/// <summary>
/// Adds the two matrices together on a per-element basis.
/// </summary>
/// <param name="a">First matrix to add.</param>
/// <param name="b">Second matrix to add.</param>
/// <param name="result">Sum of the two matrices.</param>
public static void Add(ref Matrix a, ref Matrix2X2 b, out Matrix2X2 result)
{
float m11 = a.M11 + b.M11;
float m12 = a.M12 + b.M12;
float m21 = a.M21 + b.M21;
float m22 = a.M22 + b.M22;
result.M11 = m11;
result.M12 = m12;
result.M21 = m21;
result.M22 = m22;
}
/// <summary>
/// Gets the mass matrix of the constraint.
/// </summary>
/// <param name="massMatrix">Constraint's mass matrix.</param>
public void GetMassMatrix(out Matrix2X2 massMatrix)
{
massMatrix = effectiveMassMatrix;
}
/// <summary>
/// Gets the mass matrix of the revolute limit.
/// The revolute limit is special; in terms of solving, it is
/// actually sometimes TWO constraints; a minimum plane, and a
/// maximum plane. The M11 field represents the minimum plane mass matrix
/// and the M22 field represents the maximum plane mass matrix.
/// </summary>
/// <param name="massMatrix">Mass matrix of the constraint.</param>
public void GetMassMatrix(out Matrix2X2 massMatrix)
{
massMatrix.M11 = velocityToImpulse.X;
massMatrix.M22 = velocityToImpulse.Y;
massMatrix.M12 = 0;
massMatrix.M21 = 0;
}
/// <summary>
/// Computes the transposed matrix of a matrix.
/// </summary>
/// <param name="matrix">Matrix to transpose.</param>
/// <param name="result">Transposed matrix.</param>
public static void Transpose(ref Matrix2X2 matrix, out Matrix2X2 result)
{
float m21 = matrix.M12;
result.M11 = matrix.M11;
result.M12 = matrix.M21;
result.M21 = m21;
result.M22 = matrix.M22;
}
/// <summary>
/// Subtracts the two matrices from each other on a per-element basis.
/// </summary>
/// <param name="a">First matrix to subtract.</param>
/// <param name="b">Second matrix to subtract.</param>
/// <param name="result">Difference of the two matrices.</param>
public static void Subtract(ref Matrix2X2 a, ref Matrix2X2 b, out Matrix2X2 result)
{
float m11 = a.M11 - b.M11;
float m12 = a.M12 - b.M12;
float m21 = a.M21 - b.M21;
float m22 = a.M22 - b.M22;
result.M11 = m11;
result.M12 = m12;
result.M21 = m21;
result.M22 = m22;
}
/// <summary>
/// Transforms the vector by the matrix.
/// </summary>
/// <param name="v">Vector2 to transform.</param>
/// <param name="matrix">Matrix to use as the transformation.</param>
/// <param name="result">Product of the transformation.</param>
public static void Transform(ref Vector2 v, ref Matrix2X2 matrix, out Vector2 result)
{
float vX = v.X;
float vY = v.Y;
#if !WINDOWS
result = new Vector2();
#endif
result.X = vX * matrix.M11 + vY * matrix.M21;
result.Y = vX * matrix.M12 + vY * matrix.M22;
}
/// <summary>
/// Multiplies the two matrices.
/// </summary>
/// <param name="a">First matrix to multiply.</param>
/// <param name="b">Second matrix to multiply.</param>
/// <param name="result">Product of the multiplication.</param>
public static void Multiply(ref Matrix2X3 a, ref Matrix3X2 b, out Matrix2X2 result)
{
result.M11 = a.M11 * b.M11 + a.M12 * b.M21 + a.M13 * b.M31;
result.M12 = a.M11 * b.M12 + a.M12 * b.M22 + a.M13 * b.M32;
result.M21 = a.M21 * b.M11 + a.M22 * b.M21 + a.M23 * b.M31;
result.M22 = a.M21 * b.M12 + a.M22 * b.M22 + a.M23 * b.M32;
}
/// <summary>
/// Negates every element in the matrix.
/// </summary>
/// <param name="matrix">Matrix to negate.</param>
/// <param name="result">Negated matrix.</param>
public static void Negate(ref Matrix2X2 matrix, out Matrix2X2 result)
{
float m11 = -matrix.M11;
float m12 = -matrix.M12;
float m21 = -matrix.M21;
float m22 = -matrix.M22;
result.M11 = m11;
result.M12 = m12;
result.M21 = m21;
result.M22 = m22;
}
/// <summary>
/// Inverts the given matix.
/// </summary>
/// <param name="matrix">Matrix to be inverted.</param>
/// <param name="result">Inverted matrix.</param>
public static void Invert(ref Matrix2X2 matrix, out Matrix2X2 result)
{
float determinantInverse = 1 / (matrix.M11 * matrix.M22 - matrix.M12 * matrix.M21);
float m11 = matrix.M22 * determinantInverse;
float m12 = -matrix.M12 * determinantInverse;
float m21 = -matrix.M21 * determinantInverse;
float m22 = matrix.M11 * determinantInverse;
result.M11 = m11;
result.M12 = m12;
result.M21 = m21;
result.M22 = m22;
}
/// <summary>
/// Multiplies the two matrices.
/// </summary>
/// <param name="a">First matrix to multiply.</param>
/// <param name="b">Second matrix to multiply.</param>
/// <param name="result">Product of the multiplication.</param>
public static void Multiply(ref Matrix a, ref Matrix2X2 b, out Matrix2X2 result)
{
float resultM11 = a.M11 * b.M11 + a.M12 * b.M21;
float resultM12 = a.M11 * b.M12 + a.M12 * b.M22;
float resultM21 = a.M21 * b.M11 + a.M22 * b.M21;
float resultM22 = a.M21 * b.M12 + a.M22 * b.M22;
result.M11 = resultM11;
result.M12 = resultM12;
result.M21 = resultM21;
result.M22 = resultM22;
}
/// <summary>
/// Constructs a uniform scaling matrix.
/// </summary>
/// <param name="scale">Value to use in the diagonal.</param>
/// <param name="matrix">Scaling matrix.</param>
public static void CreateScale(float scale, out Matrix2X2 matrix)
{
matrix.M11 = scale;
matrix.M22 = scale;
matrix.M12 = 0;
matrix.M21 = 0;
}
/// <summary>
/// Gets the mass matrix of the constraint.
/// </summary>
/// <param name="massMatrix">Constraint's mass matrix.</param>
public void GetMassMatrix(out Matrix2X2 massMatrix)
{
Matrix2X2.Negate(ref negativeEffectiveMassMatrix, out massMatrix);
}
///<summary>
/// Performs the frame's configuration step.
///</summary>
///<param name="dt">Timestep duration.</param>
public override void Update(float dt)
{
contactCount = contactManifoldConstraint.penetrationConstraints.count;
switch (contactCount)
{
case 1:
manifoldCenter = contactManifoldConstraint.penetrationConstraints.Elements[0].contact.Position;
break;
case 2:
Vector3.Add(ref contactManifoldConstraint.penetrationConstraints.Elements[0].contact.Position,
ref contactManifoldConstraint.penetrationConstraints.Elements[1].contact.Position,
out manifoldCenter);
manifoldCenter.X *= .5f;
manifoldCenter.Y *= .5f;
manifoldCenter.Z *= .5f;
break;
case 3:
Vector3.Add(ref contactManifoldConstraint.penetrationConstraints.Elements[0].contact.Position,
ref contactManifoldConstraint.penetrationConstraints.Elements[1].contact.Position,
out manifoldCenter);
Vector3.Add(ref contactManifoldConstraint.penetrationConstraints.Elements[2].contact.Position,
ref manifoldCenter,
out manifoldCenter);
manifoldCenter.X *= .333333333f;
manifoldCenter.Y *= .333333333f;
manifoldCenter.Z *= .333333333f;
break;
case 4:
//This isn't actually the center of the manifold. Is it good enough? Sure seems like it.
Vector3.Add(ref contactManifoldConstraint.penetrationConstraints.Elements[0].contact.Position,
ref contactManifoldConstraint.penetrationConstraints.Elements[1].contact.Position,
out manifoldCenter);
Vector3.Add(ref contactManifoldConstraint.penetrationConstraints.Elements[2].contact.Position,
ref manifoldCenter,
out manifoldCenter);
Vector3.Add(ref contactManifoldConstraint.penetrationConstraints.Elements[3].contact.Position,
ref manifoldCenter,
out manifoldCenter);
manifoldCenter.X *= .25f;
manifoldCenter.Y *= .25f;
manifoldCenter.Z *= .25f;
break;
default:
manifoldCenter = Toolbox.NoVector;
break;
}
//Compute the three dimensional relative velocity at the point.
Vector3 velocityA, velocityB;
if (entityA != null)
{
Vector3.Subtract(ref manifoldCenter, ref entityA.position, out ra);
Vector3.Cross(ref entityA.angularVelocity, ref ra, out velocityA);
Vector3.Add(ref velocityA, ref entityA.linearVelocity, out velocityA);
}
else
velocityA = new Vector3();
if (entityB != null)
{
Vector3.Subtract(ref manifoldCenter, ref entityB.position, out rb);
Vector3.Cross(ref entityB.angularVelocity, ref rb, out velocityB);
Vector3.Add(ref velocityB, ref entityB.linearVelocity, out velocityB);
}
else
velocityB = new Vector3();
Vector3.Subtract(ref velocityA, ref velocityB, out relativeVelocity);
//Get rid of the normal velocity.
Vector3 normal = contactManifoldConstraint.penetrationConstraints.Elements[0].contact.Normal;
float normalVelocityScalar = normal.X * relativeVelocity.X + normal.Y * relativeVelocity.Y + normal.Z * relativeVelocity.Z;
relativeVelocity.X -= normalVelocityScalar * normal.X;
relativeVelocity.Y -= normalVelocityScalar * normal.Y;
relativeVelocity.Z -= normalVelocityScalar * normal.Z;
//Create the jacobian entry and decide the friction coefficient.
float length = relativeVelocity.LengthSquared();
if (length > Toolbox.Epsilon)
{
length = (float)Math.Sqrt(length);
float inverseLength = 1 / length;
linearA.M11 = relativeVelocity.X * inverseLength;
linearA.M12 = relativeVelocity.Y * inverseLength;
linearA.M13 = relativeVelocity.Z * inverseLength;
friction = length > CollisionResponseSettings.StaticFrictionVelocityThreshold ?
contactManifoldConstraint.materialInteraction.KineticFriction :
contactManifoldConstraint.materialInteraction.StaticFriction;
}
else
{
friction = contactManifoldConstraint.materialInteraction.StaticFriction;
//If there was no velocity, try using the previous frame's jacobian... if it exists.
//Reusing an old one is okay since jacobians are cleared when a contact is initialized.
if (!(linearA.M11 != 0 || linearA.M12 != 0 || linearA.M13 != 0))
{
//Otherwise, just redo it all.
//Create arbitrary axes.
Vector3 axis1;
Vector3.Cross(ref normal, ref Toolbox.RightVector, out axis1);
length = axis1.LengthSquared();
if (length > Toolbox.Epsilon)
{
length = (float)Math.Sqrt(length);
float inverseLength = 1 / length;
linearA.M11 = axis1.X * inverseLength;
linearA.M12 = axis1.Y * inverseLength;
linearA.M13 = axis1.Z * inverseLength;
}
else
{
Vector3.Cross(ref normal, ref Toolbox.UpVector, out axis1);
axis1.Normalize();
linearA.M11 = axis1.X;
linearA.M12 = axis1.Y;
linearA.M13 = axis1.Z;
}
}
}
//Second axis is first axis x normal
linearA.M21 = (linearA.M12 * normal.Z) - (linearA.M13 * normal.Y);
linearA.M22 = (linearA.M13 * normal.X) - (linearA.M11 * normal.Z);
linearA.M23 = (linearA.M11 * normal.Y) - (linearA.M12 * normal.X);
//Compute angular jacobians
if (entityA != null)
{
//angularA 1 = ra x linear axis 1
angularA.M11 = (ra.Y * linearA.M13) - (ra.Z * linearA.M12);
angularA.M12 = (ra.Z * linearA.M11) - (ra.X * linearA.M13);
angularA.M13 = (ra.X * linearA.M12) - (ra.Y * linearA.M11);
//angularA 2 = ra x linear axis 2
angularA.M21 = (ra.Y * linearA.M23) - (ra.Z * linearA.M22);
angularA.M22 = (ra.Z * linearA.M21) - (ra.X * linearA.M23);
angularA.M23 = (ra.X * linearA.M22) - (ra.Y * linearA.M21);
}
//angularB 1 = linear axis 1 x rb
if (entityB != null)
{
angularB.M11 = (linearA.M12 * rb.Z) - (linearA.M13 * rb.Y);
angularB.M12 = (linearA.M13 * rb.X) - (linearA.M11 * rb.Z);
angularB.M13 = (linearA.M11 * rb.Y) - (linearA.M12 * rb.X);
//angularB 2 = linear axis 2 x rb
angularB.M21 = (linearA.M22 * rb.Z) - (linearA.M23 * rb.Y);
angularB.M22 = (linearA.M23 * rb.X) - (linearA.M21 * rb.Z);
angularB.M23 = (linearA.M21 * rb.Y) - (linearA.M22 * rb.X);
}
//Compute inverse effective mass matrix
Matrix2X2 entryA, entryB;
//these are the transformed coordinates
Matrix2X3 transform;
Matrix3X2 transpose;
if (entityADynamic)
{
Matrix2X3.Multiply(ref angularA, ref entityA.inertiaTensorInverse, out transform);
Matrix2X3.Transpose(ref angularA, out transpose);
Matrix2X2.Multiply(ref transform, ref transpose, out entryA);
entryA.M11 += entityA.inverseMass;
entryA.M22 += entityA.inverseMass;
}
else
{
entryA = new Matrix2X2();
}
if (entityBDynamic)
{
Matrix2X3.Multiply(ref angularB, ref entityB.inertiaTensorInverse, out transform);
Matrix2X3.Transpose(ref angularB, out transpose);
Matrix2X2.Multiply(ref transform, ref transpose, out entryB);
entryB.M11 += entityB.inverseMass;
entryB.M22 += entityB.inverseMass;
}
else
{
entryB = new Matrix2X2();
}
velocityToImpulse.M11 = -entryA.M11 - entryB.M11;
velocityToImpulse.M12 = -entryA.M12 - entryB.M12;
velocityToImpulse.M21 = -entryA.M21 - entryB.M21;
velocityToImpulse.M22 = -entryA.M22 - entryB.M22;
Matrix2X2.Invert(ref velocityToImpulse, out velocityToImpulse);
}
private static float ComputeNorm(ref Matrix2X2 m)
{
//Would a square-based norm be faster and sufficient ?
//Huge number of branches in this
float norm = MathHelper.Max(Math.Abs(m.M11), Math.Abs(m.M12));
norm = MathHelper.Max(norm, Math.Abs(m.M21));
norm = MathHelper.Max(norm, Math.Abs(m.M22));
return norm;
}
private bool Get2X2InverseMassMatrix(int indexA, int indexB, out Matrix2X2 massMatrix)
{
massMatrix.M11 = GetMassMatrixEntry(indexA, indexA);
massMatrix.M12 = GetMassMatrixEntry(indexA, indexB);
massMatrix.M21 = massMatrix.M12; // getMassMatrixEntry(indexB, indexA);
massMatrix.M22 = GetMassMatrixEntry(indexB, indexB);
return ComputeNorm(ref massMatrix) < ConditionNumberLimit;
}