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/*
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* This file is a part of Poly2Tri-C
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* (c) Barak Itkin <lightningismyname@gmail.com>
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* http://code.google.com/p/poly2tri-c/
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*
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without modification,
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* are permitted provided that the following conditions are met:
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*
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* * Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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* * Neither the name of Poly2Tri nor the names of its contributors may be
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* used to endorse or promote products derived from this software without specific
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* prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <glib.h>
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#include "point.h"
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#include "edge.h"
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#include "triangle.h"
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#include "vedge.h"
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#include "cdt-flipfix.h"
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static P2trEdge* p2tr_cdt_try_flip (P2trCDT *self,
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P2trEdge *to_flip);
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/* This function implements "Lawson's algorithm", also known as "The
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* diagonal swapping algorithm". This algorithm takes a CDT, and a list
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* of triangles that were formed by the insertion of a new point into
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* the triangular mesh, and makes the triangulation a CDT once more. Its
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* logic is explained below:
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*
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* If a point is added to an existing triangular mesh then
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* circumcircles are formed for all new triangles formed. If any of
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* the neighbours lie inside the circumcircle of any triangle, then a
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* quadrilateral is formed using the triangle and its neighbour. The
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* diagonals of this quadrilateral are swapped to give a new
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* triangulation. This process is continued till there are no more
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* faulty triangles and no more swaps are required.
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*
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* The description above may seem slightly inaccurate, as it does not
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* consider the case were the diagonals can not be swapped since the
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* quadrilateral is concave (then swapping the diagonals would result
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* in a diagonal outside the quad, which is undesired).
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*
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* However, the description above is accurate. If the opposite point
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* is inside the circular cut created by the edge, then since the
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* circular cut is inside the infinite area created by extending the
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* two other edges of the triangle, therefor the point is also inside
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* that area - meaning that the quadrilateral is not concave!
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*/
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void
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p2tr_cdt_flip_fix (P2trCDT *self,
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P2trVEdgeSet *candidates)
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{
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P2trEdge *edge;
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P2trVEdge *vedge;
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while (p2tr_vedge_set_pop (candidates, &vedge))
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{
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if (! p2tr_vedge_try_get_and_unref (vedge, &edge))
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continue;
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if (! edge->constrained
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/* TODO: we probably don't need this check... */
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&& ! p2tr_edge_is_removed (edge))
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{
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/* If the edge is not constrained, then it should be
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* a part of two triangles */
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P2trPoint *A = P2TR_EDGE_START(edge), *B = edge->end;
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P2trPoint *C1 = p2tr_triangle_get_opposite_point (edge->tri, edge, FALSE);
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P2trPoint *C2 = p2tr_triangle_get_opposite_point (edge->mirror->tri, edge->mirror, FALSE);
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P2trEdge *flipped = p2tr_cdt_try_flip (self, edge);
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if (flipped != NULL)
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{
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p2tr_vedge_set_add (candidates, p2tr_point_get_edge_to (A, C1, TRUE));
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p2tr_vedge_set_add (candidates, p2tr_point_get_edge_to (A, C2, TRUE));
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p2tr_vedge_set_add (candidates, p2tr_point_get_edge_to (B, C1, TRUE));
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p2tr_vedge_set_add (candidates, p2tr_point_get_edge_to (B, C2, TRUE));
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p2tr_edge_unref (flipped);
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}
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}
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p2tr_edge_unref (edge);
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}
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}
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/**
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* Try to flip a given edge, If successfull, return the new edge (reffed!),
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* otherwise return NULL
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*/
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P2trEdge*
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p2tr_cdt_try_flip (P2trCDT *self,
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P2trEdge *to_flip)
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{
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/* C
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* / | \
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* B-----A to_flip: A->B
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* \ | / to_flip.Tri: ABC
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* D
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*/
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P2trPoint *A, *B, *C, *D;
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P2trEdge *AB, *CA, *AD, *DB, *BC, *DC;
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g_assert (! to_flip->constrained && ! to_flip->delaunay);
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A = P2TR_EDGE_START (to_flip);
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B = to_flip->end;
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C = p2tr_triangle_get_opposite_point (to_flip->tri, to_flip, FALSE);
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D = p2tr_triangle_get_opposite_point (to_flip->mirror->tri, to_flip->mirror, FALSE);
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AB = to_flip;
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/* Check if the quadriliteral ADBC is concave (because if it is, we
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* can't flip the edge) */
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if (p2tr_triangle_circumcircle_contains_point (AB->tri, &D->c) != P2TR_INCIRCLE_IN)
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return NULL;
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CA = p2tr_point_get_edge_to (C, A, FALSE);
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AD = p2tr_point_get_edge_to (A, D, FALSE);
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DB = p2tr_point_get_edge_to (D, B, FALSE);
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BC = p2tr_point_get_edge_to (B, C, FALSE);
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p2tr_edge_remove (AB);
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DC = p2tr_mesh_new_edge (self->mesh, D, C, FALSE);
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p2tr_triangle_unref (p2tr_mesh_new_triangle (self->mesh,
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CA, AD, DC));
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p2tr_triangle_unref (p2tr_mesh_new_triangle (self->mesh,
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DB, BC, DC->mirror));
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return DC;
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}
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