public static Quaternion Slerp(Quaternion from, Quaternion to, double t, bool useShortestPath)
{
//For more information on how this works see:
//Chapter 10 in "Essential Mathermatics for Games & Interactive Applications"
//James M. Van Verth & Lars M. Bishop
//Slerp(p,q,t) = (sin((1-t)angle) * p + sin(t*angle) * q) / sin(angle)
//Interpolate along a sphere between the two quaternions
//Find the angle between the two axis
double fromNorm = from.Norm;
double toNorm = to.Norm;
from.Normalize();
to.Normalize();
double fromDotTo = from.X * to.X + from.Y * to.Y + from.Z * to.Z + from.W * to.W;
if (useShortestPath) {
if (fromDotTo < 0) {
//Need to negate one of the quaternions
to = new Quaternion(-to.X, -to.Y, -to.Z, -to.W);
fromDotTo *= -1;
}
}
if (fromDotTo < -1) {
fromDotTo = -1;
}
else if (fromDotTo > 1) {
fromDotTo = 1;
}
double angleInRadians = System.Math.Acos(fromDotTo);
double sinAngle = System.Math.Sin(angleInRadians);
//Be careful about division by zero
if (MathHelper.IsZero(sinAngle)) {
//Just lerp instead of slerp
return new Quaternion(from.X + (to.X - from.X) * t,
from.Y + (to.Y - from.Y) * t,
from.Z + (to.Z - from.Z) * t,
from.W + (to.W - from.W) * t);
}
else {
double sinFrom = System.Math.Sin((1.0 - t) * angleInRadians) / sinAngle;
double sinTo = System.Math.Sin(t * angleInRadians) / sinAngle;
//Scale from FromNorm to toNorm depending on t. When t==0 then
//scale == fromNorm, when t==1 scale == toNorm
double scale = 1;//fromNorm * System.Math.Pow((toNorm / fromNorm), t);
return new Quaternion(scale * (from.X * sinFrom + to.X * sinTo),
scale * (from.Y * sinFrom + to.Y * sinTo),
scale * (from.Z * sinFrom + to.Z * sinTo),
scale * (from.W * sinFrom + to.W * sinTo));
}
}
public static Quaternion Slerp(Quaternion from, Quaternion to, double t, bool useShortestPath)
{
//For more information on how this works see:
//Chapter 10 in "Essential Mathermatics for Games & Interactive Applications"
//James M. Van Verth & Lars M. Bishop
//Slerp(p,q,t) = (sin((1-t)angle) * p + sin(t*angle) * q) / sin(angle)
//Interpolate along a sphere between the two quaternions
//Find the angle between the two axis
double fromNorm = from.Norm;
double toNorm = to.Norm;
from.Normalize();
to.Normalize();
double fromDotTo = from.X * to.X + from.Y * to.Y + from.Z * to.Z + from.W * to.W;
if (useShortestPath)
{
if (fromDotTo < 0)
{
//Need to negate one of the quaternions
to = new Quaternion(-to.X, -to.Y, -to.Z, -to.W);
fromDotTo *= -1;
}
}
if (fromDotTo < -1)
{
fromDotTo = -1;
}
else if (fromDotTo > 1)
{
fromDotTo = 1;
}
double angleInRadians = System.Math.Acos(fromDotTo);
double sinAngle = System.Math.Sin(angleInRadians);
//Be careful about division by zero
if (MathHelper.IsZero(sinAngle))
{
//Just lerp instead of slerp
return(new Quaternion(from.X + (to.X - from.X) * t,
from.Y + (to.Y - from.Y) * t,
from.Z + (to.Z - from.Z) * t,
from.W + (to.W - from.W) * t));
}
else
{
double sinFrom = System.Math.Sin((1.0 - t) * angleInRadians) / sinAngle;
double sinTo = System.Math.Sin(t * angleInRadians) / sinAngle;
//Scale from FromNorm to toNorm depending on t. When t==0 then
//scale == fromNorm, when t==1 scale == toNorm
double scale = 1;//fromNorm * System.Math.Pow((toNorm / fromNorm), t);
return(new Quaternion(scale * (from.X * sinFrom + to.X * sinTo),
scale * (from.Y * sinFrom + to.Y * sinTo),
scale * (from.Z * sinFrom + to.Z * sinTo),
scale * (from.W * sinFrom + to.W * sinTo)));
}
}
