public static void ComputeSpringiness(ref SpringSettingsWide settings, float dt, float constraintCount,
out Vector <float> positionErrorToVelocity, out Vector <float> effectiveMassCFMScale, out Vector <float> softnessImpulseScale)
{
//The only difference between this implementation and the above implementation is that CFM is scaled by constraintCount.
//This is derived from stiffness and damping. Since we want N constraints together to be as stiff as 1 constraint of the given spring settings,
//we compute CFM and ERP from stiffness and damping coefficients that are scaled by 1/N. Omitting the derivation, it turns out
//that just scales the CFM by N.
var frequencyDt = settings.NaturalFrequency * new Vector <float>(dt);
var twiceDampingRatio = settings.DampingRatio * new Vector <float>(2f); //Could precompute.
positionErrorToVelocity = settings.NaturalFrequency / (frequencyDt + twiceDampingRatio);
var extra = new Vector <float>(constraintCount) / (frequencyDt * (frequencyDt + twiceDampingRatio));
effectiveMassCFMScale = Vector <float> .One / (Vector <float> .One + extra);
softnessImpulseScale = extra * effectiveMassCFMScale;
}
public static void ComputeSpringiness(ref SpringSettingsWide settings, float dt,
out Vector <float> positionErrorToVelocity, out Vector <float> effectiveMassCFMScale, out Vector <float> softnessImpulseScale)
{
//For more information behind these values, check the Inequality1DOF constraint comments.
//softenedEffectiveMass = effectiveMass * (1 + (naturalFrequency^2 * dt^2 + 2 * dampingRatio * naturalFrequency * dt)^-1)^-1
//CFM/dt * softenedEffectiveMass:
//(naturalFrequency^2 * dt^2 + 2 * dampingRatio * naturalFrequency * dt)^-1 * (1 + (naturalFrequency^2 * dt^2 + 2 * dampingRatio * naturalFrequency * dt)^-1)^-1
//ERP = (naturalFrequency * dt) * (naturalFrequency * dt + 2 * dampingRatio)^-1
//"ERP" is the error reduction per frame. Note that it can never exceed 1 given physically valid input.
//Since it is a *per frame* term, note that the position error is additionally scaled by inverseDt to get the target velocity
//needed to accomplish the desired error reduction in one frame.
var frequencyDt = settings.NaturalFrequency * new Vector <float>(dt);
var twiceDampingRatio = settings.DampingRatio * new Vector <float>(2); //Could precompute.
positionErrorToVelocity = settings.NaturalFrequency / (frequencyDt + twiceDampingRatio);
var extra = Vector <float> .One / (frequencyDt * (frequencyDt + twiceDampingRatio));
effectiveMassCFMScale = Vector <float> .One / (Vector <float> .One + extra);
softnessImpulseScale = extra * effectiveMassCFMScale;
}