/// <summary> Constructs a Penetration Sweep object, with all its attributes set.
/// This constructor is public only for testing purposes. The static method
/// {@link PenetrationSweep#GetPenetrationDepth(Intersection, Intersection, Vector2f, Vector2f[], Vector2f[])}
/// should be called to get the penetration depth.
///
/// </summary>
/// <param name="normal">The collision normal
/// </param>
/// <param name="sweepDir">The sweep direction
/// </param>
/// <param name="intersectionStart">The start bound of the intersection Area
/// </param>
/// <param name="intersectionEnd">The end bound of the intersection Area.
/// </param>
public PenetrationSweep(Vector2f normal, Vector2f sweepDir, Vector2f intersectionStart, Vector2f intersectionEnd)
: base()
{
this.normal = normal;
this.sweepDir = sweepDir;
this.startDist = intersectionStart.Dot(sweepDir);
this.endDist = intersectionEnd.Dot(sweepDir);
}
/// <summary> Get point on this polygon's hull that is closest to p.
///
/// TODO: make this thing return a negative value when it is contained in the polygon
///
/// </summary>
/// <param name="p">The point to search the closest point for
/// </param>
/// <returns> the nearest point on this vertex' hull
/// </returns>
public override ROVector2f GetNearestPoint(ROVector2f p)
{
// TODO: this can be done with a kind of binary search
float r = System.Single.MaxValue;
float l;
Vector2f v;
int m = - 1;
for (int i = 0; i < vertices.Length; i++)
{
v = new Vector2f(vertices[i]);
v.Sub(p);
l = v.x * v.x + v.y * v.y;
if (l < r)
{
r = l;
m = i;
}
}
// the closest point could be on one of the closest point's edges
// this happens when the angle between v[m-1]-v[m] and p-v[m] is
// smaller than 90 degrees, same for v[m+1]-v[m]
int length = vertices.Length;
Vector2f pm = new Vector2f(p);
pm.Sub(vertices[m]);
Vector2f l1 = new Vector2f(vertices[(m - 1 + length) % length]);
l1.Sub(vertices[m]);
Vector2f l2 = new Vector2f(vertices[(m + 1) % length]);
l2.Sub(vertices[m]);
Vector2f normal;
if (pm.Dot(l1) > 0)
{
normal = MathUtil.GetNormal(vertices[(m - 1 + length) % length], vertices[m]);
}
else if (pm.Dot(l2) > 0)
{
normal = MathUtil.GetNormal(vertices[m], vertices[(m + 1) % length]);
}
else
{
return vertices[m];
}
normal.Scale(- pm.Dot(normal));
normal.Add(p);
return normal;
}
/// <summary> Apply the friction impulse from each contact.
///
/// </summary>
/// <param name="dt">The amount of time to Step the simulation by
/// </param>
/// <param name="invDT">The inverted time
/// </param>
/// <param name="damping">The percentage of energy to retain through out
/// collision. (1 = no loss, 0 = total loss)
/// </param>
internal virtual void PreStep(float invDT, float dt, float damping)
{
float allowedPenetration = 0.01f;
float biasFactor = 0.8f;
for (int i = 0; i < numContacts; ++i)
{
Contact c = contacts[i];
c.normal.Normalise();
Vector2f r1 = new Vector2f(c.position);
r1.Sub(body1.GetPosition());
Vector2f r2 = new Vector2f(c.position);
r2.Sub(body2.GetPosition());
// Precompute normal mass, tangent mass, and bias.
float rn1 = r1.Dot(c.normal);
float rn2 = r2.Dot(c.normal);
float kNormal = body1.InvMass + body2.InvMass;
kNormal += body1.InvI * (r1.Dot(r1) - rn1 * rn1) + body2.InvI * (r2.Dot(r2) - rn2 * rn2);
c.massNormal = damping / kNormal;
Vector2f tangent = MathUtil.Cross(c.normal, 1.0f);
float rt1 = r1.Dot(tangent);
float rt2 = r2.Dot(tangent);
float kTangent = body1.InvMass + body2.InvMass;
kTangent += body1.InvI * (r1.Dot(r1) - rt1 * rt1) + body2.InvI * (r2.Dot(r2) - rt2 * rt2);
c.massTangent = damping / kTangent;
// Compute restitution
// Relative velocity at contact
Vector2f relativeVelocity = new Vector2f(body2.Velocity);
relativeVelocity.Add(MathUtil.Cross(r2, body2.AngularVelocity));
relativeVelocity.Sub(body1.Velocity);
relativeVelocity.Sub(MathUtil.Cross(r1, body1.AngularVelocity));
float combinedRestitution = (body1.Restitution * body2.Restitution);
float relVel = c.normal.Dot(relativeVelocity);
c.restitution = combinedRestitution * (- relVel);
c.restitution = System.Math.Max(c.restitution, 0);
float penVel = (- c.separation) / dt;
if (c.restitution >= penVel)
{
c.bias = 0;
}
else
{
c.bias = (- biasFactor) * invDT * System.Math.Min(0.0f, c.separation + allowedPenetration);
}
// apply damping
c.accumulatedNormalImpulse *= damping;
// Apply normal + friction impulse
Vector2f impulse = MathUtil.Scale(c.normal, c.accumulatedNormalImpulse);
impulse.Add(MathUtil.Scale(tangent, c.accumulatedTangentImpulse));
body1.AdjustVelocity(MathUtil.Scale(impulse, - body1.InvMass));
body1.AdjustAngularVelocity((- body1.InvI) * MathUtil.Cross(r1, impulse));
body2.AdjustVelocity(MathUtil.Scale(impulse, body2.InvMass));
body2.AdjustAngularVelocity(body2.InvI * MathUtil.Cross(r2, impulse));
// rest bias
c.biasImpulse = 0;
}
}
// private static Vector2f r1 = new Vector2f();
// private static Vector2f r2 = new Vector2f();
// private static Vector2f relativeVelocity = new Vector2f();
// private static Vector2f impulse = new Vector2f();
// private static Vector2f Pb = new Vector2f();
// private static Vector2f tmp = new Vector2f();
//
// /**
// * Apply the impulse accumlated at the contact points maintained
// * by this arbiter.
// */
// void ApplyImpulse() {
// Body b1 = body1;
// Body b2 = body2;
//
// for (int i = 0; i < numContacts; ++i)
// {
// Contact c = contacts[i];
//
// r1.set(c.position);
// r1.Sub(b1.GetPosition());
// r2.set(c.position);
// r2.Sub(b2.GetPosition());
//
// // Relative velocity at contact
// relativeVelocity.set(b2.getVelocity());
// relativeVelocity.Add(MathUtil.Cross(b2.getAngularVelocity(), r2));
// relativeVelocity.Sub(b1.getVelocity());
// relativeVelocity.Sub(MathUtil.Cross(b1.getAngularVelocity(), r1));
//
// // Compute normal impulse with bias.
// float vn = relativeVelocity.Dot(c.normal);
//
// // bias caculations are now handled seperately hence we only
// // handle the real impulse caculations here
// //float normalImpulse = c.massNormal * ((c.restitution - vn) + c.bias);
// float normalImpulse = c.massNormal * (c.restitution - vn);
//
// // Clamp the accumulated impulse
// float oldNormalImpulse = c.accumulatedNormalImpulse;
// c.accumulatedNormalImpulse = Math.max(oldNormalImpulse + normalImpulse, 0.0f);
// normalImpulse = c.accumulatedNormalImpulse - oldNormalImpulse;
//
// if (normalImpulse != 0) {
// // Apply contact impulse
// impulse.set(c.normal);
// impulse.Scale(normalImpulse);
//
// tmp.set(impulse);
// tmp.Scale(-b1.getInvMass());
// b1.AdjustVelocity(tmp);
// b1.AdjustAngularVelocity(-(b1.getInvI() * MathUtil.Cross(r1, impulse)));
//
// tmp.set(impulse);
// tmp.Scale(b2.getInvMass());
// b2.AdjustVelocity(tmp);
// b2.AdjustAngularVelocity(b2.getInvI() * MathUtil.Cross(r2, impulse));
// }
//
// // Compute bias impulse
// // NEW STUFF FOR SEPERATING BIAS
// relativeVelocity.set(b2.getBiasedVelocity());
// relativeVelocity.Add(MathUtil.Cross(b2.getBiasedAngularVelocity(), r2));
// relativeVelocity.Sub(b1.getBiasedVelocity());
// relativeVelocity.Sub(MathUtil.Cross(b1.getBiasedAngularVelocity(), r1));
// float vnb = relativeVelocity.Dot(c.normal);
//
// float biasImpulse = c.massNormal * (-vnb + c.bias);
// float oldBiasImpulse = c.biasImpulse;
// c.biasImpulse = Math.max(oldBiasImpulse + biasImpulse, 0.0f);
// biasImpulse = c.biasImpulse - oldBiasImpulse;
//
// if (biasImpulse != 0) {
// Pb.set(c.normal);
// Pb.Scale(biasImpulse);
//
// tmp.set(Pb);
// tmp.Scale(-b1.getInvMass());
// b1.AdjustBiasedVelocity(tmp);
// b1.AdjustBiasedAngularVelocity(-(b1.getInvI() * MathUtil.Cross(r1, Pb)));
//
// tmp.set(Pb);
// tmp.Scale(b2.getInvMass());
// b2.AdjustBiasedVelocity(tmp);
// b2.AdjustBiasedAngularVelocity((b2.getInvI() * MathUtil.Cross(r2, Pb)));
// }
// // END NEW STUFF
//
// //
// // Compute friction (tangent) impulse
// //
// float maxTangentImpulse = friction * c.accumulatedNormalImpulse;
//
// // Relative velocity at contact
// relativeVelocity.set(b2.getVelocity());
// relativeVelocity.Add(MathUtil.Cross(b2.getAngularVelocity(), r2));
// relativeVelocity.Sub(b1.getVelocity());
// relativeVelocity.Sub(MathUtil.Cross(b1.getAngularVelocity(), r1));
//
// Vector2f tangent = MathUtil.Cross(c.normal, 1.0f);
// float vt = relativeVelocity.Dot(tangent);
// float tangentImpulse = c.massTangent * (-vt);
//
// // Clamp friction
// float oldTangentImpulse = c.accumulatedTangentImpulse;
// c.accumulatedTangentImpulse = MathUtil.Clamp(oldTangentImpulse + tangentImpulse, -maxTangentImpulse, maxTangentImpulse);
// tangentImpulse = c.accumulatedTangentImpulse - oldTangentImpulse;
//
// // Apply contact impulse
// if ((tangentImpulse > 0.1f) || (tangentImpulse < -0.1f)) {
// impulse = MathUtil.Scale(tangent, tangentImpulse);
//
// tmp.set(impulse);
// tmp.Scale(-b1.getInvMass());
// b1.AdjustVelocity(tmp);
// b1.AdjustAngularVelocity(-b1.getInvI() * MathUtil.Cross(r1, impulse));
//
// tmp.set(impulse);
// tmp.Scale(b2.getInvMass());
// b2.AdjustVelocity(tmp);
// b2.AdjustAngularVelocity(b2.getInvI() * MathUtil.Cross(r2, impulse));
// }
// }
// }
/// <summary> Apply the impulse accumlated at the contact points maintained
/// by this arbiter.
/// </summary>
internal virtual void ApplyImpulse()
{
Body b1 = body1;
Body b2 = body2;
for (int i = 0; i < numContacts; ++i)
{
Contact c = contacts[i];
Vector2f r1 = new Vector2f(c.position);
r1.Sub(b1.GetPosition());
Vector2f r2 = new Vector2f(c.position);
r2.Sub(b2.GetPosition());
// Relative velocity at contact
Vector2f relativeVelocity = new Vector2f(b2.Velocity);
relativeVelocity.Add(MathUtil.Cross(b2.AngularVelocity, r2));
relativeVelocity.Sub(b1.Velocity);
relativeVelocity.Sub(MathUtil.Cross(b1.AngularVelocity, r1));
// Compute normal impulse with bias.
float vn = relativeVelocity.Dot(c.normal);
// bias caculations are now handled seperately hence we only
// handle the real impulse caculations here
//float normalImpulse = c.massNormal * ((c.restitution - vn) + c.bias);
float normalImpulse = c.massNormal * (c.restitution - vn);
// Clamp the accumulated impulse
float oldNormalImpulse = c.accumulatedNormalImpulse;
c.accumulatedNormalImpulse = System.Math.Max(oldNormalImpulse + normalImpulse, 0.0f);
normalImpulse = c.accumulatedNormalImpulse - oldNormalImpulse;
// Apply contact impulse
Vector2f impulse = MathUtil.Scale(c.normal, normalImpulse);
b1.AdjustVelocity(MathUtil.Scale(impulse, - b1.InvMass));
b1.AdjustAngularVelocity(- (b1.InvI * MathUtil.Cross(r1, impulse)));
b2.AdjustVelocity(MathUtil.Scale(impulse, b2.InvMass));
b2.AdjustAngularVelocity(b2.InvI * MathUtil.Cross(r2, impulse));
// Compute bias impulse
// NEW STUFF FOR SEPERATING BIAS
relativeVelocity.Reconfigure(b2.BiasedVelocity);
relativeVelocity.Add(MathUtil.Cross(b2.BiasedAngularVelocity, r2));
relativeVelocity.Sub(b1.BiasedVelocity);
relativeVelocity.Sub(MathUtil.Cross(b1.BiasedAngularVelocity, r1));
float vnb = relativeVelocity.Dot(c.normal);
float biasImpulse = c.massNormal * (- vnb + c.bias);
float oldBiasImpulse = c.biasImpulse;
c.biasImpulse = System.Math.Max(oldBiasImpulse + biasImpulse, 0.0f);
biasImpulse = c.biasImpulse - oldBiasImpulse;
Vector2f Pb = MathUtil.Scale(c.normal, biasImpulse);
b1.AdjustBiasedVelocity(MathUtil.Scale(Pb, - b1.InvMass));
b1.AdjustBiasedAngularVelocity(- (b1.InvI * MathUtil.Cross(r1, Pb)));
b2.AdjustBiasedVelocity(MathUtil.Scale(Pb, b2.InvMass));
b2.AdjustBiasedAngularVelocity((b2.InvI * MathUtil.Cross(r2, Pb)));
// END NEW STUFF
//
// Compute friction (tangent) impulse
//
float maxTangentImpulse = friction * c.accumulatedNormalImpulse;
// Relative velocity at contact
relativeVelocity.Reconfigure(b2.Velocity);
relativeVelocity.Add(MathUtil.Cross(b2.AngularVelocity, r2));
relativeVelocity.Sub(b1.Velocity);
relativeVelocity.Sub(MathUtil.Cross(b1.AngularVelocity, r1));
Vector2f tangent = MathUtil.Cross(c.normal, 1.0f);
float vt = relativeVelocity.Dot(tangent);
float tangentImpulse = c.massTangent * (- vt);
// Clamp friction
float oldTangentImpulse = c.accumulatedTangentImpulse;
c.accumulatedTangentImpulse = MathUtil.Clamp(oldTangentImpulse + tangentImpulse, - maxTangentImpulse, maxTangentImpulse);
tangentImpulse = c.accumulatedTangentImpulse - oldTangentImpulse;
// Apply contact impulse
impulse = MathUtil.Scale(tangent, tangentImpulse);
b1.AdjustVelocity(MathUtil.Scale(impulse, - b1.InvMass));
b1.AdjustAngularVelocity((- b1.InvI) * MathUtil.Cross(r1, impulse));
b2.AdjustVelocity(MathUtil.Scale(impulse, b2.InvMass));
b2.AdjustAngularVelocity(b2.InvI * MathUtil.Cross(r2, impulse));
}
}
/// <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)
{
// calculate the spring's vector (pointing from body1 to body2) and Length
spring = new Vector2f(body2.GetPosition());
spring.Add(r2);
spring.Sub(body1.GetPosition());
spring.Sub(r1);
springLength = spring.Length();
// the spring vector needs to be normalized for ApplyImpulse as well!
spring.Normalise();
// calculate the spring's forces
// note that although theoretically invDT could never be 0
// but here it can
float springConst;
if (springLength < minSpringSize || springLength > maxSpringSize)
{
// 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);
// the mass normal or 'k'
float rn1 = r1.Dot(spring);
float rn2 = r2.Dot(spring);
float kNormal = body1.InvMass + body2.InvMass;
kNormal += body1.InvI * (r1.Dot(r1) - rn1 * rn1) + body2.InvI * (r2.Dot(r2) - rn2 * rn2);
massNormal = 1 / kNormal;
// The spring is broken so apply force to correct it
// note that we use biased velocities for this
float springImpulse = invDT != 0?brokenSpringConst * (springLength - springSize) / invDT:0;
Vector2f impulse = MathUtil.Scale(spring, springImpulse);
body1.AdjustBiasedVelocity(MathUtil.Scale(impulse, body1.InvMass));
body1.AdjustBiasedAngularVelocity((body1.InvI * MathUtil.Cross(r1, impulse)));
body2.AdjustBiasedVelocity(MathUtil.Scale(impulse, - body2.InvMass));
body2.AdjustBiasedAngularVelocity(- (body2.InvI * MathUtil.Cross(r2, impulse)));
isBroken = true;
return ;
}
else if (springLength < springSize)
{
springConst = compressedSpringConst;
isBroken = false;
}
else
{
// if ( springLength >= springSize )
springConst = stretchedSpringConst;
isBroken = false;
}
float springImpulse2 = invDT != 0?springConst * (springLength - springSize) / invDT:0;
// apply the spring's forces
Vector2f impulse2 = MathUtil.Scale(spring, springImpulse2);
body1.AdjustVelocity(MathUtil.Scale(impulse2, body1.InvMass));
body1.AdjustAngularVelocity((body1.InvI * MathUtil.Cross(r1, impulse2)));
body2.AdjustVelocity(MathUtil.Scale(impulse2, - body2.InvMass));
body2.AdjustAngularVelocity(- (body2.InvI * MathUtil.Cross(r2, impulse2)));
}
/// <summary> Apply the impulse caused by the joint to the bodies attached.</summary>
public virtual void ApplyImpulse()
{
if (isBroken)
{
// calculate difference in velocity
// TODO: share this code with BasicJoint and Arbiter
Vector2f relativeVelocity = new Vector2f(body2.Velocity);
relativeVelocity.Add(MathUtil.Cross(body2.AngularVelocity, r2));
relativeVelocity.Sub(body1.Velocity);
relativeVelocity.Sub(MathUtil.Cross(body1.AngularVelocity, r1));
// project the relative velocity onto the spring vector and apply the mass normal
float normalImpulse = massNormal * relativeVelocity.Dot(spring);
// // TODO: Clamp the accumulated impulse?
// float oldNormalImpulse = accumulatedNormalImpulse;
// accumulatedNormalImpulse = Math.max(oldNormalImpulse + normalImpulse, 0.0f);
// normalImpulse = accumulatedNormalImpulse - oldNormalImpulse;
// only apply the impulse if we are pushing or pulling in the right way
// i.e. pulling if the string is overstretched and pushing if it is too compressed
if (springLength < minSpringSize && normalImpulse < 0 || springLength > maxSpringSize && normalImpulse > 0)
{
// now apply the impulses to the bodies
Vector2f impulse = MathUtil.Scale(spring, normalImpulse);
body1.AdjustVelocity(MathUtil.Scale(impulse, body1.InvMass));
body1.AdjustAngularVelocity((body1.InvI * MathUtil.Cross(r1, impulse)));
body2.AdjustVelocity(MathUtil.Scale(impulse, - body2.InvMass));
body2.AdjustAngularVelocity(- (body2.InvI * MathUtil.Cross(r2, impulse)));
}
}
}
