From 837407dc50da83b4a4859a22f2f963f104c31b22 Mon Sep 17 00:00:00 2001 From: "Kenji Brameld (TRACLabs)" <122934495+kbrameld@users.noreply.github.com> Date: Mon, 6 May 2024 12:24:40 -0500 Subject: [PATCH 1/2] Improve padding of meshes using weighted vertex normals (#238) --- include/geometric_shapes/shapes.h | 3 +- src/shapes.cpp | 82 +++++++++++++++++-------------- test/test_shapes.cpp | 15 +++--- 3 files changed, 55 insertions(+), 45 deletions(-) diff --git a/include/geometric_shapes/shapes.h b/include/geometric_shapes/shapes.h index 414bae0c..9d481e0c 100644 --- a/include/geometric_shapes/shapes.h +++ b/include/geometric_shapes/shapes.h @@ -321,7 +321,8 @@ class Mesh : public Shape /** \brief Compute the normals of each triangle from its vertices via cross product. */ void computeTriangleNormals(); - /** \brief Compute vertex normals by averaging from adjacent triangle normals. + /** \brief Compute vertex normals by averaging from adjacent triangle normals, weighted using magnitude of + * angles formed by adjacent triangles at the vertex. Calls computeTriangleNormals() if needed. */ void computeVertexNormals(); diff --git a/src/shapes.cpp b/src/shapes.cpp index 012055d3..536aaa7e 100644 --- a/src/shapes.cpp +++ b/src/shapes.cpp @@ -394,23 +394,15 @@ void Mesh::scaleAndPadd(double scaleX, double scaleY, double scaleZ, double padd double dy = vertices[i3 + 1] - sy; double dz = vertices[i3 + 2] - sz; - // length of vector - double norm = sqrt(dx * dx + dy * dy + dz * dz); - if (norm > 1e-6) - { - vertices[i3] = sx + dx * (scaleX + paddX / norm); - vertices[i3 + 1] = sy + dy * (scaleY + paddY / norm); - vertices[i3 + 2] = sz + dz * (scaleZ + paddZ / norm); - } - else - { - double ndx = ((dx > 0) ? dx + paddX : dx - paddX); - double ndy = ((dy > 0) ? dy + paddY : dy - paddY); - double ndz = ((dz > 0) ? dz + paddZ : dz - paddZ); - vertices[i3] = sx + ndx; - vertices[i3 + 1] = sy + ndy; - vertices[i3 + 2] = sz + ndz; - } + // Scaled coordinate + double scaledX = sx + dx * scaleX; + double scaledY = sy + dy * scaleY; + double scaledZ = sz + dz * scaleZ; + + // Padding in each direction + vertices[i3] = scaledX + vertex_normals[i3] * paddX; + vertices[i3 + 1] = scaledY + vertex_normals[i3 + 1] * paddY; + vertices[i3 + 2] = scaledZ + vertex_normals[i3 + 2] * paddZ; } } @@ -523,7 +515,8 @@ void Mesh::computeVertexNormals() computeTriangleNormals(); if (vertex_count && !vertex_normals) vertex_normals = new double[vertex_count * 3]; - EigenSTL::vector_Vector3d avg_normals(vertex_count, Eigen::Vector3d(0, 0, 0)); + Eigen::Map> mapped_normals(vertex_normals, 3, vertex_count); + mapped_normals.setZero(); for (unsigned int tIdx = 0; tIdx < triangle_count; ++tIdx) { @@ -535,26 +528,43 @@ void Mesh::computeVertexNormals() unsigned int v2 = triangles[tIdx3_1]; unsigned int v3 = triangles[tIdx3_2]; - avg_normals[v1][0] += triangle_normals[tIdx3]; - avg_normals[v1][1] += triangle_normals[tIdx3_1]; - avg_normals[v1][2] += triangle_normals[tIdx3_2]; - - avg_normals[v2][0] += triangle_normals[tIdx3]; - avg_normals[v2][1] += triangle_normals[tIdx3_1]; - avg_normals[v2][2] += triangle_normals[tIdx3_2]; - - avg_normals[v3][0] += triangle_normals[tIdx3]; - avg_normals[v3][1] += triangle_normals[tIdx3_1]; - avg_normals[v3][2] += triangle_normals[tIdx3_2]; + // Get angles for each vertex at this triangle + Eigen::Map p1{ vertices + 3 * v1, 3 }; + Eigen::Map p2{ vertices + 3 * v2, 3 }; + Eigen::Map p3{ vertices + 3 * v3, 3 }; + + // Use re-arranged dot product equation to calculate angle between two vectors + auto angleBetweenVectors = [](const Eigen::Vector3d& vec1, const Eigen::Vector3d& vec2) -> double { + double vec1_norm = vec1.norm(); + double vec2_norm = vec2.norm(); + + // Handle the case where either vector has zero length, to prevent division-by-zero + if (vec1_norm == 0.0 || vec2_norm == 0.0) + return 0.0; + + return std::acos(vec1.dot(vec2) / (vec1_norm * vec2_norm)); + }; + + // Use law of cosines to compute angles + auto ang1 = angleBetweenVectors(p2 - p1, p3 - p1); + auto ang2 = angleBetweenVectors(p1 - p2, p3 - p2); + auto ang3 = angleBetweenVectors(p1 - p3, p2 - p3); + + // Weight normal with angle + Eigen::Map triangle_normal{ triangle_normals + tIdx3, 3 }; + mapped_normals.col(v1) += triangle_normal * ang1; + mapped_normals.col(v2) += triangle_normal * ang2; + mapped_normals.col(v3) += triangle_normal * ang3; } - for (std::size_t i = 0; i < avg_normals.size(); ++i) + + // Normalize each column of the matrix + for (int i = 0; i < mapped_normals.cols(); ++i) { - if (avg_normals[i].squaredNorm() > 0.0) - avg_normals[i].normalize(); - unsigned int i3 = i * 3; - vertex_normals[i3] = avg_normals[i][0]; - vertex_normals[i3 + 1] = avg_normals[i][1]; - vertex_normals[i3 + 2] = avg_normals[i][2]; + auto mapped_normal = mapped_normals.col(i); + if (mapped_normal.squaredNorm() != 0.0) + { + mapped_normal.normalize(); + } } } diff --git a/test/test_shapes.cpp b/test/test_shapes.cpp index ac8c4a83..56370e95 100644 --- a/test/test_shapes.cpp +++ b/test/test_shapes.cpp @@ -270,10 +270,10 @@ TEST(Mesh, ScaleAndPadd) EXPECT_DOUBLE_EQ(mesh2->vertices[22], -2.0); EXPECT_DOUBLE_EQ(mesh2->vertices[23], 2.0); - // padding actually means extending each vertices' direction vector by the padding value, - // not extending it along each axis by the same amount + // for a right-angled corner, the vertex normal vector points away equally from the three sides, and hence + // padding is applied equally in x, y and z, such that the total distance the vertex moves is equal to 1.0. mesh2->padd(1.0); - const double pos = 2.0 * (1 + 1.0 / sqrt(12)); + const double pos = 2.0 + 1.0 / sqrt(3); EXPECT_DOUBLE_EQ(mesh2->vertices[0], pos); EXPECT_DOUBLE_EQ(mesh2->vertices[1], pos); @@ -308,7 +308,7 @@ TEST(Mesh, ScaleAndPadd) EXPECT_DOUBLE_EQ(mesh2->vertices[23], pos); mesh2->scaleAndPadd(2.0, 1.0); - const double pos2 = pos * (2.0 + 1.0 / sqrt(3 * pos * pos)); + const double pos2 = pos * 2.0 + 1.0 / sqrt(3); EXPECT_DOUBLE_EQ(mesh2->vertices[0], pos2); EXPECT_DOUBLE_EQ(mesh2->vertices[1], pos2); @@ -417,10 +417,9 @@ TEST(Mesh, ScaleAndPadd) EXPECT_DOUBLE_EQ(mesh2->vertices[23], pos4z); mesh2->padd(1.0, 2.0, 3.0); - const double norm5 = sqrt(pos4x * pos4x + pos4y * pos4y + pos4z * pos4z); - const double pos5x = pos4x * (1.0 + 1.0 / norm5); - const double pos5y = pos4y * (1.0 + 2.0 / norm5); - const double pos5z = pos4z * (1.0 + 3.0 / norm5); + const double pos5x = pos4x + (1.0 / sqrt(3)); + const double pos5y = pos4y + (2.0 / sqrt(3)); + const double pos5z = pos4z + (3.0 / sqrt(3)); EXPECT_DOUBLE_EQ(mesh2->vertices[0], pos5x); EXPECT_DOUBLE_EQ(mesh2->vertices[1], pos5y); From 630a88c976849a944e2417e705c3a36c799675c4 Mon Sep 17 00:00:00 2001 From: Mike Lanighan Date: Tue, 16 Jul 2024 18:18:11 -0500 Subject: [PATCH 2/2] Use eigen to compute angle between vertex normals to avoid nans --- src/shapes.cpp | 15 +++------------ 1 file changed, 3 insertions(+), 12 deletions(-) diff --git a/src/shapes.cpp b/src/shapes.cpp index 536aaa7e..f347b50d 100644 --- a/src/shapes.cpp +++ b/src/shapes.cpp @@ -398,7 +398,6 @@ void Mesh::scaleAndPadd(double scaleX, double scaleY, double scaleZ, double padd double scaledX = sx + dx * scaleX; double scaledY = sy + dy * scaleY; double scaledZ = sz + dz * scaleZ; - // Padding in each direction vertices[i3] = scaledX + vertex_normals[i3] * paddX; vertices[i3 + 1] = scaledY + vertex_normals[i3 + 1] * paddY; @@ -533,19 +532,11 @@ void Mesh::computeVertexNormals() Eigen::Map p2{ vertices + 3 * v2, 3 }; Eigen::Map p3{ vertices + 3 * v3, 3 }; - // Use re-arranged dot product equation to calculate angle between two vectors + // Use eigen to calculate angle between the two vectors auto angleBetweenVectors = [](const Eigen::Vector3d& vec1, const Eigen::Vector3d& vec2) -> double { - double vec1_norm = vec1.norm(); - double vec2_norm = vec2.norm(); - - // Handle the case where either vector has zero length, to prevent division-by-zero - if (vec1_norm == 0.0 || vec2_norm == 0.0) - return 0.0; - - return std::acos(vec1.dot(vec2) / (vec1_norm * vec2_norm)); + Eigen::AngleAxisd a(Eigen::Quaterniond::FromTwoVectors(vec1, vec2)); + return a.angle(); }; - - // Use law of cosines to compute angles auto ang1 = angleBetweenVectors(p2 - p1, p3 - p1); auto ang2 = angleBetweenVectors(p1 - p2, p3 - p2); auto ang3 = angleBetweenVectors(p1 - p3, p2 - p3);