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Improved Loop regular patch approximations of irregular features:

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- updated LoopPatchBuilder with new Gregory to Box-spline conversion matrix
This commit is contained in:
barry 2019-06-07 17:55:31 -07:00
parent d8619b2997
commit cb79eab120
1 changed files with 32 additions and 35 deletions
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67
opensubdiv/far/loopPatchBuilder.cpp
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@ -1748,17 +1748,13 @@ convertToLoop(SourcePatch const & sourcePatch, SparseMatrix<REAL> & matrix) {
// the quartic case). So it is possible to construct shapes with a Gregory
// or Bezier triangle that cannot be represented by the Box-spline.
//
// The solution fit a Box-spline patch to the constructed Gregory patch with
// 12 constraints: position, first derivatives and mixed partial at each of
// the 3 corners. We used the mixed partial (the twist vector) to constrain
// the interior of the patch somehow, otherwise results produce a lot of
// interior bulging in an effort to satisfy boundary constraints.
// The solution fits a Box-spline patch to the constructed Gregory patch with
// a set of constraints. With quartic boundary curves, 12 constraints on the
// boundary curve make this tightly constrained. Such a set of constraints
// is rank deficient (11 instead of 12) so an additional constraint on the
// midpoint of the patch is included and a conversion matrix is constructed
// from the pseudo-inverse of the 13 constraints.
//
// Given both position and tangent continuity here are compromised for the
// general case -- and at considerable expense (in terms of computation and
// the full set of local control points that result) -- its worth exploring
// simpler solutions for the case of the isolated corner.
//
// For the full 12x15 conversion matrix from 15-point quartic Bezier patch
// back to a Box spline patch, the matrix rows and columns are ordered
// according to control point orientations used elsewhere. Correllation of
@ -1770,34 +1766,35 @@ convertToLoop(SourcePatch const & sourcePatch, SparseMatrix<REAL> & matrix) {
// As with conversion from Gregory to BSpline for Catmark, one of the face
// points is chosen as a Bezier point in the conversion rather than combining
// the pair (which would avoid slight asymmetric artefacts of the choice).
// And given the solution now depends primarily on the boundary, its not
// necessary to construct a full Gregory patch with enforced continuity.
//
REAL const gregoryToLoopMatrix[12][15] = {
{ 9.33333f, 5.33333f, -6.f, -0.66666f, 0.33333f,-18.66667f, 4.f, 6.f,
-0.66666f, 8.f, -8.f, 0.f, 1.33333f, 1.33333f, -0.666667f},
{ 0.33333f, -0.66666f, 8.f, 1.33333f, -0.66666f, -0.66666f, -2.f, -8.f,
1.33333f, 0.f, 0.f, 0.f, 1.33333f, 1.33333f, -0.666667f},
{-6.66667f, 13.33333f,-14.f, 7.33333f, 8.33333f, 13.33333f,-20.f, 14.f,
-16.66667f, -8.f, 8.f, 0.f, 1.33333f, 1.33333f, -0.666667f},
{ 9.33333f,-18.66667f, 8.f, 1.33333f, -0.66666f, 5.33333f, 4.f, -8.f,
1.33333f, -6.f, 6.f, 0.f, -0.66666f, -0.66666f, 0.333333f},
{-1.66667f, 3.33333f, -2.f, -0.66666f, 0.33333f, 3.33333f, -2.f, 2.f,
-0.66666f, -2.f, 2.f, 0.f, -0.66666f, -0.66666f, 0.333333f},
{ 1.33333f, -2.66667f, 0.f, 1.33333f, -0.66666f, -2.66667f, 4.f, 0.f,
1.33333f, 2.f, -2.f, 0.f, -0.66666f, -0.66666f, 0.333333f},
{ 6.33333f,-12.66667f, 14.f,-16.66667f, 8.33333f,-12.66667f, 22.f,-14.f,
7.33333f, 6.f, -6.f, 0.f, -0.66666f, -0.66666f, 0.333333f},
{ 0.33333f, -0.66666f, 0.f, 1.33333f, -0.66666f, -0.66666f, -2.f, 0.f,
1.33333f, 8.f, -8.f, 0.f, 1.33333f, 1.33333f, -0.666667f},
{ 1.33333f, -2.66667f, 2.f, -0.66666f, 0.33333f, -2.66667f, 4.f, -2.f,
-0.66666f, 0.f, 0.f, 0.f, 1.33333f, 1.33333f, -0.666667f},
{-7.66667f, 15.33333f, -8.f, 1.33333f, -0.66666f, 15.33333f,-26.f, 8.f,
1.33333f, -8.f, 8.f, 0.f, 1.33333f, 1.33333f, -0.666667f},
{-6.66667f, 13.33333f, -8.f, 1.33333f, -0.66666f, 13.33333f,-20.f, 8.f,
1.33333f,-14.f, 14.f, 0.f, 7.33333f,-16.66667f, 8.333333f},
{ 6.33333f,-12.66667f, 6.f, -0.66666f, 0.33333f,-12.66667f, 22.f, -6.f,
-0.66666f, 14.f,-14.f, 0.f,-16.66667f, 7.33333f, 8.333333f}
{ 8.214411f, 7.571190f, -7.690082f, 2.237840f, -1.118922f,-16.428828f, 0.666666f, 0.666666f,
2.237835f, 6.309870f, 0.666666f, -1.690100f, -0.428812f, -0.428805f, 0.214407f },
{ -0.304687f, 0.609374f, 6.752593f, 0.609374f, -0.304687f, 0.609378f, -3.333333f, -3.333333f,
0.609378f, -1.247389f, -3.333333f, -1.247389f, 3.276037f, 3.276037f, -1.638020f },
{ -1.118922f, 2.237840f, -7.690082f, 7.571190f, 8.214411f, 2.237835f, 0.666666f, 0.666666f,
-16.428828f, -1.690100f, 0.666666f, 6.309870f, -0.428805f, -0.428812f, 0.214407f },
{ 8.214411f,-16.428828f, 6.309870f, -0.428812f, 0.214407f, 7.571190f, 0.666666f, 0.666666f,
-0.428805f, -7.690082f, 0.666666f, -1.690100f, 2.237840f, 2.237835f, -1.118922f },
{ -0.813368f, 1.626735f, -0.773435f, -1.039929f, 0.519965f, 1.626735f, 0.666666f, 0.666666f,
-1.039930f, -0.773435f, 0.666666f, 1.226558f, -1.039929f, -1.039930f, 0.519965f },
{ 0.519965f, -1.039929f, -0.773435f, 1.626735f, -0.813368f, -1.039930f, 0.666666f, 0.666666f,
1.626735f, 1.226558f, 0.666666f, -0.773435f, -1.039930f, -1.039929f, 0.519965f },
{ 0.214407f, -0.428812f, 6.309870f,-16.428828f, 8.214411f, -0.428805f, 0.666666f, 0.666666f,
7.571190f, -1.690100f, 0.666666f, -7.690082f, 2.237835f, 2.237840f, -1.118922f },
{ -0.304687f, 0.609378f, -1.247389f, 3.276037f, -1.638020f, 0.609374f, -3.333333f, -3.333333f,
3.276037f, 6.752593f, -3.333333f, -1.247389f, 0.609374f, 0.609378f, -0.304687f },
{ 0.519965f, -1.039930f, 1.226558f, -1.039930f, 0.519965f, -1.039929f, 0.666666f, 0.666666f,
-1.039929f, -0.773435f, 0.666666f, -0.773435f, 1.626735f, 1.626735f, -0.813368f },
{ -1.638020f, 3.276037f, -1.247389f, 0.609378f, -0.304687f, 3.276037f, -3.333333f, -3.333333f,
0.609374f, -1.247389f, -3.333333f, 6.752593f, 0.609378f, 0.609374f, -0.304687f },
{ -1.118922f, 2.237835f, -1.690100f, -0.428805f, 0.214407f, 2.237840f, 0.666666f, 0.666666f,
-0.428812f, -7.690082f, 0.666666f, 6.309870f, 7.571190f,-16.428828f, 8.214411f },
{ 0.214407f, -0.428805f, -1.690100f, 2.237835f, -1.118922f, -0.428812f, 0.666666f, 0.666666f,
2.237840f, 6.309870f, 0.666666f, -7.690082f,-16.428828f, 7.571190f, 8.214411f }
};
int const gRowIndices[15] = { 0,1,15,7,5, 2,4,8,6, 17,14,16, 11,12, 10 };
SparseMatrix<REAL> G;