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/*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#ifndef __BLI_DELAUNAY_2D_H__
#define __BLI_DELAUNAY_2D_H__
/** \file
* \ingroup bli
*/
#ifdef __cplusplus
extern "C" {
#endif
/**
* Interface for Constrained Delaunay Triangulation (CDT) in 2D.
*
* The input is a set of vertices, edges between those vertices,
* and faces using those vertices.
* Those inputs are called "constraints". The output must contain
* those constraints, or at least edges, points, and vertices that
* may be pieced together to form the constraints. Part of the
* work of doing the CDT is to detect intersections and mergers
* among the input elements, so these routines are also useful
* for doing 2D intersection.
*
* The output is a triangulation of the plane that includes the
* constraints in the above sense, and also satisfies the
* "Delaunay condition" as modified to take into account that
* the constraints must be there: for every non-constrained edge
* in the output, there is a circle through the endpoints that
* does not contain any of the vertices directly connected to
* those endpoints. What this means in practice is that as
* much as possible the triangles look "nice" -- not too long
* and skinny.
*
* Optionally, the output can be a subset of the triangulation
* (but still containing all of the constraints), to get the
* effect of 2D intersection.
*
* The underlying method is incremental, but we need to know
* beforehand a bounding box for all of the constraints.
* This code can be extended in the future to allow for
* deletion of constraints, if there is a use in Blender
* for dynamically maintaining a triangulation.
*/
/**
* Input to Constrained Delaunay Triangulation.
* There are verts_len vertices, whose coordinates
* are given by vert_coords. For the rest of the input,
* vertices are referred to by indices into that array.
* Edges and Faces are optional. If provided, they will
* appear in the output triangulation ("constraints").
* One can provide faces and not edges -- the edges
* implied by the faces will be inferred.
*
* The edges are given by pairs of vertex indices.
* The faces are given in a triple `(faces, faces_start_table, faces_len_table)`
* to represent a list-of-lists as follows:
* the vertex indices for a counterclockwise traversal of
* face number `i` starts at `faces_start_table[i]` and has `faces_len_table[i]`
* elements.
*
* The edges implied by the faces are automatically added
* and need not be put in the edges array, which is intended
* as a way to specify edges that are not part of any face.
*
* Some notes about some special cases and how they are handled:
* - Input faces can have any number of vertices greater than 2. Depending
* on the output option, ngons may be triangulated or they may remain
* as ngons.
* - Input faces may have repeated vertices. Output faces will not,
* except when the CDT_CONSTRAINTS output option is used.
* - Input faces may have edges that self-intersect, but currently the labeling
* of which output faces have which input faces may not be done correctly,
* since the labeling relies on the inside being on the left of edges
* as one traverses the face. Output faces will not self-intersect.
* - Input edges, including those implied by the input faces, may have
* zero-length or near-zero-length edges (nearness as determined by epsilon),
* but those edges will not be in the output.
* - Input edges (including face edges) can overlap or nearly overlap each other.
* The output edges will not overlap, but instead be divided into as many
* edges as necessary to represent each overlap regime.
* - Input vertices may be coincide with, or nearly coincide with (as determined
* by epsilon) other input vertices. Only one representative will survive
* in the output. If an input vertex is within epsilon of an edge (including
* an added triangulation edge), it will be snapped to that edge, so the
* output coordinates may not exactly match the input coordinates in all cases.
* - Wire edges (those not part of faces) and isolated vertices are allowed in
* the input. If they are inside faces, they will be incorporated into the
* triangulation of those faces.
*
* Epsilon is used for "is it near enough" distance calculations.
* If zero is supplied for epsilon, an internal value of 1e-8 used
* instead, since this code will not work correctly if it is not allowed
* to merge "too near" vertices.
*
* Normally, if epsilon is non-zero, there is an "input modify" pass which
* checks to see if some vertices are within epsilon of other edges, and
* snapping them to those edges if so. You can skip this pass by setting
* skip_input_modify to true. (This is also useful in some unit tests.)
*/
typedef struct CDT_input {
int verts_len;
int edges_len;
int faces_len;
float (*vert_coords)[2];
int (*edges)[2];
int *faces;
int *faces_start_table;
int *faces_len_table;
float epsilon;
bool skip_input_modify;
} CDT_input;
/**
* A representation of the triangulation for output.
* See #CDT_input for the representation of the output
* vertices, edges, and faces, all represented in
* a similar way to the input.
*
* The output may have merged some input vertices together,
* if they were closer than some epsilon distance.
* The output edges may be overlapping sub-segments of some
* input edges; or they may be new edges for the triangulation.
* The output faces may be pieces of some input faces, or they
* may be new.
*
* In the same way that faces lists-of-lists were represented by
* a run-together array and a "start" and "len" extra array,
* similar triples are used to represent the output to input
* mapping of vertices, edges, and faces.
*
* Those triples are:
* - verts_orig, verts_orig_start_table, verts_orig_len_table
* - edges_orig, edges_orig_start_table, edges_orig_len_table
* - faces_orig, faces_orig_start_table, faces_orig_len_table
*
* For edges, the edges_orig triple can also say which original face
* edge is part of a given output edge. If an index in edges_orig
* is greater than the input's edges_len, then subtract input's edges_len
* from it to some number i: then the face edge that starts from the
* input vertex at input's faces[i] is the corresponding face edge.
* for convenience, face_edge_offset in the result will be the input's
* edges_len, so that this conversion can be easily done by the caller.
*/
typedef struct CDT_result {
int verts_len;
int edges_len;
int faces_len;
int face_edge_offset;
float (*vert_coords)[2];
int (*edges)[2];
int *faces;
int *faces_start_table;
int *faces_len_table;
int *verts_orig;
int *verts_orig_start_table;
int *verts_orig_len_table;
int *edges_orig;
int *edges_orig_start_table;
int *edges_orig_len_table;
int *faces_orig;
int *faces_orig_start_table;
int *faces_orig_len_table;
} CDT_result;
/** What triangles and edges of CDT are desired when getting output? */
typedef enum CDT_output_type {
/** All triangles, outer boundary is convex hull. */
CDT_FULL,
/** All triangles fully enclosed by constraint edges or faces. */
CDT_INSIDE,
/** Only point, edge, and face constraints, and their intersections. */
CDT_CONSTRAINTS,
/**
* Like CDT_CONSTRAINTS, but keep enough
* edges so that any output faces that came from input faces can be made as valid
* #BMesh faces in Blender: that is,
* no vertex appears more than once and no isolated holes in faces.
*/
CDT_CONSTRAINTS_VALID_BMESH
} CDT_output_type;
/**
* API interface to CDT.
* This returns a pointer to an allocated CDT_result.
* When the caller is finished with it, the caller
* should use #BLI_delaunay_2d_cdt_free() to free it.
*/
CDT_result *BLI_delaunay_2d_cdt_calc(const CDT_input *input, const CDT_output_type output_type);
void BLI_delaunay_2d_cdt_free(CDT_result *result);
#ifdef __cplusplus
}
#endif
#endif /* __BLI_DELAUNAY_2D_H__ */
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