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Optimize barycentric coordinate computation #164

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Optimize barycentric coordinate computation #164

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5603d1a
Optimize `cartesianVectorToBarycentric`
Ameobea Oct 12, 2023
49c5e22
Clean up barycentric conversion code
Ameobea Oct 17, 2023
3dcfaad
Remove unused declaration
Ameobea Oct 17, 2023
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1 change: 0 additions & 1 deletion include/geometrycentral/surface/barycentric_coordinate_helpers.h
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Expand Up @@ -23,7 +23,6 @@ double displacementLength2(Vector3 displacement, Vector3 triangleLengths);
double displacementLength(Vector3 displacement, Vector3 triangleLengths);

// Convert between cartesian and barycentric coordinates
Vector3 cartesianVectorToBarycentric(const std::array<Vector2, 3>& vertCoords, Vector2 faceVec);
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why delete this?

Vector2 barycentricDisplacementToCartesian(const std::array<Vector2, 3>& vertCoords, Vector3 baryVec);

// Normalize to sum to 1 (does nothing else)
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20 changes: 0 additions & 20 deletions include/geometrycentral/surface/barycentric_coordinate_helpers.ipp
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Expand Up @@ -25,26 +25,6 @@ inline Vector2 barycentricDisplacementToCartesian(const std::array<Vector2, 3>&
return vertCoords[0] * baryVec.x + vertCoords[1] * baryVec.y + vertCoords[2] * baryVec.z;
}

inline Vector3 cartesianVectorToBarycentric(const std::array<Vector2, 3>& vertCoords, Vector2 faceVec, bool verbose) {


// Build matrix for linear transform problem
// (last constraint comes from chosing the displacement vector with sum = 0)
Eigen::Matrix3d A;
Eigen::Vector3d rhs;
const std::array<Vector2, 3>& c = vertCoords; // short name
A << c[0].x, c[1].x, c[2].x, c[0].y, c[1].y, c[2].y, 1., 1., 1.;
rhs << faceVec.x, faceVec.y, 0.;

// Solve
Eigen::Vector3d result = A.colPivHouseholderQr().solve(rhs);
Vector3 resultBary{result(0), result(1), result(2)};

resultBary = normalizeBarycentricDisplacement(resultBary);

return resultBary;
}

// Allows not-normalized input
inline Vector3 normalizeBarycentric(Vector3 baryCoords) {
double s = sum(baryCoords);
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49 changes: 21 additions & 28 deletions src/surface/trace_geodesic.cpp
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Expand Up @@ -52,35 +52,28 @@ inline Vector2 baryCoordsToFaceCoords(const std::array<Vector2, 3>& vertCoords,
return vertCoords[0] * baryCoord.x + vertCoords[1] * baryCoord.y + vertCoords[2] * baryCoord.z;
}

// Specialized barycentric coordinate conversion by solving the system of equations directly
// via Cramer's rule. Significantly faster than using a generic solver from Eigen.
//
// Adapted from: https://gamedev.stackexchange.com/a/23745
//
// Which itself is from: http://realtimecollisiondetection.net/ by Christer Ericson
inline Vector3 cartesianVectorToBarycentric(const std::array<Vector2, 3>& vertCoords, Vector2 faceVec) {


// Build matrix for linear transform problem
// (last constraint comes from chosing the displacement vector with sum = 0)
Eigen::Matrix3d A;
Eigen::Vector3d rhs;
const std::array<Vector2, 3>& c = vertCoords; // short name
A << c[0].x, c[1].x, c[2].x, c[0].y, c[1].y, c[2].y, 1., 1., 1.;
rhs << faceVec.x, faceVec.y, 0.;

// Solve
Eigen::Vector3d result = A.colPivHouseholderQr().solve(rhs);
Vector3 resultBary{result(0), result(1), result(2)};

resultBary = normalizeBarycentricDisplacement(resultBary);

if (TRACE_PRINT) {
cout << " cartesianVectorToBarycentric() " << endl;
cout << " input = " << faceVec << endl;
cout << " positions = " << vertCoords[0] << " " << vertCoords[1] << " " << vertCoords[2] << endl;
cout << " transform result = " << resultBary << endl;
cout << " transform back = " << barycentricDisplacementToCartesian(vertCoords, resultBary) << endl;
cout << " A = " << endl << A << endl;
cout << " rhs = " << endl << rhs << endl;
cout << " Ax = " << endl << A * result << endl;
}

return resultBary;
Vector2 v0 = vertCoords[1] - vertCoords[0];
Vector2 v1 = vertCoords[2] - vertCoords[0];
Vector2 v2 = faceVec - vertCoords[0];

double d00 = dot(v0, v0);
double d01 = dot(v0, v1);
double d11 = dot(v1, v1);
double d20 = dot(v2, v0);
double d21 = dot(v2, v1);
double denom = d00 * d11 - d01 * d01;

double v = (d11 * d20 - d01 * d21) / denom;
double w = (d00 * d21 - d01 * d20) / denom;
double u = 0. - v - w;
return Vector3{u, v, w};
}

// Converts tCross from halfedge to edge coordinates, handling sign conventions
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