/*!
SLCurveBezier::subdivideRender adds points along the curve to the point vector
renderPoints by recursively subdividing the curve with the Casteljau scheme.
*/
void SLCurveBezier::subdivideRender(SLVVec3f &renderPoints,
const SLMat4f &wm,
SLfloat epsilon,
const SLVec3f& P0, const SLVec3f& P1,
const SLVec3f& P2, const SLVec3f& P3)
{
// add first point transformed by wm if not already in the list
if (renderPoints.size()==0)
renderPoints.push_back(wm.multVec(P0));
else if (P0 != renderPoints[renderPoints.size()-1])
renderPoints.push_back(wm.multVec(P0));
// check to see if basically straight
SLfloat Lmin = P0.distance(P3);
SLfloat Lmax = P0.distance(P1) + P1.distance(P2) + P2.distance(P3);
SLfloat diff = Lmin - Lmax;
if (diff*diff < epsilon) return;
// otherwise get control points for subdivision
SLVec3f L1 = (P0 + P1) * 0.5f;
SLVec3f H = (P1 + P2) * 0.5f;
SLVec3f L2 = (L1 + H) * 0.5f;
SLVec3f R2 = (P2 + P3) * 0.5f;
SLVec3f R1 = (H + R2) * 0.5f;
SLVec3f mid = (L2 + R1) * 0.5f;
// subdivide
subdivideRender(renderPoints, wm, epsilon, P0, L1, L2, mid);
subdivideRender(renderPoints, wm, epsilon, mid, R1, R2, P3);
}
/*!
SLCurveBezier::subdivideLength calculates length of Bezier curve by recursive
midpoint subdivision.
*/
SLfloat SLCurveBezier::subdivideLength(const SLVec3f& P0,
const SLVec3f& P1,
const SLVec3f& P2,
const SLVec3f& P3)
{
// check to see if basically straight
SLfloat Lmin = P0.distance(P3);
SLfloat Lmax = P0.distance(P1) + P1.distance(P2) + P2.distance(P3);
SLfloat diff = Lmin - Lmax;
if (diff*diff < 1.0e-3f)
return 0.5f*(Lmin + Lmax);
// otherwise get control points for subdivision
SLVec3f L1 = (P0 + P1) * 0.5f;
SLVec3f H = (P1 + P2) * 0.5f;
SLVec3f L2 = (L1 + H ) * 0.5f;
SLVec3f R2 = (P2 + P3) * 0.5f;
SLVec3f R1 = (H + R2) * 0.5f;
SLVec3f mid = (L2 + R1) * 0.5f;
// subdivide
return subdivideLength(P0, L1, L2, mid) + subdivideLength(mid, R1, R2, P3);
}
