.Vect{circle.Radius, circle.Radius}
return AABB{
vect.Sub(center, rv),
vect.Add(center, rv),
}
}
func (spring *DampedSpring) PreStep(dt float32) {
a := spring.BodyA
b := spring.BodyB
spring.r1 = transform.RotateVect(spring.Anchor1, transform.Rotation{a.rot.X, a.rot.Y})
spring.r2 = transform.RotateVect(spring.Anchor2, transform.Rotation{a.rot.X, a.rot.Y})
delta := vect.Sub(vect.Add(b.p, spring.r2), vect.Add(a.p, spring.r1))
dist := vect.Length(delta)
if dist == 0 {
dist = float32(math.Inf(1))
}
spring.n = vect.Mult(delta, 1.0/dist)
k := k_scalar(a, b, spring.r1, spring.r2, spring.n)
spring.nMass = 1.0 / k
spring.targetVRN = 0.0
spring.vCoef = float32(1.0 - math.Exp(float64(-spring.Damping*dt*k)))
fSpring := spring.SpringForceFunc(spring, dist)
apply_impulses(a, b, spring.r1, spring.r2, vect.Mult(spring.n, fSpring*dt))
}
func (this *PivotJoint) ApplyImpulse() {
a, b := this.BodyA, this.BodyB
r1, r2 := this.r1, this.r2
// compute relative velocity
vr := relative_velocity2(a, b, r1, r2)
// compute normal impulse
j := mult_k(vect.Sub(this.bias, vr), this.k1, this.k2)
jOld := this.jAcc
this.jAcc = vect.Clamp(vect.Add(this.jAcc, j), this.jMaxLen)
j = vect.Sub(this.jAcc, jOld)
// apply impulse
apply_impulses(a, b, this.r1, this.r2, j)
}
func circle2segmentFunc(contacts []*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 := vect.FAbs(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, 0)
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 (segment *SegmentShape) Moment(mass float32) float32 {
offset := vect.Mult(vect.Add(segment.A, segment.B), 0.5)
return float32(mass) * (vect.DistSqr(segment.B, segment.A)/12.0 + vect.LengthSqr(offset))
}
func relative_velocity2(a, b *Body, r1, r2 vect.Vect) vect.Vect {
v1 := vect.Add(b.v, vect.Mult(vect.Perp(r2), b.w))
v2 := vect.Add(a.v, vect.Mult(vect.Perp(r1), a.w))
return vect.Sub(v1, v2)
}
//returns the center of the aabb
func (aabb *AABB) Center() vect.Vect {
return vect.Mult(vect.Add(aabb.Lower, aabb.Upper), 0.5)
}
func seg2polyFunc(contacts []*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, hashPair(seg.Shape.Hash(), 0))
}
if poly.ContainsVert(vb) {
nextContact(contacts, &num).reset(vb, poly_n, poly_min, hashPair(seg.Shape.Hash(), 1))
}
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
}