/// <summary> /// Calculates value and derivative of the position of the sphere with respect to whichDeriv /// </summary> float CalculateErrorDerivative() { DualVector3 thisYBasis = optimizer.vec("yBasis"), thisZBasis = optimizer.vec("zBasis"); thisYBasis = thisYBasis.Normalize(); thisZBasis = thisZBasis.Normalize(); DualVector3 thisXBasis = thisYBasis.Cross(thisZBasis); thisYBasis = thisZBasis.Cross(thisXBasis); //THIS IS A FULLY DIFFERENTIABLE RIGID TRANSFORM - NO SINGULARITIES //Also Single Covers the space (when non-uniform scaling is disabled) DualVector3 scale = optimizer.vec("scale"); DualMatrix4x3 thisTransform = new DualMatrix4x3(thisXBasis * scale.x, thisYBasis * scale.y, thisZBasis * scale.z, optimizer.vec("position")); //Sum the Squared Errors DualNumber error = new DualNumber(); for (int i = 0; i < icoVerts.Length; i++) { DualVector3 thisPoint = thisTransform * icoVerts[i]; DualVector3 basePoint = baseTransformMatrix * icoVerts[i]; if (drawDebug) { Debug.DrawLine(thisPoint, basePoint); } error += (thisPoint - basePoint).SqrMagnitude(); } //Divide by Number of Squared Errors error /= icoVerts.Length; return(error.Derivative); }
/// <summary> /// Calculates value and derivative of the position of the arm with respect to whichDeriv /// </summary> DualNumber ArmFKError(Vector3 clampedPos, int whichDeriv) { DualNumber thetaVar = whichDeriv == 0 ? DualNumber.Variable(theta) : DualNumber.Constant(theta); DualNumber phiVar = whichDeriv == 1 ? DualNumber.Variable(phi) : DualNumber.Constant(phi); baseJoint = new DualVector3(Math.Sin(thetaVar), Math.Cos(thetaVar), new DualNumber()); endJoint = baseJoint + new DualVector3(Math.Sin(thetaVar + phiVar), Math.Cos(thetaVar + phiVar), new DualNumber()); return(((DualVector3)clampedPos - endJoint).SqrMagnitude()); }
public float CalcErrorDerivative(string scalarKey) { DualNumber scalar = new DualNumber(); if (CalculateErrorDerivative != null && scalars.TryGetValue(scalarKey, out scalar)) { scalars[scalarKey] = new DualNumber(scalar.Value, 1f); float errorDerivative = CalculateErrorDerivative(); scalars[scalarKey] = new DualNumber(scalar.Value, 0f); return(errorDerivative); } return(0f); }
/// <summary> /// Calculates value and derivative of the position of the arm with respect to whichDeriv /// </summary> static DualNumber[] ArmFK(float theta, float phi, int whichDeriv) { DualNumber thetaVar = whichDeriv == 0 ? DualNumber.Variable(theta) : DualNumber.Constant(theta); DualNumber phiVar = whichDeriv == 1 ? DualNumber.Variable(phi) : DualNumber.Constant(phi); DualNumber[] outputValues = { Math.Sin(thetaVar), //X Position of First Joint Math.Cos(thetaVar), //Y Position of First Joint Math.Sin(thetaVar) + Math.Sin(thetaVar + phiVar), //X Position of Second Joint Math.Cos(thetaVar) + Math.Cos(thetaVar + phiVar), //Y Position of Second Joint }; return(outputValues); }
/// <summary> /// Calculates value and derivative of the position of the sphere with respect to whichDeriv /// </summary> DualNumber SphereFittingError(int whichDeriv, bool drawDebug) { DualVector3 thisPosition = new DualVector3( whichDeriv == 0 ? DualNumber.Variable(transform.position.x) : DualNumber.Constant(transform.position.x), whichDeriv == 1 ? DualNumber.Variable(transform.position.y) : DualNumber.Constant(transform.position.y), whichDeriv == 2 ? DualNumber.Variable(transform.position.z) : DualNumber.Constant(transform.position.z)); DualVector3 thisYBasis = new DualVector3( whichDeriv == 3 ? DualNumber.Variable(transform.up.x) : DualNumber.Constant(transform.up.x), whichDeriv == 4 ? DualNumber.Variable(transform.up.y) : DualNumber.Constant(transform.up.y), whichDeriv == 5 ? DualNumber.Variable(transform.up.z) : DualNumber.Constant(transform.up.z)); DualVector3 thisZBasis = new DualVector3( whichDeriv == 6 ? DualNumber.Variable(transform.forward.x) : DualNumber.Constant(transform.forward.x), whichDeriv == 7 ? DualNumber.Variable(transform.forward.y) : DualNumber.Constant(transform.forward.y), whichDeriv == 8 ? DualNumber.Variable(transform.forward.z) : DualNumber.Constant(transform.forward.z)); DualVector3 thisScale = new DualVector3( whichDeriv == 9 ? DualNumber.Variable(transform.localScale.x) : DualNumber.Constant(transform.localScale.x), whichDeriv == 10 ? DualNumber.Variable(transform.localScale.y) : DualNumber.Constant(transform.localScale.y), whichDeriv == 11 ? DualNumber.Variable(transform.localScale.z) : DualNumber.Constant(transform.localScale.z)); thisYBasis = thisYBasis.Normalize(); thisZBasis = thisZBasis.Normalize(); DualVector3 thisXBasis = thisYBasis.Cross(thisZBasis); thisYBasis = thisZBasis.Cross(thisXBasis); //THIS IS A FULLY DIFFERENTIABLE RIGID TRANSFORM - NO SINGULARITIES DualMatrix4x3 thisTransform = new DualMatrix4x3(thisXBasis * thisScale.x, thisYBasis * thisScale.y, thisZBasis * thisScale.z, thisPosition); //Sum the Squared Errors DualNumber error = new DualNumber(); for (int i = 0; i < icoVerts.Length; i++) { DualVector3 thisPoint = thisTransform * icoVerts[i]; DualVector3 basePoint = baseTransformMatrix * icoVerts[i]; if (drawDebug) { Debug.DrawLine(thisPoint, basePoint); } error += (thisPoint - basePoint).SqrMagnitude(); } //Divide by Number of Squared Errors error /= icoVerts.Length; return(error); }
/// <summary> /// Calculates value and derivative of the position of the sphere with respect to whichDeriv /// </summary> DualNumber SphereFittingError(int whichDeriv, bool drawDebug) { DualVector3 spherePosition = new DualVector3( whichDeriv == 0 ? DualNumber.Variable(transform.position.x) : DualNumber.Constant(transform.position.x), whichDeriv == 1 ? DualNumber.Variable(transform.position.y) : DualNumber.Constant(transform.position.y), whichDeriv == 2 ? DualNumber.Variable(transform.position.z) : DualNumber.Constant(transform.position.z)); DualNumber radius = whichDeriv == 3 ? DualNumber.Variable(transform.localScale.x) : DualNumber.Constant(transform.localScale.x); //Sum the Squared Errors DualNumber error = new DualNumber(); for (int i = 0; i < icoVerts.Length; i++) { error += DistFromSurface(baseSphere.position, baseSphere.localScale.x * 0.5f, spherePosition + (radius * icoVerts[i]), drawDebug).Squared(); } //Divide by Number of Squared Errors error /= icoVerts.Length; return(error); }
/// <summary> /// Calculates value and derivative of the position of the sphere with respect to whichDeriv /// </summary> float CalculateErrorDerivative() { DualVector3 thisYBasis = optimizer.vec("yBasis"), thisZBasis = optimizer.vec("zBasis"), thisXBasis = optimizer.num("xScale") * (thisYBasis.Cross(thisZBasis)).Normalize(); //thisYBasis = /*thisYBasis.Magnitude() */ (thisZBasis.Cross(thisXBasis)).Normalize(); //Sum the Squared Errors DualNumber error = new DualNumber(); for (int i = 0; i < originalVerts.Length; i++) { DualVector3 thisPoint = (thisXBasis * thisXBasis.Normalize().Dot(originalVerts[i])) + (thisYBasis * thisYBasis.Normalize().Dot(originalVerts[i])) + (thisZBasis * thisZBasis.Normalize().Dot(originalVerts[i])); DualVector3 basePoint = bodyVerts[i]; //if (true) { Debug.DrawLine(thisPoint, basePoint); } error += (thisPoint - basePoint).SqrMagnitude(); } //Divide by Number of Squared Errors error /= originalVerts.Length; return(error.Derivative); }
private DualNumber f2(DualNumber x) { return(x * x * x + x); }
private DualNumber f1(DualNumber x) { return(x * x + new DualNumber(2) * x + new DualNumber(1)); }
public void SummationDiff() { DualNumber c = new DualNumber(2, 1); Assert.AreEqual((f1(c) + f2(c)).FPrime, SummationDiffExpected(c.F)); }