/// <summary> Precaculate everything and apply initial impulse before the
/// simulation Step takes place
///
/// </summary>
/// <param name="invDT">The amount of time the simulation is being stepped by
/// </param>
public virtual void PreStep(float invDT)
{
// Pre-compute anchors, mass matrix, and bias.
Matrix2f rot1 = new Matrix2f(body1.Rotation);
Matrix2f rot2 = new Matrix2f(body2.Rotation);
r1 = MathUtil.Mul(rot1, localAnchor1);
r2 = MathUtil.Mul(rot2, localAnchor2);
// deltaV = deltaV0 + K * impulse
// invM = [(1/m1 + 1/m2) * eye(2) - skew(r1) * invI1 * skew(r1) - skew(r2) * invI2 * skew(r2)]
// = [1/m1+1/m2 0 ] + invI1 * [r1.y*r1.y -r1.x*r1.y] + invI2 * [r1.y*r1.y -r1.x*r1.y]
// [ 0 1/m1+1/m2] [-r1.x*r1.y r1.x*r1.x] [-r1.x*r1.y r1.x*r1.x]
Matrix2f K1 = new Matrix2f();
K1.col1.x = body1.InvMass + body2.InvMass; K1.col2.x = 0.0f;
K1.col1.y = 0.0f; K1.col2.y = body1.InvMass + body2.InvMass;
Matrix2f K2 = new Matrix2f();
K2.col1.x = body1.InvI * r1.y * r1.y; K2.col2.x = (- body1.InvI) * r1.x * r1.y;
K2.col1.y = (- body1.InvI) * r1.x * r1.y; K2.col2.y = body1.InvI * r1.x * r1.x;
Matrix2f K3 = new Matrix2f();
K3.col1.x = body2.InvI * r2.y * r2.y; K3.col2.x = (- body2.InvI) * r2.x * r2.y;
K3.col1.y = (- body2.InvI) * r2.x * r2.y; K3.col2.y = body2.InvI * r2.x * r2.x;
Matrix2f K = MathUtil.Add(MathUtil.Add(K1, K2), K3);
M = K.Invert();
Vector2f p1 = new Vector2f(body1.GetPosition());
p1.Add(r1);
Vector2f p2 = new Vector2f(body2.GetPosition());
p2.Add(r2);
Vector2f dp = new Vector2f(p2);
dp.Sub(p1);
bias = new Vector2f(dp);
bias.Scale(- 0.1f);
bias.Scale(invDT);
// Apply accumulated impulse.
accumulatedImpulse.Scale(relaxation);
if (!body1.Static)
{
Vector2f accum1 = new Vector2f(accumulatedImpulse);
accum1.Scale(- body1.InvMass);
body1.AdjustVelocity(accum1);
body1.AdjustAngularVelocity(- (body1.InvI * MathUtil.Cross(r1, accumulatedImpulse)));
}
if (!body2.Static)
{
Vector2f accum2 = new Vector2f(accumulatedImpulse);
accum2.Scale(body2.InvMass);
body2.AdjustVelocity(accum2);
body2.AdjustAngularVelocity(body2.InvI * MathUtil.Cross(r2, accumulatedImpulse));
}
}
/// <seealso cref="Silver.Weight.Raw.Collide.Collider.Collide(Silver.Weight.Raw.Contact[], Silver.Weight.Raw.Body, Silver.Weight.Raw.Body)">
/// </seealso>
public virtual int Collide(Contact[] contacts, Body bodyA, Body bodyB)
{
int numContacts = 0;
Line line = (Line) bodyA.Shape;
Box box = (Box) bodyB.Shape;
Vector2f lineVec = new Vector2f(line.DX, line.DY);
lineVec.Normalise();
Vector2f axis = new Vector2f(- line.DY, line.DX);
axis.Normalise();
Vector2f res = new Vector2f();
line.Start.ProjectOntoUnit(axis, res);
float linePos = GetProp(res, axis);
Vector2f c = MathUtil.Sub(bodyB.GetPosition(), bodyA.GetPosition());
c.ProjectOntoUnit(axis, res);
float centre = GetProp(res, axis);
Vector2f[] pts = box.GetPoints(bodyB.GetPosition(), bodyB.Rotation);
float[] tangent = new float[4];
float[] proj = new float[4];
int outOfRange = 0;
for (int i = 0; i < 4; i++)
{
pts[i].Sub(bodyA.GetPosition());
pts[i].ProjectOntoUnit(axis, res);
tangent[i] = GetProp(res, axis);
pts[i].ProjectOntoUnit(lineVec, res);
proj[i] = GetProp(res, new Vector2f(line.DX, line.DY));
if ((proj[i] >= 1) || (proj[i] <= 0))
{
outOfRange++;
}
}
if (outOfRange == 4)
{
return 0;
}
Vector2f normal = new Vector2f(axis);
if (centre < linePos)
{
if (!line.BlocksInnerEdge)
{
return 0;
}
normal.Scale(- 1);
for (int i = 0; i < 4; i++)
{
if (tangent[i] > linePos)
{
if (proj[i] < 0)
{
Vector2f onAxis = new Vector2f();
Line leftLine = new Line(GetPt(pts, i - 1), pts[i]);
Line rightLine = new Line(GetPt(pts, i + 1), pts[i]);
leftLine.getClosestPoint(line.Start, res);
res.ProjectOntoUnit(axis, onAxis);
float left = GetProp(onAxis, axis);
rightLine.getClosestPoint(line.Start, res);
res.ProjectOntoUnit(axis, onAxis);
float right = GetProp(onAxis, axis);
if ((left > 0) && (right > 0))
{
Vector2f pos = new Vector2f(bodyA.GetPosition());
pos.Add(line.Start);
ResolveEndPointCollision(pos, bodyA, bodyB, normal, leftLine, rightLine, contacts[numContacts], i);
numContacts++;
}
}
else if (proj[i] > 1)
{
Vector2f onAxis = new Vector2f();
Line leftLine = new Line(GetPt(pts, i - 1), pts[i]);
Line rightLine = new Line(GetPt(pts, i + 1), pts[i]);
leftLine.getClosestPoint(line.End, res);
res.ProjectOntoUnit(axis, onAxis);
float left = GetProp(onAxis, axis);
rightLine.getClosestPoint(line.End, res);
res.ProjectOntoUnit(axis, onAxis);
float right = GetProp(onAxis, axis);
if ((left > 0) && (right > 0))
{
Vector2f pos = new Vector2f(bodyA.GetPosition());
pos.Add(line.End);
ResolveEndPointCollision(pos, bodyA, bodyB, normal, leftLine, rightLine, contacts[numContacts], i);
numContacts++;
}
}
else
{
pts[i].ProjectOntoUnit(lineVec, res);
res.Add(bodyA.GetPosition());
contacts[numContacts].Separation = - (tangent[i] - linePos);
contacts[numContacts].Position = new Vector2f(res);
contacts[numContacts].Normal = normal;
contacts[numContacts].Feature = new FeaturePair(i);
numContacts++;
}
}
}
}
else
{
if (!line.BlocksOuterEdge)
{
return 0;
}
for (int i = 0; i < 4; i++)
{
if (tangent[i] < linePos)
{
if (proj[i] < 0)
{
Vector2f onAxis = new Vector2f();
Line leftLine = new Line(GetPt(pts, i - 1), pts[i]);
Line rightLine = new Line(GetPt(pts, i + 1), pts[i]);
leftLine.getClosestPoint(line.Start, res);
res.ProjectOntoUnit(axis, onAxis);
float left = GetProp(onAxis, axis);
rightLine.getClosestPoint(line.Start, res);
res.ProjectOntoUnit(axis, onAxis);
float right = GetProp(onAxis, axis);
if ((left < 0) && (right < 0))
{
Vector2f pos = new Vector2f(bodyA.GetPosition());
pos.Add(line.Start);
ResolveEndPointCollision(pos, bodyA, bodyB, normal, leftLine, rightLine, contacts[numContacts], i);
numContacts++;
}
}
else if (proj[i] > 1)
{
Vector2f onAxis = new Vector2f();
Line leftLine = new Line(GetPt(pts, i - 1), pts[i]);
Line rightLine = new Line(GetPt(pts, i + 1), pts[i]);
leftLine.getClosestPoint(line.End, res);
res.ProjectOntoUnit(axis, onAxis);
float left = GetProp(onAxis, axis);
rightLine.getClosestPoint(line.End, res);
res.ProjectOntoUnit(axis, onAxis);
float right = GetProp(onAxis, axis);
if ((left < 0) && (right < 0))
{
Vector2f pos = new Vector2f(bodyA.GetPosition());
pos.Add(line.End);
ResolveEndPointCollision(pos, bodyA, bodyB, normal, leftLine, rightLine, contacts[numContacts], i);
numContacts++;
}
}
else
{
pts[i].ProjectOntoUnit(lineVec, res);
res.Add(bodyA.GetPosition());
contacts[numContacts].Separation = - (linePos - tangent[i]);
contacts[numContacts].Position = new Vector2f(res);
contacts[numContacts].Normal = normal;
contacts[numContacts].Feature = new FeaturePair();
numContacts++;
}
}
}
}
if (numContacts > 2)
{
throw new System.SystemException("LineBoxCollision: > 2 contacts");
}
return numContacts;
}
/// <summary> Apply the impulse caused by the joint to the bodies attached.</summary>
public virtual void ApplyImpulse()
{
Vector2f dv = new Vector2f(body2.Velocity);
dv.Add(MathUtil.Cross(body2.AngularVelocity, r2));
dv.Sub(body1.Velocity);
dv.Sub(MathUtil.Cross(body1.AngularVelocity, r1));
dv.Scale(- 1);
dv.Add(bias); // TODO: is this baumgarte stabilization?
if (dv.LengthSquared() == 0)
{
return ;
}
Vector2f impulse = MathUtil.Mul(M, dv);
if (!body1.Static)
{
Vector2f delta1 = new Vector2f(impulse);
delta1.Scale(- body1.InvMass);
body1.AdjustVelocity(delta1);
body1.AdjustAngularVelocity((- body1.InvI) * MathUtil.Cross(r1, impulse));
}
if (!body2.Static)
{
Vector2f delta2 = new Vector2f(impulse);
delta2.Scale(body2.InvMass);
body2.AdjustVelocity(delta2);
body2.AdjustAngularVelocity(body2.InvI * MathUtil.Cross(r2, impulse));
}
accumulatedImpulse.Add(impulse);
}
/// <summary> Step the simulation. Currently anything other than 1/60f as a
/// Step leads to unpredictable results - hence the default Step
/// fixes us to this Step
///
/// </summary>
/// <param name="dt">The amount of time to Step
/// </param>
public virtual void Step(float dt)
{
BodyList bodies = ActiveBodies;
JointList joints = ActiveJoints;
float invDT = dt > 0.0f?1.0f / dt:0.0f;
if (restingBodyDetection)
{
for (int i = 0; i < bodies.Size(); ++i)
{
Body b = bodies.Item(i);
b.StartFrame();
}
for (int i = 0; i < joints.Size(); ++i)
{
Joint j = joints.Item(i);
j.Body1.IsResting = false;
j.Body2.IsResting = false;
}
}
BroadPhase(dt);
for (int i = 0; i < bodies.Size(); ++i)
{
Body b = bodies.Item(i);
if (b.InvMass == 0.0f)
{
continue;
}
if (b.Resting && restingBodyDetection)
{
continue;
}
Vector2f temp = new Vector2f(b.GetForce());
temp.Scale(b.InvMass);
if (b.GravityEffected)
{
temp.Add(gravity);
}
temp.Scale(dt);
b.AdjustVelocity(temp);
Vector2f damping = new Vector2f(b.Velocity);
damping.Scale((- b.Damping) * b.InvMass);
b.AdjustVelocity(damping);
b.AdjustAngularVelocity(dt * b.InvI * b.Torque);
b.AdjustAngularVelocity((- b.AngularVelocity) * b.InvI * b.RotDamping);
}
for (int i = 0; i < arbiters.size(); i++)
{
Arbiter arb = arbiters.Item(i);
if (!restingBodyDetection || !arb.HasRestingPair())
{
arb.PreStep(invDT, dt, damping);
}
}
for (int i = 0; i < joints.Size(); ++i)
{
Joint j = joints.Item(i);
j.PreStep(invDT);
}
for (int i = 0; i < iterations; ++i)
{
for (int k = 0; k < arbiters.size(); k++)
{
Arbiter arb = arbiters.Item(k);
if (!restingBodyDetection || !arb.HasRestingPair())
{
arb.ApplyImpulse();
}
else
{
arb.Body1.Collided(arb.Body2);
arb.Body2.Collided(arb.Body1);
}
}
for (int k = 0; k < joints.Size(); ++k)
{
Joint j = joints.Item(k);
j.ApplyImpulse();
}
}
for (int i = 0; i < bodies.Size(); ++i)
{
Body b = bodies.Item(i);
if (b.InvMass == 0.0f)
{
continue;
}
if (restingBodyDetection)
{
if (b.Resting)
{
continue;
}
}
b.AdjustPosition(b.Velocity, dt);
b.AdjustPosition(b.BiasedVelocity, dt);
b.AdjustRotation(dt * b.AngularVelocity);
b.AdjustRotation(dt * b.BiasedAngularVelocity);
b.ResetBias();
b.SetForce(0, 0);
b.Torque = 0;
}
if (restingBodyDetection)
{
for (int i = 0; i < bodies.Size(); ++i)
{
Body b = bodies.Item(i);
b.EndFrame();
}
}
}