/**
* @param[out] tensor The 3x3 inertia tensor matrix of the shape in local-space
* coordinates
* @param mass Mass to use to compute the inertia tensor of the collision shape
*/
void BoxShape::computeLocalInertiaTensor(Matrix3x3& tensor, decimal mass) const {
decimal factor = (decimal(1.0) / decimal(3.0)) * mass;
Vector3 realExtent = mExtent + Vector3(mMargin, mMargin, mMargin);
decimal xSquare = realExtent.x * realExtent.x;
decimal ySquare = realExtent.y * realExtent.y;
decimal zSquare = realExtent.z * realExtent.z;
tensor.setAllValues(factor * (ySquare + zSquare), 0.0, 0.0,
0.0, factor * (xSquare + zSquare), 0.0,
0.0, 0.0, factor * (xSquare + ySquare));
}
/**
* @param[out] tensor The 3x3 inertia tensor matrix of the shape in local-space
* coordinates
* @param mass Mass to use to compute the inertia tensor of the collision shape
*/
void CapsuleShape::computeLocalInertiaTensor(Matrix3x3& tensor, decimal mass) const {
// The inertia tensor formula for a capsule can be found in : Game Engine Gems, Volume 1
decimal height = mHalfHeight + mHalfHeight;
decimal radiusSquare = mRadius * mRadius;
decimal heightSquare = height * height;
decimal radiusSquareDouble = radiusSquare + radiusSquare;
decimal factor1 = decimal(2.0) * mRadius / (decimal(4.0) * mRadius + decimal(3.0) * height);
decimal factor2 = decimal(3.0) * height / (decimal(4.0) * mRadius + decimal(3.0) * height);
decimal sum1 = decimal(0.4) * radiusSquareDouble;
decimal sum2 = decimal(0.75) * height * mRadius + decimal(0.5) * heightSquare;
decimal sum3 = decimal(0.25) * radiusSquare + decimal(1.0 / 12.0) * heightSquare;
decimal IxxAndzz = factor1 * mass * (sum1 + sum2) + factor2 * mass * sum3;
decimal Iyy = factor1 * mass * sum1 + factor2 * mass * decimal(0.25) * radiusSquareDouble;
tensor.setAllValues(IxxAndzz, 0.0, 0.0,
0.0, Iyy, 0.0,
0.0, 0.0, IxxAndzz);
}
