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Wildmeshing Toolkit
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Turn a set of 2D curve networks into one tagged triangle mesh. More...
#include <EmbedCurves.hpp>
Public Member Functions | |
| EmbedCurves (const std::vector< std::string > &input_paths, const std::vector< Matrix3d > &input_transform={}, const double tol_rel=-1, const double tol_abs=-1) | |
| void | simplify_curves (const double eps, const bool use_exact_envelope, const int num_threads=0) |
| Simplify the input curves while staying within the eps envelope. | |
| bool | embed_curves (const bool tag_from_winding_number=true) |
| Compute the exact arrangement of the (simplified) curve union. | |
| void | consolidate () |
| Remove vertices not referenced by any output face. | |
| const MatrixXd & | V_emb () const |
| const MatrixXr & | V_emb_r () const |
| const MatrixXi & | F_emb () const |
| const MatrixSi & | F_tags () const |
| const MatrixXd & | V_curves () const |
| The simplified input curves – what the envelope is built from. | |
| const MatrixXi & | E_curves () const |
| const MatrixXi & | E_constrained () const |
| The constrained edges of the arrangement, i.e. the output edges tiling the input. | |
| std::pair< Vector2d, Vector2d > | bbox_curves_minmax () const |
| void | write_curves_obj (const std::string &filename) const |
Public Attributes | |
| int | m_num_threads = 0 |
Private Member Functions | |
| void | tag_from_winding_number () |
| One binary tag column per input, set where that input's winding number at a face barycenter exceeds 0.5. | |
| void | tag_from_provenance () |
| Decide the face tags from the arrangement's segment provenance. | |
Private Attributes | |
| std::vector< MatrixXd > | m_Vs |
| Per input, as read: kept separate because the winding number is per input. | |
| std::vector< MatrixXi > | m_Es |
| MatrixXd | m_V_curves |
| The union, which is what gets simplified and arranged. | |
| MatrixXi | m_E_curves |
| std::vector< size_t > | m_E_input |
| std::vector< std::vector< size_t > > | m_E_constrained_inputs |
| Per row of m_E_constrained: which inputs tile it. Only filled for tag_from_provenance. | |
| MatrixXd | m_V_emb |
| MatrixXr | m_V_emb_r |
| MatrixXi | m_F_emb |
| MatrixXi | m_E_constrained |
| MatrixSi | m_F_tags |
Turn a set of 2D curve networks into one tagged triangle mesh.
The 2D counterpart of EmbedSurface, member for member, with each 3D primitive replaced by the 2D one:
read_triangle_mesh + 4x4 transform read_input_curves + 3x3 transform simplify_surface (ShortestEdgeCollapse) simplify_curves (simplify_segments) delaunay_box_mesh + embed_tri_in_poly embed_segments (grid is inside it) winding_number (solid angle) winding_number_2d T_emb (Nx4), T_tags (#T x #inputs) F_emb (Nx3), F_tags (#F x #inputs)
The tagging contract is identical and is what makes this a simwild input rather than a triwild one: tag i is set on a cell when input i's winding number at the cell's barycenter exceeds 0.5, so a cell inside two inputs carries both tags and the material interfaces fall out of where adjacent cells disagree.
Unlike the 3D path there is no separate background mesh to build: the 2D arrangement triangulates every point it is handed, so the background grid is just extra points appended to the same array (wmtk::utils::embed_segments does that).
| wmtk::components::simwild::EmbedCurves::EmbedCurves | ( | const std::vector< std::string > & | input_paths, |
| const std::vector< Matrix3d > & | input_transform = {}, |
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| const double | tol_rel = -1, |
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| const double | tol_abs = -1 |
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| ) |
| input_paths | one curve network per entry, as OBJ 'v'/'l' polylines |
| input_transform | 3x3 homogeneous transform per input; identity where omitted |
| tol_rel,tol_abs | merge input vertices closer than this (negative disables) |
| bool wmtk::components::simwild::EmbedCurves::embed_curves | ( | const bool | tag_from_winding_number = true | ) |
Compute the exact arrangement of the (simplified) curve union.
| tag_from_winding_number | Decide each face's tags by evaluating the winding number of every input at its barycenter (the default), rather than by propagating them across the arrangement's own segment provenance. See tag_from_provenance. |
| void wmtk::components::simwild::EmbedCurves::simplify_curves | ( | const double | eps, |
| const bool | use_exact_envelope, | ||
| const int | num_threads = 0 |
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| ) |
Simplify the input curves while staying within the eps envelope.
Must be a small envelope: the winding-number tags below are evaluated against the ORIGINAL per-input curves, not the simplified union, so moving the curves too far makes the tags disagree with the geometry. Same constraint EmbedSurface documents.
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Decide the face tags from the arrangement's segment provenance.
The exact alternative to tag_from_winding_number, and the 2D twin of EmbedSurface::tag_from_provenance. Each constrained output edge knows which input segments it tiles, hence which input curves; tags then propagate combinatorially, starting from a face on the outside of the bounding box and flipping membership of an input whenever an edge belonging to it is crossed. Every input curve must be closed – an open polyline encloses nothing – and a traversal that disagrees with itself says so rather than returning a tagging that depends on the order it walked in.
It also removes the mismatch the winding-number route documents: those tags are evaluated against the ORIGINAL per-input curves while the arrangement is of the SIMPLIFIED union, so the two can disagree near a curve the simplification moved.
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private |
One binary tag column per input, set where that input's winding number at a face barycenter exceeds 0.5.
Auto-corrects an inverted input orientation and warns when an input claims nothing, as triwild's compute_winding_numbers does and the 3D tag_from_winding_number does not.
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private |
Per row of m_E_curves: which input it came from. Kept alongside m_E_curves across the simplification, so the arrangement's provenance can be read back in input terms.
1.9.8