/// <summary> /// Modifies a contribution using a transform, position, and weight. /// </summary> /// <param name="transform">Transform to use to modify the contribution.</param> /// <param name="center">Center to use to modify the contribution.</param> /// <param name="baseContribution">Original unmodified contribution.</param> /// <param name="weight">Weight of the contribution.</param> /// <param name="contribution">Transformed contribution.</param> public static void TransformContribution(ref RigidTransform transform, ref Vector3 center, ref Matrix3x3 baseContribution, float weight, out Matrix3x3 contribution) { Matrix3x3 rotation; Matrix3x3.CreateFromQuaternion(ref transform.Orientation, out rotation); Matrix3x3 temp; //Do angular transformed contribution first... Matrix3x3.MultiplyTransposed(ref rotation, ref baseContribution, out temp); Matrix3x3.Multiply(ref temp, ref rotation, out temp); contribution = temp; //Now add in the offset from the origin. Vector3 offset; Vector3.Subtract(ref transform.Position, ref center, out offset); Matrix3x3 innerProduct; Matrix3x3.CreateScale(offset.LengthSquared(), out innerProduct); Matrix3x3 outerProduct; Matrix3x3.CreateOuterProduct(ref offset, ref offset, out outerProduct); Matrix3x3.Subtract(ref innerProduct, ref outerProduct, out temp); Matrix3x3.Add(ref contribution, ref temp, out contribution); Matrix3x3.Multiply(ref contribution, weight, out contribution); }
/// <summary> /// Calculates necessary information for velocity solving. /// Called by preStep(float dt) /// </summary> /// <param name="dt">Time in seconds since the last update.</param> public override void Update(float dt) { Matrix3x3.Transform(ref localAnchorA, ref connectionA.orientationMatrix, out worldOffsetA); Matrix3x3.Transform(ref localAnchorB, ref connectionB.orientationMatrix, out worldOffsetB); float errorReductionParameter; springSettings.ComputeErrorReductionAndSoftness(dt, 1 / dt, out errorReductionParameter, out softness); //Mass Matrix Matrix3x3 k; Matrix3x3 linearComponent; Matrix3x3.CreateCrossProduct(ref worldOffsetA, out rACrossProduct); Matrix3x3.CreateCrossProduct(ref worldOffsetB, out rBCrossProduct); if (connectionA.isDynamic && connectionB.isDynamic) { Matrix3x3.CreateScale(connectionA.inverseMass + connectionB.inverseMass, out linearComponent); Matrix3x3 angularComponentA, angularComponentB; Matrix3x3.Multiply(ref rACrossProduct, ref connectionA.inertiaTensorInverse, out angularComponentA); Matrix3x3.Multiply(ref rBCrossProduct, ref connectionB.inertiaTensorInverse, out angularComponentB); Matrix3x3.Multiply(ref angularComponentA, ref rACrossProduct, out angularComponentA); Matrix3x3.Multiply(ref angularComponentB, ref rBCrossProduct, out angularComponentB); Matrix3x3.Subtract(ref linearComponent, ref angularComponentA, out k); Matrix3x3.Subtract(ref k, ref angularComponentB, out k); } else if (connectionA.isDynamic && !connectionB.isDynamic) { Matrix3x3.CreateScale(connectionA.inverseMass, out linearComponent); Matrix3x3 angularComponentA; Matrix3x3.Multiply(ref rACrossProduct, ref connectionA.inertiaTensorInverse, out angularComponentA); Matrix3x3.Multiply(ref angularComponentA, ref rACrossProduct, out angularComponentA); Matrix3x3.Subtract(ref linearComponent, ref angularComponentA, out k); } else if (!connectionA.isDynamic && connectionB.isDynamic) { Matrix3x3.CreateScale(connectionB.inverseMass, out linearComponent); Matrix3x3 angularComponentB; Matrix3x3.Multiply(ref rBCrossProduct, ref connectionB.inertiaTensorInverse, out angularComponentB); Matrix3x3.Multiply(ref angularComponentB, ref rBCrossProduct, out angularComponentB); Matrix3x3.Subtract(ref linearComponent, ref angularComponentB, out k); } else { throw new InvalidOperationException("Cannot constrain two kinematic bodies."); } k.M11 += softness; k.M22 += softness; k.M33 += softness; Matrix3x3.Invert(ref k, out massMatrix); Vector3.Add(ref connectionB.position, ref worldOffsetB, out error); Vector3.Subtract(ref error, ref connectionA.position, out error); Vector3.Subtract(ref error, ref worldOffsetA, out error); Vector3.Multiply(ref error, -errorReductionParameter, out biasVelocity); //Ensure that the corrective velocity doesn't exceed the max. float length = biasVelocity.LengthSquared(); if (length > maxCorrectiveVelocitySquared) { float multiplier = maxCorrectiveVelocity / (float)Math.Sqrt(length); biasVelocity.X *= multiplier; biasVelocity.Y *= multiplier; biasVelocity.Z *= multiplier; } }
///<summary> /// Performs the frame's configuration step. ///</summary> ///<param name="dt">Timestep duration.</param> public override void Update(float dt) { //Transform point into world space. Matrix3x3.Transform(ref localPoint, ref entity.orientationMatrix, out r); Vector3.Add(ref r, ref entity.position, out worldPoint); float updateRate = 1 / dt; if (settings.mode == MotorMode.Servomechanism) { Vector3.Subtract(ref settings.servo.goal, ref worldPoint, out error); float separationDistance = error.Length(); if (separationDistance > Toolbox.BigEpsilon) { float errorReduction; settings.servo.springSettings.ComputeErrorReductionAndSoftness(dt, updateRate, out errorReduction, out usedSoftness); //The rate of correction can be based on a constant correction velocity as well as a 'spring like' correction velocity. //The constant correction velocity could overshoot the destination, so clamp it. float correctionSpeed = MathHelper.Min(settings.servo.baseCorrectiveSpeed, separationDistance * updateRate) + separationDistance * errorReduction; Vector3.Multiply(ref error, correctionSpeed / separationDistance, out biasVelocity); //Ensure that the corrective velocity doesn't exceed the max. float length = biasVelocity.LengthSquared(); if (length > settings.servo.maxCorrectiveVelocitySquared) { float multiplier = settings.servo.maxCorrectiveVelocity / (float)Math.Sqrt(length); biasVelocity.X *= multiplier; biasVelocity.Y *= multiplier; biasVelocity.Z *= multiplier; } } else { //Wouldn't want to use a bias from an earlier frame. biasVelocity = new Vector3(); } } else { usedSoftness = settings.velocityMotor.softness * updateRate; biasVelocity = settings.velocityMotor.goalVelocity; error = Vector3.Zero; } //Compute the maximum force that can be applied this frame. ComputeMaxForces(settings.maximumForce, dt); //COMPUTE EFFECTIVE MASS MATRIX //Transforms a change in velocity to a change in momentum when multiplied. Matrix3x3 linearComponent; Matrix3x3.CreateScale(entity.inverseMass, out linearComponent); Matrix3x3 rACrossProduct; Matrix3x3.CreateCrossProduct(ref r, out rACrossProduct); Matrix3x3 angularComponentA; Matrix3x3.Multiply(ref rACrossProduct, ref entity.inertiaTensorInverse, out angularComponentA); Matrix3x3.Multiply(ref angularComponentA, ref rACrossProduct, out angularComponentA); Matrix3x3.Subtract(ref linearComponent, ref angularComponentA, out effectiveMassMatrix); effectiveMassMatrix.M11 += usedSoftness; effectiveMassMatrix.M22 += usedSoftness; effectiveMassMatrix.M33 += usedSoftness; Matrix3x3.Invert(ref effectiveMassMatrix, out effectiveMassMatrix); }