Files
OrcaSlicer-bambulab/deps_src/mcut/include/mcut/internal/cdt/triangulate.h
2026-05-11 19:29:55 +01:00

2121 lines
81 KiB
C++

/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at https://mozilla.org/MPL/2.0/. */
#ifndef CDT_vW1vZ0lO8rS4gY4uI4fB
#define CDT_vW1vZ0lO8rS4gY4uI4fB
#include "mcut/internal/cdt/kdtree.h"
#include "mcut/internal/cdt/utils.h"
#include <algorithm>
#include <cstdlib>
#include <iterator>
#include <stack>
#include <stdexcept>
#include <utility>
#include <vector>
/// Namespace containing triangulation functionality
namespace cdt {
/// @addtogroup API
/// @{
/**
* Enum of strategies specifying order in which a range of vertices is inserted
* @note vertex_insertion_order_t::RANDOM will only randomize order of
* inserting in triangulation, vertex indices will be preserved as they were
* specified in the final triangulation
*/
struct vertex_insertion_order_t {
/**
* The Enum itself
* @note needed to pre c++11 compilers that don't support 'class enum'
*/
enum Enum {
RANDOM, ///< vertices will be inserted in random order
AS_GIVEN, ///< vertices will be inserted in the same order as provided
};
};
/// Enum of what type of geometry used to embed triangulation into
struct super_geometry_type_t {
/**
* The Enum itself
* @note needed to pre c++11 compilers that don't support 'class enum'
*/
enum Enum {
SUPER_TRIANGLE, ///< conventional super-triangle
CUSTOM, ///< user-specified custom geometry (e.g., grid)
};
};
/**
* Enum of strategies for treating intersecting constraint edges
*/
struct action_on_intersecting_constraint_edges_t {
/**
* The Enum itself
* @note needed to pre c++11 compilers that don't support 'class enum'
*/
enum Enum {
IGNORE, ///< constraint edge intersections are not checked
RESOLVE, ///< constraint edge intersections are resolved
};
};
/**
* Type used for storing layer depths for triangles
* @note layer_depth_t should support 60K+ layers, which could be to much or
* too little for some use cases. Feel free to re-define this typedef.
*/
typedef unsigned short layer_depth_t;
typedef layer_depth_t boundary_overlap_count_t;
namespace detail {
/// Needed for c++03 compatibility (no uniform initialization available)
template <typename T>
std::array<T, 3> arr3(const T& v0, const T& v1, const T& v2)
{
const std::array<T, 3> out = { v0, v1, v2 };
return out;
}
namespace defaults {
const std::size_t nTargetVerts = 0;
const super_geometry_type_t::Enum superGeomType = super_geometry_type_t::SUPER_TRIANGLE;
const vertex_insertion_order_t::Enum vertexInsertionOrder = vertex_insertion_order_t::RANDOM;
const action_on_intersecting_constraint_edges_t::Enum intersectingEdgesStrategy = action_on_intersecting_constraint_edges_t::IGNORE;
const float minDistToConstraintEdge(0);
} // namespace defaults
// add element to 'to' if not already in 'to'
template <typename T, typename Allocator1>
void insert_unique(std::vector<T, Allocator1>& to, const T& elem)
{
if (std::find(to.begin(), to.end(), elem) == to.end()) {
to.push_back(elem);
}
}
// add elements of 'from' that are not present in 'to' to 'to'
template <typename T, typename Allocator1, typename Allocator2>
void insert_unique(
std::vector<T, Allocator1>& to,
const std::vector<T, Allocator2>& from)
{
typedef typename std::vector<T, Allocator2>::const_iterator Cit;
to.reserve(to.size() + from.size());
for (Cit cit = from.begin(); cit != from.end(); ++cit) {
insert_unique(to, *cit);
}
}
} // namespace detail
/**
* @defgroup triangulator_t triangulator_t Class
* Class performing triangulations.
*/
/// @{
/**
* Data structure representing a 2D constrained Delaunay triangulation
*
* @tparam T type of vertex coordinates (e.g., float, double)
* @tparam TNearPointLocator class providing locating near point for efficiently
* inserting new points. Provides methods: 'add_point(vPos, iV)' and
* 'nearPoint(vPos) -> iV'
*/
template <typename T, typename TNearPointLocator = locator_kdtree_t<T>>
class triangulator_t {
public:
// typedef std::vector<vec2_<T>> vec2_vector_t; ///< Vertices vector
std::vector<vec2_<T>> vertices; ///< triangulation's vertices
std::vector<triangle_t> triangles; ///< triangulation's triangles
std::unordered_set<edge_t> fixedEdges; ///< triangulation's constraints (fixed edges)
/**
* triangles adjacent to each vertex
* @note will be reset to empty when super-triangle is removed and
* triangulation is finalized. To re-calculate adjacent triangles use
* cdt::get_vertex_to_triangles_map helper
*/
std::vector<std::vector<std::uint32_t>> vertTris;
/** Stores count of overlapping boundaries for a fixed edge. If no entry is
* present for an edge: no boundaries overlap.
* @note map only has entries for fixed for edges that represent overlapping
* boundaries
* @note needed for handling depth calculations and hole-removel in case of
* overlapping boundaries
*/
std::unordered_map<edge_t, boundary_overlap_count_t> overlapCount;
/** Stores list of original edges represented by a given fixed edge
* @note map only has entries for edges where multiple original fixed edges
* overlap or where a fixed edge is a part of original edge created by
* conforming Delaunay triangulation vertex insertion
*/
std::unordered_map<edge_t, std::vector<edge_t>> pieceToOriginals;
/*____ API _____*/
/// Default constructor
triangulator_t();
/**
* Constructor
* @param vertexInsertionOrder strategy used for ordering vertex insertions
*/
triangulator_t(vertex_insertion_order_t::Enum vertexInsertionOrder);
/**
* Constructor
* @param vertexInsertionOrder strategy used for ordering vertex insertions
* @param intersectingEdgesStrategy strategy for treating intersecting
* constraint edges
* @param minDistToConstraintEdge distance within which point is considered
* to be lying on a constraint edge. Used when adding constraints to the
* triangulation.
*/
triangulator_t(
vertex_insertion_order_t::Enum vertexInsertionOrder,
action_on_intersecting_constraint_edges_t::Enum intersectingEdgesStrategy,
T minDistToConstraintEdge);
/**
* Constructor
* @param vertexInsertionOrder strategy used for ordering vertex insertions
* @param nearPtLocator class providing locating near point for efficiently
* inserting new points
* @param intersectingEdgesStrategy strategy for treating intersecting
* constraint edges
* @param minDistToConstraintEdge distance within which point is considered
* to be lying on a constraint edge. Used when adding constraints to the
* triangulation.
*/
triangulator_t(
vertex_insertion_order_t::Enum vertexInsertionOrder,
const TNearPointLocator& nearPtLocator,
action_on_intersecting_constraint_edges_t::Enum intersectingEdgesStrategy,
T minDistToConstraintEdge);
/**
* Insert custom point-types specified by iterator range and X/Y-getters
* @tparam TVertexIter iterator that dereferences to custom point type
* @tparam TGetVertexCoordX function object getting x coordinate from
* vertex. Getter signature: const TVertexIter::value_type& -> T
* @tparam TGetVertexCoordY function object getting y coordinate from
* vertex. Getter signature: const TVertexIter::value_type& -> T
* @param first beginning of the range of vertices to add
* @param last end of the range of vertices to add
* @param get_x_coord getter of X-coordinate
* @param get_y_coord getter of Y-coordinate
*/
template <
typename TVertexIter,
typename TGetVertexCoordX,
typename TGetVertexCoordY>
void insert_vertices(
TVertexIter first,
TVertexIter last,
TGetVertexCoordX get_x_coord,
TGetVertexCoordY get_y_coord);
/**
* Insert vertices into triangulation
* @param vertices vector of vertices to insert
*/
void insert_vertices(const std::vector<vec2_<T>>& vertices);
/**
* Insert constraints (custom-type fixed edges) into triangulation
* @note Each fixed edge is inserted by deleting the triangles it crosses,
* followed by the triangulation of the polygons on each side of the edge.
* <b> No new vertices are inserted.</b>
* @note If some edge appears more than once in the input this means that
* multiple boundaries overlap at the edge and impacts how hole detection
* algorithm of triangulator_t::erase_outer_triangles_and_holes works.
* <b>Make sure there are no erroneous duplicates.</b>
* @tparam TEdgeIter iterator that dereferences to custom edge type
* @tparam TGetEdgeVertexStart function object getting start vertex index
* from an edge.
* Getter signature: const TEdgeIter::value_type& -> std::uint32_t
* @tparam TGetEdgeVertexEnd function object getting end vertex index from
* an edge. Getter signature: const TEdgeIter::value_type& -> std::uint32_t
* @param first beginning of the range of edges to add
* @param last end of the range of edges to add
* @param getStart getter of edge start vertex index
* @param getEnd getter of edge end vertex index
*/
template <
typename TEdgeIter,
typename TGetEdgeVertexStart,
typename TGetEdgeVertexEnd>
void insert_edges(
TEdgeIter first,
TEdgeIter last,
TGetEdgeVertexStart getStart,
TGetEdgeVertexEnd getEnd);
/**
* Insert constraint edges into triangulation
* @note Each fixed edge is inserted by deleting the triangles it crosses,
* followed by the triangulation of the polygons on each side of the edge.
* <b> No new vertices are inserted.</b>
* @note If some edge appears more than once in the input this means that
* multiple boundaries overlap at the edge and impacts how hole detection
* algorithm of triangulator_t::erase_outer_triangles_and_holes works.
* <b>Make sure there are no erroneous duplicates.</b>
* @tparam edges constraint edges
*/
void insert_edges(const std::vector<edge_t>& edges);
/*!
* Returns:
* - intersected triangle index
* - index of point on the left of the line
* - index of point on the right of the line
* If left point is right on the line: no triangle is intersected:
* - triangle index is no-neighbor (invalid)
* - index of point on the line
* - index of point on the right of the line
*/
std::tuple<std::uint32_t, std::uint32_t, std::uint32_t>
get_intersected_triangle(
const std::uint32_t iA,
const std::vector<std::uint32_t>& candidates,
const vec2_<T>& a,
const vec2_<T>& b,
const T orientationTolerance) const
{
typedef std::vector<std::uint32_t>::const_iterator TriIndCit;
for (TriIndCit it = candidates.begin(); it != candidates.end(); ++it) {
const std::uint32_t iT = *it;
const triangle_t t = triangles[iT];
const std::uint32_t i = get_vertex_index(t, iA);
const std::uint32_t iP2 = t.vertices[ccw(i)];
const T orientP2 = orient2d(vertices[iP2], a, b);
const point_to_line_location_t::Enum locP2 = classify_orientation(orientP2);
if (locP2 == point_to_line_location_t::RIGHT_SIDE) {
const std::uint32_t iP1 = t.vertices[cw(i)];
const T orientP1 = orient2d(vertices[iP1], a, b);
const point_to_line_location_t::Enum locP1 = classify_orientation(orientP1);
if (locP1 == point_to_line_location_t::COLLINEAR) {
return std::make_tuple(null_neighbour, iP1, iP1);
}
if (locP1 == point_to_line_location_t::LEFT_SIDE) {
if (orientationTolerance) {
T closestOrient;
std::uint32_t iClosestP;
if (std::abs(orientP1) <= std::abs(orientP2)) {
closestOrient = orientP1;
iClosestP = iP1;
} else {
closestOrient = orientP2;
iClosestP = iP2;
}
if (classify_orientation(
closestOrient, orientationTolerance)
== point_to_line_location_t::COLLINEAR) {
return std::make_tuple(null_neighbour, iClosestP, iClosestP);
}
}
return std::make_tuple(iT, iP1, iP2);
}
}
}
throw std::runtime_error("Could not find vertex triangle intersected by "
"edge. Note: can be caused by duplicate points.");
}
/// Returns indices of four resulting triangles
/* Inserting a point on the edge between two triangles
* T1 (top) v1
* /|\
* n1 / | \ n4
* / | \
* / T1' | Tnew1\
* v2-------v-------v4
* \ Tnew2| T2' /
* \ | /
* n2 \ | / n3
* \|/
* T2 (bottom) v3
*/
std::stack<std::uint32_t> insert_point_on_edge(
const std::uint32_t v,
const std::uint32_t iT1,
const std::uint32_t iT2)
{
const std::uint32_t iTnew1 = add_triangle();
const std::uint32_t iTnew2 = add_triangle();
triangle_t& t1 = triangles[iT1];
triangle_t& t2 = triangles[iT2];
std::uint32_t i = get_opposite_vertex_index(t1, iT2);
const std::uint32_t v1 = t1.vertices[i];
const std::uint32_t v2 = t1.vertices[ccw(i)];
const std::uint32_t n1 = t1.neighbors[i];
const std::uint32_t n4 = t1.neighbors[cw(i)];
i = get_opposite_vertex_index(t2, iT1);
const std::uint32_t v3 = t2.vertices[i];
const std::uint32_t v4 = t2.vertices[ccw(i)];
const std::uint32_t n3 = t2.neighbors[i];
const std::uint32_t n2 = t2.neighbors[cw(i)];
// add new triangles and change existing ones
using detail::arr3;
t1 = triangle_t::make(arr3(v1, v2, v), arr3(n1, iTnew2, iTnew1));
t2 = triangle_t::make(arr3(v3, v4, v), arr3(n3, iTnew1, iTnew2));
triangles[iTnew1] = triangle_t::make(arr3(v1, v, v4), arr3(iT1, iT2, n4));
triangles[iTnew2] = triangle_t::make(arr3(v3, v, v2), arr3(iT2, iT1, n2));
// make and add new vertex
add_adjacent_triangles(v, iT1, iTnew2, iT2, iTnew1);
// adjust neighboring triangles and vertices
change_neighbour(n4, iT1, iTnew1);
change_neighbour(n2, iT2, iTnew2);
add_adjacent_triangle(v1, iTnew1);
add_adjacent_triangle(v3, iTnew2);
remove_adjacent_triangle(v2, iT2);
add_adjacent_triangle(v2, iTnew2);
remove_adjacent_triangle(v4, iT1);
add_adjacent_triangle(v4, iTnew1);
// return newly added triangles
std::stack<std::uint32_t> newTriangles;
newTriangles.push(iT1);
newTriangles.push(iTnew2);
newTriangles.push(iT2);
newTriangles.push(iTnew1);
return newTriangles;
}
std::array<std::uint32_t, 2> trianglesAt(const vec2_<T>& pos) const
{
std::array<std::uint32_t, 2> out = { null_neighbour, null_neighbour };
for (std::uint32_t i = std::uint32_t(0); i < std::uint32_t(triangles.size()); ++i) {
const triangle_t& t = triangles[i];
const vec2_<T>& v1 = vertices[t.vertices[0]];
const vec2_<T>& v2 = vertices[t.vertices[1]];
const vec2_<T>& v3 = vertices[t.vertices[2]];
const point_to_triangle_location_t::Enum loc = locate_point_wrt_triangle(pos, v1, v2, v3);
if (loc == point_to_triangle_location_t::OUTSIDE)
continue;
out[0] = i;
if (check_on_edge(loc))
out[1] = t.neighbors[edge_neighbour(loc)];
return out;
}
throw std::runtime_error("No triangle was found at position");
}
/**
* Ensure that triangulation conforms to constraints (fixed edges)
* @note For each fixed edge that is not present in the triangulation its
* midpoint is recursively added until the original edge is represented by a
* sequence of its pieces. <b> New vertices are inserted.</b>
* @note If some edge appears more than once the input this
* means that multiple boundaries overlap at the edge and impacts how hole
* detection algorithm of triangulator_t::erase_outer_triangles_and_holes works.
* <b>Make sure there are no erroneous duplicates.</b>
* @tparam TEdgeIter iterator that dereferences to custom edge type
* @tparam TGetEdgeVertexStart function object getting start vertex index
* from an edge.
* Getter signature: const TEdgeIter::value_type& -> std::uint32_t
* @tparam TGetEdgeVertexEnd function object getting end vertex index from
* an edge. Getter signature: const TEdgeIter::value_type& -> std::uint32_t
* @param first beginning of the range of edges to add
* @param last end of the range of edges to add
* @param getStart getter of edge start vertex index
* @param getEnd getter of edge end vertex index
*/
template <
typename TEdgeIter,
typename TGetEdgeVertexStart,
typename TGetEdgeVertexEnd>
void conform_to_edges(
TEdgeIter first,
TEdgeIter last,
TGetEdgeVertexStart getStart,
TGetEdgeVertexEnd getEnd);
/*!
* Returns:
* - intersected triangle index
* - index of point on the left of the line
* - index of point on the right of the line
* If left point is right on the line: no triangle is intersected:
* - triangle index is no-neighbor (invalid)
* - index of point on the line
* - index of point on the right of the line
*/
std::tuple<std::uint32_t, std::uint32_t, std::uint32_t>
TintersectedTriangle(
const std::uint32_t iA,
const std::vector<std::uint32_t>& candidates,
const vec2_<T>& a,
const vec2_<T>& b,
const T orientationTolerance = T(0)) const
{
typedef std::vector<std::uint32_t>::const_iterator TriIndCit;
for (TriIndCit it = candidates.begin(); it != candidates.end(); ++it) {
const std::uint32_t iT = *it;
const triangle_t t = triangles[iT];
const std::uint32_t i = get_vertex_index(t, iA);
const std::uint32_t iP2 = t.vertices[ccw(i)];
const T orientP2 = orient2D(vertices[iP2], a, b);
const point_to_line_location_t::Enum locP2 = classify_orientation(orientP2);
if (locP2 == point_to_line_location_t::RIGHT_SIDE) {
const std::uint32_t iP1 = t.vertices[cw(i)];
const T orientP1 = orient2D(vertices[iP1], a, b);
const point_to_line_location_t::Enum locP1 = classify_orientation(orientP1);
if (locP1 == point_to_line_location_t::COLLINEAR) {
return std::make_tuple(null_neighbour, iP1, iP1);
}
if (locP1 == point_to_line_location_t::LEFT_SIDE) {
if (orientationTolerance) {
T closestOrient;
std::uint32_t iClosestP;
if (std::abs(orientP1) <= std::abs(orientP2)) {
closestOrient = orientP1;
iClosestP = iP1;
} else {
closestOrient = orientP2;
iClosestP = iP2;
}
if (classify_orientation(
closestOrient, orientationTolerance)
== point_to_line_location_t::COLLINEAR) {
return std::make_tuple(null_neighbour, iClosestP, iClosestP);
}
}
return std::make_tuple(iT, iP1, iP2);
}
}
}
throw std::runtime_error("Could not find vertex triangle intersected by "
"edge. Note: can be caused by duplicate points.");
}
/// Returns indices of three resulting triangles
/* Insert point into triangle: split into 3 triangles:
* - create 2 new triangles
* - re-use old triangle for the 3rd
* v3
* / | \
* / | \ <-- original triangle (t)
* / | \
* n3 / | \ n2
* /newT2|newT1\
* / v \
* / __/ \__ \
* / __/ \__ \
* / _/ t' \_ \
* v1 ___________________ v2
* n1
*/
std::stack<std::uint32_t> insert_point_in_triangle(
const std::uint32_t v,
const std::uint32_t iT)
{
const std::uint32_t iNewT1 = add_triangle();
const std::uint32_t iNewT2 = add_triangle();
triangle_t& t = triangles[iT];
const std::array<std::uint32_t, 3> vv = t.vertices;
const std::array<std::uint32_t, 3> nn = t.neighbors;
const std::uint32_t v1 = vv[0], v2 = vv[1], v3 = vv[2];
const std::uint32_t n1 = nn[0], n2 = nn[1], n3 = nn[2];
// make two new triangles and convert current triangle to 3rd new
// triangle
using detail::arr3;
triangles[iNewT1] = triangle_t::make(arr3(v2, v3, v), arr3(n2, iNewT2, iT));
triangles[iNewT2] = triangle_t::make(arr3(v3, v1, v), arr3(n3, iT, iNewT1));
t = triangle_t::make(arr3(v1, v2, v), arr3(n1, iNewT1, iNewT2));
// make and add a new vertex
add_adjacent_triangles(v, iT, iNewT1, iNewT2);
// adjust lists of adjacent triangles for v1, v2, v3
add_adjacent_triangle(v1, iNewT2);
add_adjacent_triangle(v2, iNewT1);
remove_adjacent_triangle(v3, iT);
add_adjacent_triangle(v3, iNewT1);
add_adjacent_triangle(v3, iNewT2);
// change triangle neighbor's neighbors to new triangles
change_neighbour(n2, iT, iNewT1);
change_neighbour(n3, iT, iNewT2);
// return newly added triangles
std::stack<std::uint32_t> newTriangles;
newTriangles.push(iT);
newTriangles.push(iNewT1);
newTriangles.push(iNewT2);
return newTriangles;
}
std::array<std::uint32_t, 2> walking_search_triangle_at(
const vec2_<T>& pos) const
{
std::array<std::uint32_t, 2> out = { null_neighbour, null_neighbour };
// Query for a vertex close to pos, to start the search
const std::uint32_t startVertex = m_nearPtLocator.nearPoint(pos, vertices);
const std::uint32_t iT = walk_triangles(startVertex, pos);
// Finished walk, locate point in current triangle
const triangle_t& t = triangles[iT];
const vec2_<T>& v1 = vertices[t.vertices[0]];
const vec2_<T>& v2 = vertices[t.vertices[1]];
const vec2_<T>& v3 = vertices[t.vertices[2]];
const point_to_triangle_location_t::Enum loc = locate_point_wrt_triangle(pos, v1, v2, v3);
if (loc == point_to_triangle_location_t::OUTSIDE)
throw std::runtime_error("No triangle was found at position");
out[0] = iT;
if (check_on_edge(loc))
out[1] = t.neighbors[edge_neighbour(loc)];
return out;
}
/**
* Ensure that triangulation conforms to constraints (fixed edges)
* @note For each fixed edge that is not present in the triangulation its
* midpoint is recursively added until the original edge is represented by a
* sequence of its pieces. <b> New vertices are inserted.</b>
* @note If some edge appears more than once the input this
* means that multiple boundaries overlap at the edge and impacts how hole
* detection algorithm of triangulator_t::erase_outer_triangles_and_holes works.
* <b>Make sure there are no erroneous duplicates.</b>
* @tparam edges edges to conform to
*/
void conform_to_edges(const std::vector<edge_t>& edges);
/**
* Erase triangles adjacent to super triangle
*
* @note does nothing if custom geometry is used
*/
void eraseSuperTriangle();
/// Erase triangles outside of constrained boundary using growing
void erase_outer_triangles();
/**
* Erase triangles outside of constrained boundary and auto-detected holes
*
* @note detecting holes relies on layer peeling based on layer depth
* @note supports overlapping or touching boundaries
*/
void erase_outer_triangles_and_holes();
/**
* Call this method after directly setting custom super-geometry via
* vertices and triangles members
*/
void initialise_with_custom_supergeometry();
/**
* Check if the triangulation was finalized with `erase...` method and
* super-triangle was removed.
* @return true if triangulation is finalized, false otherwise
*/
bool is_finalized() const;
/**
* Calculate depth of each triangle in constraint triangulation. Supports
* overlapping boundaries.
*
* Perform depth peeling from super triangle to outermost boundary,
* then to next boundary and so on until all triangles are traversed.@n
* For example depth is:
* - 0 for triangles outside outermost boundary
* - 1 for triangles inside boundary but outside hole
* - 2 for triangles in hole
* - 3 for triangles in island and so on...
* @return vector where element at index i stores depth of i-th triangle
*/
std::vector<layer_depth_t>
calculate_triangle_depths() const
{
std::vector<layer_depth_t> triDepths(
triangles.size(), std::numeric_limits<layer_depth_t>::max());
std::stack<std::uint32_t> seeds(std::deque<std::uint32_t>(1, vertTris[0].front()));
layer_depth_t layerDepth = 0;
layer_depth_t deepestSeedDepth = 0;
std::unordered_map<layer_depth_t, std::unordered_set<std::uint32_t>> seedsByDepth;
do {
const std::unordered_map<std::uint32_t, layer_depth_t>& newSeeds = peel_layer(seeds, layerDepth, triDepths);
seedsByDepth.erase(layerDepth);
typedef std::unordered_map<std::uint32_t, layer_depth_t>::const_iterator Iter;
for (Iter it = newSeeds.begin(); it != newSeeds.end(); ++it) {
deepestSeedDepth = std::max(deepestSeedDepth, it->second);
seedsByDepth[it->second].insert(it->first);
}
const std::unordered_set<std::uint32_t>& nextLayerSeeds = seedsByDepth[layerDepth + 1];
seeds = std::stack<std::uint32_t>(
std::deque<std::uint32_t>(nextLayerSeeds.begin(), nextLayerSeeds.end()));
++layerDepth;
} while (!seeds.empty() || deepestSeedDepth > layerDepth);
return triDepths;
}
/**
* @defgroup Advanced Advanced triangulator_t Methods
* Advanced methods for manually modifying the triangulation from
* outside. Please only use them when you know what you are doing.
*/
/// @{
/**
* Flip an edge between two triangle.
* @note Advanced method for manually modifying the triangulation from
* outside. Please call it when you know what you are doing.
* @param iT first triangle
* @param iTopo second triangle
*/
void do_edgeflip(std::uint32_t iT, std::uint32_t iTopo);
/**
* Remove triangles with specified indices.
* Adjust internal triangulation state accordingly.
* @param removedTriangles indices of triangles to remove
*/
void remove_triangles(const std::unordered_set<std::uint32_t>& removedTriangles);
/// @}
private:
/*____ Detail __*/
void add_super_triangle(const box2d_t<T>& box);
void create_vertex(const vec2_<T>& pos, const std::vector<std::uint32_t>& tris);
void insert_vertex(std::uint32_t iVert);
void enforce_delaunay_property_using_edge_flips(
const vec2_<T>& v,
std::uint32_t iVert,
std::stack<std::uint32_t>& triStack);
/// Flip fixed edges and return a list of flipped fixed edges
std::vector<edge_t> insert_vertex_and_flip_fixed_edges(std::uint32_t iVert);
/**
* Insert an edge into constraint Delaunay triangulation
* @param edge edge to insert
* @param originalEdge original edge inserted edge is part of
*/
void insert_edge(edge_t edge, edge_t originalEdge);
/**
* Conform Delaunay triangulation to a fixed edge by recursively inserting
* mid point of the edge and then conforming to its halves
* @param edge fixed edge to conform to
* @param originalEdges original edges that new edge is piece of
* @param overlaps count of overlapping boundaries at the edge. Only used
* when re-introducing edge with overlaps > 0
* @param orientationTolerance tolerance for orient2d predicate,
* values [-tolerance,+tolerance] are considered as 0.
*/
void conform_to_edge(
edge_t edge,
std::vector<edge_t> originalEdges,
boundary_overlap_count_t overlaps);
std::uint32_t walk_triangles(std::uint32_t startVertex, const vec2_<T>& pos) const;
bool check_is_edgeflip_needed(
const vec2_<T>& v,
std::uint32_t iV,
std::uint32_t iV1,
std::uint32_t iV2,
std::uint32_t iV3) const;
bool
check_is_edgeflip_needed(const vec2_<T>& v, std::uint32_t iT, std::uint32_t iTopo, std::uint32_t iVert) const;
void change_neighbour(std::uint32_t iT, std::uint32_t oldNeighbor, std::uint32_t newNeighbor);
void change_neighbour(
std::uint32_t iT,
std::uint32_t iVedge1,
std::uint32_t iVedge2,
std::uint32_t newNeighbor);
void add_adjacent_triangle(std::uint32_t iVertex, std::uint32_t iTriangle);
void
add_adjacent_triangles(std::uint32_t iVertex, std::uint32_t iT1, std::uint32_t iT2, std::uint32_t iT3);
void add_adjacent_triangles(
std::uint32_t iVertex,
std::uint32_t iT1,
std::uint32_t iT2,
std::uint32_t iT3,
std::uint32_t iT4);
void remove_adjacent_triangle(std::uint32_t iVertex, std::uint32_t iTriangle);
std::uint32_t triangulate_pseudo_polygon(
std::uint32_t ia,
std::uint32_t ib,
std::vector<std::uint32_t>::const_iterator pointsFirst,
std::vector<std::uint32_t>::const_iterator pointsLast);
std::uint32_t find_delaunay_point(
std::uint32_t ia,
std::uint32_t ib,
std::vector<std::uint32_t>::const_iterator pointsFirst,
std::vector<std::uint32_t>::const_iterator pointsLast) const;
std::uint32_t pseudo_polygon_outer_triangle(std::uint32_t ia, std::uint32_t ib) const;
std::uint32_t add_triangle(const triangle_t& t); // note: invalidates iterators!
std::uint32_t add_triangle(); // note: invalidates triangle iterators!
/**
* Remove super-triangle (if used) and triangles with specified indices.
* Adjust internal triangulation state accordingly.
* @removedTriangles indices of triangles to remove
*/
void finalise_triangulation(const std::unordered_set<std::uint32_t>& removedTriangles);
std::unordered_set<std::uint32_t> grow_to_boundary(std::stack<std::uint32_t> seeds) const;
void fixEdge(
const edge_t& edge,
const boundary_overlap_count_t overlaps)
{
fixedEdges.insert(edge);
overlapCount[edge] = overlaps; // override overlap counter
}
void fixEdge(const edge_t& edge)
{
if (!fixedEdges.insert(edge).second) {
++overlapCount[edge]; // if edge is already fixed increment the counter
}
}
void fixEdge(
const edge_t& edge,
const edge_t& originalEdge)
{
fixEdge(edge);
if (edge != originalEdge)
detail::insert_unique(pieceToOriginals[edge], originalEdge);
}
/**
* Flag triangle as dummy
* @note Advanced method for manually modifying the triangulation from
* outside. Please call it when you know what you are doing.
* @param iT index of a triangle to flag
*/
void make_dummies(const std::uint32_t iT)
{
const triangle_t& t = triangles[iT];
typedef std::array<std::uint32_t, 3>::const_iterator VCit;
for (VCit iV = t.vertices.begin(); iV != t.vertices.end(); ++iV)
remove_adjacent_triangle(*iV, iT);
typedef std::array<std::uint32_t, 3>::const_iterator NCit;
for (NCit iTn = t.neighbors.begin(); iTn != t.neighbors.end(); ++iTn)
change_neighbour(*iTn, iT, null_neighbour);
m_dummyTris.push_back(iT);
}
/**
* Erase all dummy triangles
* @note Advanced method for manually modifying the triangulation from
* outside. Please call it when you know what you are doing.
*/
void erase_dummies()
{
if (m_dummyTris.empty())
return;
const std::unordered_set<std::uint32_t> dummySet(m_dummyTris.begin(), m_dummyTris.end());
std::unordered_map<std::uint32_t, std::uint32_t> triIndMap;
triIndMap[null_neighbour] = null_neighbour;
for (std::uint32_t iT(0), iTnew(0); iT < std::uint32_t(triangles.size()); ++iT) {
if (dummySet.count(iT))
continue;
triIndMap[iT] = iTnew;
triangles[iTnew] = triangles[iT];
iTnew++;
}
triangles.erase(triangles.end() - dummySet.size(), triangles.end());
// remap adjacent triangle indices for vertices
typedef typename std::vector<std::vector<std::uint32_t>>::iterator VertTrisIt;
for (VertTrisIt vTris = vertTris.begin(); vTris != vertTris.end(); ++vTris) {
for (std::vector<std::uint32_t>::iterator iT = vTris->begin(); iT != vTris->end(); ++iT)
*iT = triIndMap[*iT];
}
// remap neighbor indices for triangles
for (std::vector<triangle_t>::iterator t = triangles.begin(); t != triangles.end(); ++t) {
std::array<std::uint32_t, 3>& nn = t->neighbors;
for (std::array<std::uint32_t, 3>::iterator iN = nn.begin(); iN != nn.end(); ++iN)
*iN = triIndMap[*iN];
}
// clear dummy triangles
m_dummyTris = std::vector<std::uint32_t>();
}
/**
* Depth-peel a layer in triangulation, used when calculating triangle
* depths
*
* It takes starting seed triangles, traverses neighboring triangles, and
* assigns given layer depth to the traversed triangles. Traversal is
* blocked by constraint edges. Triangles behind constraint edges are
* recorded as seeds of next layer and returned from the function.
*
* @param seeds indices of seed triangles
* @param layerDepth current layer's depth to mark triangles with
* @param[in, out] triDepths depths of triangles
* @return triangles of the deeper layers that are adjacent to the peeled
* layer. To be used as seeds when peeling deeper layers.
*/
std::unordered_map<std::uint32_t, layer_depth_t>
peel_layer(
std::stack<std::uint32_t> seeds,
const layer_depth_t layerDepth,
std::vector<layer_depth_t>& triDepths) const
{
std::unordered_map<std::uint32_t, layer_depth_t> behindBoundary;
while (!seeds.empty()) {
const std::uint32_t iT = seeds.top();
seeds.pop();
triDepths[iT] = layerDepth;
behindBoundary.erase(iT);
const triangle_t& t = triangles[iT];
for (std::uint32_t i(0); i < std::uint32_t(3); ++i) {
const edge_t opEdge(t.vertices[ccw(i)], t.vertices[cw(i)]);
const std::uint32_t iN = t.neighbors[get_opposite_neighbour_from_vertex(i)];
if (iN == null_neighbour || triDepths[iN] <= layerDepth)
continue;
if (fixedEdges.count(opEdge)) {
const std::unordered_map<edge_t, layer_depth_t>::const_iterator cit = overlapCount.find(opEdge);
const layer_depth_t triDepth = cit == overlapCount.end()
? layerDepth + 1
: layerDepth + cit->second + 1;
behindBoundary[iN] = triDepth;
continue;
}
seeds.push(iN);
}
}
return behindBoundary;
}
std::vector<std::uint32_t> m_dummyTris;
TNearPointLocator m_nearPtLocator;
std::size_t m_nTargetVerts;
super_geometry_type_t::Enum m_superGeomType;
vertex_insertion_order_t::Enum m_vertexInsertionOrder;
action_on_intersecting_constraint_edges_t::Enum m_intersectingEdgesStrategy;
T m_minDistToConstraintEdge;
};
/// @}
/// @}
namespace detail {
static std::mt19937 randGenerator(9001);
template <class RandomIt>
void random_shuffle(RandomIt first, RandomIt last)
{
typename std::iterator_traits<RandomIt>::difference_type i, n;
n = last - first;
for (i = n - 1; i > 0; --i) {
std::swap(first[i], first[randGenerator() % (i + 1)]);
}
}
} // namespace detail
//-----------------------
// triangulator_t methods
//-----------------------
template <typename T, typename TNearPointLocator>
template <
typename TVertexIter,
typename TGetVertexCoordX,
typename TGetVertexCoordY>
void triangulator_t<T, TNearPointLocator>::insert_vertices(
const TVertexIter first,
const TVertexIter last,
TGetVertexCoordX get_x_coord,
TGetVertexCoordY get_y_coord)
{
if (is_finalized()) {
throw std::runtime_error(
"triangulator_t was finalized with 'erase...' method. Inserting new "
"vertices is not possible");
}
detail::randGenerator.seed(9001); // ensure deterministic behavior
if (vertices.empty()) {
add_super_triangle(expand_with_points<T>(first, last, get_x_coord, get_y_coord));
}
const std::size_t nExistingVerts = vertices.size();
vertices.reserve(nExistingVerts + std::distance(first, last));
for (TVertexIter it = first; it != last; ++it) {
create_vertex(vec2_<T>::make(get_x_coord(*it), get_y_coord(*it)), std::vector<std::uint32_t>());
}
switch (m_vertexInsertionOrder) {
case vertex_insertion_order_t::AS_GIVEN: {
for (TVertexIter it = first; it != last; ++it) {
insert_vertex(std::uint32_t(nExistingVerts + std::distance(first, it)));
}
break;
}
case vertex_insertion_order_t::RANDOM: {
std::vector<std::uint32_t> ii(std::distance(first, last));
typedef std::vector<std::uint32_t>::iterator Iter;
std::uint32_t value = static_cast<std::uint32_t>(nExistingVerts);
for (Iter it = ii.begin(); it != ii.end(); ++it, ++value)
*it = value;
detail::random_shuffle(ii.begin(), ii.end());
for (Iter it = ii.begin(); it != ii.end(); ++it)
insert_vertex(*it);
break;
}
}
}
template <typename T, typename TNearPointLocator>
template <
typename TEdgeIter,
typename TGetEdgeVertexStart,
typename TGetEdgeVertexEnd>
void triangulator_t<T, TNearPointLocator>::insert_edges(
TEdgeIter first,
const TEdgeIter last,
TGetEdgeVertexStart getStart,
TGetEdgeVertexEnd getEnd)
{
if (is_finalized()) {
throw std::runtime_error(
"triangulator_t was finalized with 'erase...' method. Inserting new "
"edges is not possible");
}
for (; first != last; ++first) {
// +3 to account for super-triangle vertices
const edge_t edge(
std::uint32_t(getStart(*first) + m_nTargetVerts),
std::uint32_t(getEnd(*first) + m_nTargetVerts));
insert_edge(edge, edge);
}
erase_dummies();
}
template <typename T, typename TNearPointLocator>
template <
typename TEdgeIter,
typename TGetEdgeVertexStart,
typename TGetEdgeVertexEnd>
void triangulator_t<T, TNearPointLocator>::conform_to_edges(
TEdgeIter first,
const TEdgeIter last,
TGetEdgeVertexStart getStart,
TGetEdgeVertexEnd getEnd)
{
if (is_finalized()) {
throw std::runtime_error(
"triangulator_t was finalized with 'erase...' method. Conforming to "
"new edges is not possible");
}
for (; first != last; ++first) {
// +3 to account for super-triangle vertices
const edge_t e(
std::uint32_t(getStart(*first) + m_nTargetVerts),
std::uint32_t(getEnd(*first) + m_nTargetVerts));
conform_to_edge(e, std::vector<edge_t>(1, e), 0);
}
erase_dummies();
}
} // namespace cdt
#ifndef CDT_USE_AS_COMPILED_LIBRARY
//#include "triangulator_t.hpp"
#include <algorithm>
#include <cassert>
#include <deque>
#include <stdexcept>
namespace cdt {
template <typename T, typename TNearPointLocator>
triangulator_t<T, TNearPointLocator>::triangulator_t()
: m_nTargetVerts(detail::defaults::nTargetVerts)
, m_superGeomType(detail::defaults::superGeomType)
, m_vertexInsertionOrder(detail::defaults::vertexInsertionOrder)
, m_intersectingEdgesStrategy(detail::defaults::intersectingEdgesStrategy)
, m_minDistToConstraintEdge(detail::defaults::minDistToConstraintEdge)
{
}
template <typename T, typename TNearPointLocator>
triangulator_t<T, TNearPointLocator>::triangulator_t(
const vertex_insertion_order_t::Enum vertexInsertionOrder)
: m_nTargetVerts(detail::defaults::nTargetVerts)
, m_superGeomType(detail::defaults::superGeomType)
, m_vertexInsertionOrder(vertexInsertionOrder)
, m_intersectingEdgesStrategy(detail::defaults::intersectingEdgesStrategy)
, m_minDistToConstraintEdge(detail::defaults::minDistToConstraintEdge)
{
}
template <typename T, typename TNearPointLocator>
triangulator_t<T, TNearPointLocator>::triangulator_t(
const vertex_insertion_order_t::Enum vertexInsertionOrder,
const action_on_intersecting_constraint_edges_t::Enum intersectingEdgesStrategy,
const T minDistToConstraintEdge)
: m_nTargetVerts(detail::defaults::nTargetVerts)
, m_superGeomType(detail::defaults::superGeomType)
, m_vertexInsertionOrder(vertexInsertionOrder)
, m_intersectingEdgesStrategy(intersectingEdgesStrategy)
, m_minDistToConstraintEdge(minDistToConstraintEdge)
{
}
template <typename T, typename TNearPointLocator>
triangulator_t<T, TNearPointLocator>::triangulator_t(
const vertex_insertion_order_t::Enum vertexInsertionOrder,
const TNearPointLocator& nearPtLocator,
const action_on_intersecting_constraint_edges_t::Enum intersectingEdgesStrategy,
const T minDistToConstraintEdge)
: m_nTargetVerts(detail::defaults::nTargetVerts)
, m_nearPtLocator(nearPtLocator)
, m_superGeomType(detail::defaults::superGeomType)
, m_vertexInsertionOrder(vertexInsertionOrder)
, m_intersectingEdgesStrategy(intersectingEdgesStrategy)
, m_minDistToConstraintEdge(minDistToConstraintEdge)
{
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::change_neighbour(
const std::uint32_t iT,
const std::uint32_t iVedge1,
const std::uint32_t iVedge2,
const std::uint32_t newNeighbor)
{
triangle_t& t = triangles[iT];
t.neighbors[opposite_triangle_index(t, iVedge1, iVedge2)] = newNeighbor;
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::eraseSuperTriangle()
{
if (m_superGeomType != super_geometry_type_t::SUPER_TRIANGLE)
return;
// find triangles adjacent to super-triangle's vertices
std::unordered_set<std::uint32_t> toErase;
toErase.reserve(
vertTris[0].size() + vertTris[1].size() + vertTris[2].size());
for (std::uint32_t iT(0); iT < std::uint32_t(triangles.size()); ++iT) {
triangle_t& t = triangles[iT];
if (t.vertices[0] < 3 || t.vertices[1] < 3 || t.vertices[2] < 3)
toErase.insert(iT);
}
finalise_triangulation(toErase);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::erase_outer_triangles()
{
// make dummy triangles adjacent to super-triangle's vertices
const std::stack<std::uint32_t> seed(std::deque<std::uint32_t>(1, vertTris[0].front()));
const std::unordered_set<std::uint32_t> toErase = grow_to_boundary(seed);
finalise_triangulation(toErase);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::erase_outer_triangles_and_holes()
{
const std::vector<layer_depth_t> triDepths = calculate_triangle_depths();
std::unordered_set<std::uint32_t> toErase;
toErase.reserve(triangles.size());
for (std::size_t iT = 0; iT != triangles.size(); ++iT) {
if (triDepths[iT] % 2 == 0){
toErase.insert(static_cast<std::uint32_t>(iT));
}
}
finalise_triangulation(toErase);
}
/// Remap removing super-triangle: subtract 3 from vertices
inline edge_t remap_no_supertriangle(const edge_t& e)
{
return edge_t(e.v1() - 3, e.v2() - 3);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::remove_triangles(
const std::unordered_set<std::uint32_t>& removedTriangles)
{
if (removedTriangles.empty())
return;
// remove triangles and calculate triangle index mapping
std::unordered_map<std::uint32_t, std::uint32_t> triIndMap;
for (std::uint32_t iT(0), iTnew(0); iT < std::uint32_t(triangles.size()); ++iT) {
if (removedTriangles.count(iT))
continue;
triIndMap[iT] = iTnew;
triangles[iTnew] = triangles[iT];
iTnew++;
}
triangles.erase(triangles.end() - removedTriangles.size(), triangles.end());
// adjust triangles' neighbors
vertTris = std::vector<std::vector<std::uint32_t>>();
for (std::uint32_t iT = 0; iT < triangles.size(); ++iT) {
triangle_t& t = triangles[iT];
// update neighbors to account for removed triangles
std::array<std::uint32_t, 3>& nn = t.neighbors;
for (std::array<std::uint32_t, 3>::iterator n = nn.begin(); n != nn.end(); ++n) {
if (removedTriangles.count(*n)) {
*n = null_neighbour;
} else if (*n != null_neighbour) {
*n = triIndMap[*n];
}
}
}
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::finalise_triangulation(
const std::unordered_set<std::uint32_t>& removedTriangles)
{
erase_dummies();
// remove super-triangle
if (m_superGeomType == super_geometry_type_t::SUPER_TRIANGLE) {
vertices.erase(vertices.begin(), vertices.begin() + 3);
if (removedTriangles.empty())
vertTris.erase(vertTris.begin(), vertTris.begin() + 3);
// edge_t re-mapping
{ // fixed edges
std::unordered_set<edge_t> updatedFixedEdges;
typedef std::unordered_set<edge_t>::const_iterator It;
for (It e = fixedEdges.begin(); e != fixedEdges.end(); ++e) {
updatedFixedEdges.insert(remap_no_supertriangle(*e));
}
fixedEdges = updatedFixedEdges;
}
{ // overlap count
std::unordered_map<edge_t, boundary_overlap_count_t> updatedOverlapCount;
typedef std::unordered_map<edge_t, boundary_overlap_count_t>::const_iterator
It;
for (It it = overlapCount.begin(); it != overlapCount.end(); ++it) {
updatedOverlapCount.insert(std::make_pair(
remap_no_supertriangle(it->first), it->second));
}
overlapCount = updatedOverlapCount;
}
{ // split edges mapping
std::unordered_map<edge_t, std::vector<edge_t>> updatedPieceToOriginals;
typedef std::unordered_map<edge_t, std::vector<edge_t>>::const_iterator It;
for (It it = pieceToOriginals.begin(); it != pieceToOriginals.end();
++it) {
std::vector<edge_t> ee = it->second;
for (std::vector<edge_t>::iterator eeIt = ee.begin(); eeIt != ee.end();
++eeIt) {
*eeIt = remap_no_supertriangle(*eeIt);
}
updatedPieceToOriginals.insert(
std::make_pair(remap_no_supertriangle(it->first), ee));
}
pieceToOriginals = updatedPieceToOriginals;
}
}
// remove other triangles
remove_triangles(removedTriangles);
// adjust triangle vertices: account for removed super-triangle
if (m_superGeomType == super_geometry_type_t::SUPER_TRIANGLE) {
for (std::vector<triangle_t>::iterator t = triangles.begin(); t != triangles.end();
++t) {
std::array<std::uint32_t, 3>& vv = t->vertices;
for (std::array<std::uint32_t, 3>::iterator v = vv.begin(); v != vv.end(); ++v) {
*v -= 3;
}
}
}
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::initialise_with_custom_supergeometry()
{
m_nearPtLocator.initialize(vertices);
m_nTargetVerts = vertices.size();
m_superGeomType = super_geometry_type_t::CUSTOM;
}
template <typename T, typename TNearPointLocator>
std::unordered_set<std::uint32_t> triangulator_t<T, TNearPointLocator>::grow_to_boundary(
std::stack<std::uint32_t> seeds) const
{
std::unordered_set<std::uint32_t> traversed;
while (!seeds.empty()) {
const std::uint32_t iT = seeds.top();
seeds.pop();
traversed.insert(iT);
const triangle_t& t = triangles[iT];
for (std::uint32_t i(0); i < std::uint32_t(3); ++i) {
const edge_t opEdge(t.vertices[ccw(i)], t.vertices[cw(i)]);
if (fixedEdges.count(opEdge))
continue;
const std::uint32_t iN = t.neighbors[get_opposite_neighbour_from_vertex(i)];
if (iN != null_neighbour && traversed.count(iN) == 0)
seeds.push(iN);
}
}
return traversed;
}
template <typename T, typename TNearPointLocator>
std::uint32_t triangulator_t<T, TNearPointLocator>::add_triangle(const triangle_t& t)
{
if (m_dummyTris.empty()) {
triangles.push_back(t);
return std::uint32_t(triangles.size() - 1);
}
const std::uint32_t nxtDummy = m_dummyTris.back();
m_dummyTris.pop_back();
triangles[nxtDummy] = t;
return nxtDummy;
}
template <typename T, typename TNearPointLocator>
std::uint32_t triangulator_t<T, TNearPointLocator>::add_triangle()
{
if (m_dummyTris.empty()) {
const triangle_t dummy = {
{ null_vertex, null_vertex, null_vertex },
{ null_neighbour, null_neighbour, null_neighbour }
};
triangles.push_back(dummy);
return std::uint32_t(triangles.size() - 1);
}
const std::uint32_t nxtDummy = m_dummyTris.back();
m_dummyTris.pop_back();
return nxtDummy;
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::insert_edges(
const std::vector<edge_t>& edges)
{
insert_edges(edges.begin(), edges.end(), edge_get_v1, edge_get_v2);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::conform_to_edges(
const std::vector<edge_t>& edges)
{
conform_to_edges(edges.begin(), edges.end(), edge_get_v1, edge_get_v2);
}
namespace detail {
template <typename T>
T lerp(const T& a, const T& b, const T t)
{
return (T(1) - t) * a + t * b;
}
// Precondition: ab and cd intersect normally
template <typename T>
vec2_<T> get_intersection_point_coords(
const vec2_<T>& a,
const vec2_<T>& b,
const vec2_<T>& c,
const vec2_<T>& d)
{
// interpolate point on the shorter segment
if (get_square_distance(a, b) < get_square_distance(c, d)) {
// const T a_cd = orient2d(c.x(), c.y(), d.x(), d.y(), a.x(), a.y());
// const T b_cd = orient2d(c.x(), c.y(), d.x(), d.y(), b.x(), b.y());
const T a_cd = orient2d(c, d, a);
const T b_cd = orient2d(c, d, b);
const T t = a_cd / (a_cd - b_cd);
return vec2_<T>::make(lerp(a.x(), b.x(), t), lerp(a.y(), b.y(), t));
} else {
// const T c_ab = orient2d(a.x(), a.y(), b.x(), b.y(), c.x(), c.y());
// const T d_ab = orient2d(a.x(), a.y(), b.x(), b.y(), d.x(), d.y());
const T c_ab = orient2d(a, b, c);
const T d_ab = orient2d(a, b, d);
const T t = c_ab / (c_ab - d_ab);
return vec2_<T>::make(lerp(c.x(), d.x(), t), lerp(c.y(), d.y(), t));
}
}
} // namespace detail
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::insert_edge(
const edge_t edge,
const edge_t originalEdge)
{
const std::uint32_t iA = edge.v1();
std::uint32_t iB = edge.v2();
if (iA == iB) // edge connects a vertex to itself
return;
const std::vector<std::uint32_t>& aTris = vertTris[iA];
const std::vector<std::uint32_t>& bTris = vertTris[iB];
const vec2_<T>& a = vertices[iA];
const vec2_<T>& b = vertices[iB];
if (check_vertices_share_edge(aTris, bTris)) {
fixEdge(edge, originalEdge);
return;
}
const T distanceTolerance = m_minDistToConstraintEdge == T(0)
? T(0)
: m_minDistToConstraintEdge * distance(a, b);
std::uint32_t iT;
std::uint32_t iVleft, iVright;
std::tie(iT, iVleft, iVright) = get_intersected_triangle(iA, aTris, a, b, distanceTolerance);
// if one of the triangle vertices is on the edge, move edge start
if (iT == null_neighbour) {
const edge_t edgePart(iA, iVleft);
fixEdge(edgePart, originalEdge);
return insert_edge(edge_t(iVleft, iB), originalEdge);
}
std::vector<std::uint32_t> intersected(1, iT);
std::vector<std::uint32_t> ptsLeft(1, iVleft);
std::vector<std::uint32_t> ptsRight(1, iVright);
std::uint32_t iV = iA;
triangle_t t = triangles[iT];
while (std::find(t.vertices.begin(), t.vertices.end(), iB) == t.vertices.end()) {
const std::uint32_t iTopo = get_opposite_triangle_index(t, iV);
const triangle_t& tOpo = triangles[iTopo];
const std::uint32_t iVopo = get_opposed_vertex_index(tOpo, iT);
const vec2_<T> vOpo = vertices[iVopo];
// RESOLVE intersection between two constraint edges if needed
if (m_intersectingEdgesStrategy == action_on_intersecting_constraint_edges_t::RESOLVE && fixedEdges.count(edge_t(iVleft, iVright))) {
const std::uint32_t iNewVert = static_cast<std::uint32_t>(vertices.size());
// split constraint edge that already exists in triangulation
const edge_t splitEdge(iVleft, iVright);
const edge_t half1(iVleft, iNewVert);
const edge_t half2(iNewVert, iVright);
const boundary_overlap_count_t overlaps = overlapCount[splitEdge];
// remove the edge that will be split
fixedEdges.erase(splitEdge);
overlapCount.erase(splitEdge);
// add split edge's halves
fixEdge(half1, overlaps);
fixEdge(half2, overlaps);
// maintain piece-to-original mapping
std::vector<edge_t> newOriginals(1, splitEdge);
const std::unordered_map<edge_t, std::vector<edge_t>>::const_iterator originalsIt = pieceToOriginals.find(splitEdge);
if (originalsIt != pieceToOriginals.end()) { // edge being split was split before: pass-through originals
newOriginals = originalsIt->second;
pieceToOriginals.erase(originalsIt);
}
detail::insert_unique(pieceToOriginals[half1], newOriginals);
detail::insert_unique(pieceToOriginals[half2], newOriginals);
// add a new point at the intersection of two constraint edges
const vec2_<T> newV = detail::get_intersection_point_coords(
vertices[iA],
vertices[iB],
vertices[iVleft],
vertices[iVright]);
create_vertex(newV, std::vector<std::uint32_t>());
std::stack<std::uint32_t> triStack = insert_point_on_edge(iNewVert, iT, iTopo);
enforce_delaunay_property_using_edge_flips(newV, iNewVert, triStack);
// TODO: is it's possible to re-use pseudo-polygons
// for inserting [iA, iNewVert] edge half?
insert_edge(edge_t(iA, iNewVert), originalEdge);
insert_edge(edge_t(iNewVert, iB), originalEdge);
return;
}
intersected.push_back(iTopo);
iT = iTopo;
t = triangles[iT];
const point_to_line_location_t::Enum loc = locate_point_wrt_line(vOpo, a, b, distanceTolerance);
if (loc == point_to_line_location_t::LEFT_SIDE) {
ptsLeft.push_back(iVopo);
iV = iVleft;
iVleft = iVopo;
} else if (loc == point_to_line_location_t::RIGHT_SIDE) {
ptsRight.push_back(iVopo);
iV = iVright;
iVright = iVopo;
} else // encountered point on the edge
iB = iVopo;
}
// Remove intersected triangles
typedef std::vector<std::uint32_t>::const_iterator TriIndCit;
for (TriIndCit it = intersected.begin(); it != intersected.end(); ++it)
make_dummies(*it);
// Triangulate pseudo-polygons on both sides
const std::uint32_t iTleft = triangulate_pseudo_polygon(iA, iB, ptsLeft.begin(), ptsLeft.end());
std::reverse(ptsRight.begin(), ptsRight.end());
const std::uint32_t iTright = triangulate_pseudo_polygon(iB, iA, ptsRight.begin(), ptsRight.end());
change_neighbour(iTleft, null_neighbour, iTright);
change_neighbour(iTright, null_neighbour, iTleft);
if (iB != edge.v2()) // encountered point on the edge
{
// fix edge part
const edge_t edgePart(iA, iB);
fixEdge(edgePart, originalEdge);
return insert_edge(edge_t(iB, edge.v2()), originalEdge);
} else {
fixEdge(edge, originalEdge);
}
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::conform_to_edge(
const edge_t edge,
std::vector<edge_t> originalEdges,
const boundary_overlap_count_t overlaps)
{
const std::uint32_t iA = edge.v1();
std::uint32_t iB = edge.v2();
if (iA == iB) // edge connects a vertex to itself
return;
const std::vector<std::uint32_t>& aTris = vertTris[iA];
const std::vector<std::uint32_t>& bTris = vertTris[iB];
const vec2_<T>& a = vertices[iA];
const vec2_<T>& b = vertices[iB];
if (check_vertices_share_edge(aTris, bTris)) {
overlaps > 0 ? fixEdge(edge, overlaps) : fixEdge(edge);
// avoid marking edge as a part of itself
if (!originalEdges.empty() && edge != originalEdges.front()) {
detail::insert_unique(pieceToOriginals[edge], originalEdges);
}
return;
}
const T distanceTolerance = m_minDistToConstraintEdge == T(0)
? T(0)
: m_minDistToConstraintEdge * distance(a, b);
std::uint32_t iT;
std::uint32_t iVleft, iVright;
std::tie(iT, iVleft, iVright) = get_intersected_triangle(iA, aTris, a, b, distanceTolerance);
// if one of the triangle vertices is on the edge, move edge start
if (iT == null_neighbour) {
const edge_t edgePart(iA, iVleft);
overlaps > 0 ? fixEdge(edgePart, overlaps) : fixEdge(edgePart);
detail::insert_unique(pieceToOriginals[edgePart], originalEdges);
return conform_to_edge(edge_t(iVleft, iB), originalEdges, overlaps);
}
std::uint32_t iV = iA;
triangle_t t = triangles[iT];
while (std::find(t.vertices.begin(), t.vertices.end(), iB) == t.vertices.end()) {
const std::uint32_t iTopo = get_opposite_triangle_index(t, iV);
const triangle_t& tOpo = triangles[iTopo];
const std::uint32_t iVopo = get_opposed_vertex_index(tOpo, iT);
const vec2_<T> vOpo = vertices[iVopo];
// RESOLVE intersection between two constraint edges if needed
if (m_intersectingEdgesStrategy == action_on_intersecting_constraint_edges_t::RESOLVE && fixedEdges.count(edge_t(iVleft, iVright))) {
const std::uint32_t iNewVert = static_cast<std::uint32_t>(vertices.size());
// split constraint edge that already exists in triangulation
const edge_t splitEdge(iVleft, iVright);
const edge_t half1(iVleft, iNewVert);
const edge_t half2(iNewVert, iVright);
const boundary_overlap_count_t overlaps = overlapCount[splitEdge];
// remove the edge that will be split
fixedEdges.erase(splitEdge);
overlapCount.erase(splitEdge);
// add split edge's halves
fixEdge(half1, overlaps);
fixEdge(half2, overlaps);
// maintain piece-to-original mapping
std::vector<edge_t> newOriginals(1, splitEdge);
const std::unordered_map<edge_t, std::vector<edge_t>>::const_iterator originalsIt = pieceToOriginals.find(splitEdge);
if (originalsIt != pieceToOriginals.end()) { // edge being split was split before: pass-through originals
newOriginals = originalsIt->second;
pieceToOriginals.erase(originalsIt);
}
detail::insert_unique(pieceToOriginals[half1], newOriginals);
detail::insert_unique(pieceToOriginals[half2], newOriginals);
// add a new point at the intersection of two constraint edges
const vec2_<T> newV = detail::get_intersection_point_coords(
vertices[iA],
vertices[iB],
vertices[iVleft],
vertices[iVright]);
create_vertex(newV, std::vector<std::uint32_t>());
std::stack<std::uint32_t> triStack = insert_point_on_edge(iNewVert, iT, iTopo);
enforce_delaunay_property_using_edge_flips(newV, iNewVert, triStack);
conform_to_edge(edge_t(iA, iNewVert), originalEdges, overlaps);
conform_to_edge(edge_t(iNewVert, iB), originalEdges, overlaps);
return;
}
iT = iTopo;
t = triangles[iT];
const point_to_line_location_t::Enum loc = locate_point_wrt_line(vOpo, a, b, distanceTolerance);
if (loc == point_to_line_location_t::LEFT_SIDE) {
iV = iVleft;
iVleft = iVopo;
} else if (loc == point_to_line_location_t::RIGHT_SIDE) {
iV = iVright;
iVright = iVopo;
} else // encountered point on the edge
iB = iVopo;
}
/**/
// add mid-point to triangulation
const std::uint32_t iMid = static_cast<std::uint32_t>(vertices.size());
const vec2_<T>& start = vertices[iA];
const vec2_<T>& end = vertices[iB];
create_vertex(
vec2_<T>::make((start.x() + end.x()) / T(2), (start.y() + end.y()) / T(2)),
std::vector<std::uint32_t>());
const std::vector<edge_t> flippedFixedEdges = insert_vertex_and_flip_fixed_edges(iMid);
conform_to_edge(edge_t(iA, iMid), originalEdges, overlaps);
conform_to_edge(edge_t(iMid, iB), originalEdges, overlaps);
// re-introduce fixed edges that were flipped
// and make sure overlap count is preserved
for (std::vector<edge_t>::const_iterator it = flippedFixedEdges.begin();
it != flippedFixedEdges.end();
++it) {
fixedEdges.erase(*it);
boundary_overlap_count_t prevOverlaps = 0;
const std::unordered_map<edge_t, boundary_overlap_count_t>::const_iterator
overlapsIt
= overlapCount.find(*it);
if (overlapsIt != overlapCount.end()) {
prevOverlaps = overlapsIt->second;
overlapCount.erase(overlapsIt);
}
// override overlapping boundaries count when re-inserting an edge
std::vector<edge_t> prevOriginals(1, *it);
const std::unordered_map<edge_t, std::vector<edge_t>>::const_iterator originalsIt = pieceToOriginals.find(*it);
if (originalsIt != pieceToOriginals.end()) {
prevOriginals = originalsIt->second;
}
conform_to_edge(*it, prevOriginals, prevOverlaps);
}
if (iB != edge.v2())
conform_to_edge(edge_t(iB, edge.v2()), originalEdges, overlaps);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::add_super_triangle(const box2d_t<T>& box)
{
m_nTargetVerts = 3;
m_superGeomType = super_geometry_type_t::SUPER_TRIANGLE;
const vec2_<T> center = {
(box.min.x() + box.max.x()) / T(2), (box.min.y() + box.max.y()) / T(2)
};
const T w = box.max.x() - box.min.x();
const T h = box.max.y() - box.min.y();
T r = std::sqrt(w * w + h * h) / T(2); // incircle radius
r *= T(1.1);
const T R = T(2) * r; // excircle radius
const T shiftX = R * std::sqrt(T(3)) / T(2); // R * cos(30 deg)
const vec2_<T> posV1 = { center.x() - shiftX, center.y() - r };
const vec2_<T> posV2 = { center.x() + shiftX, center.y() - r };
const vec2_<T> posV3 = { center.x(), center.y() + R };
create_vertex(posV1, std::vector<std::uint32_t>(1, std::uint32_t(0)));
create_vertex(posV2, std::vector<std::uint32_t>(1, std::uint32_t(0)));
create_vertex(posV3, std::vector<std::uint32_t>(1, std::uint32_t(0)));
const triangle_t superTri = {
{ std::uint32_t(0), std::uint32_t(1), std::uint32_t(2) },
{ null_neighbour, null_neighbour, null_neighbour }
};
add_triangle(superTri);
m_nearPtLocator.initialize(vertices);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::create_vertex(
const vec2_<T>& pos,
const std::vector<std::uint32_t>& tris)
{
vertices.push_back(pos);
vertTris.push_back(tris);
}
template <typename T, typename TNearPointLocator>
std::vector<edge_t>
triangulator_t<T, TNearPointLocator>::insert_vertex_and_flip_fixed_edges(
const std::uint32_t iVert)
{
std::vector<edge_t> flippedFixedEdges;
const vec2_<T>& v = vertices[iVert];
std::array<std::uint32_t, 2> trisAt = walking_search_triangle_at(v);
std::stack<std::uint32_t> triStack = trisAt[1] == null_neighbour
? insert_point_in_triangle(iVert, trisAt[0])
: insert_point_on_edge(iVert, trisAt[0], trisAt[1]);
while (!triStack.empty()) {
const std::uint32_t iT = triStack.top();
triStack.pop();
const triangle_t& t = triangles[iT];
const std::uint32_t iTopo = get_opposite_triangle_index(t, iVert);
if (iTopo == null_neighbour)
continue;
/*
* v3 original edge: (v1, v3)
* /|\ flip-candidate edge: (v, v2)
* / | \
* / | \
* / | \
* new vertex--> v | v2
* \ | /
* \ | /
* \ | /
* \|/
* v1
*/
const triangle_t& tOpo = triangles[iTopo];
const std::uint32_t i = get_opposite_vertex_index(tOpo, iT);
const std::uint32_t iV2 = tOpo.vertices[i];
const std::uint32_t iV1 = tOpo.vertices[cw(i)];
const std::uint32_t iV3 = tOpo.vertices[ccw(i)];
if (check_is_edgeflip_needed(v, iVert, iV1, iV2, iV3)) {
// if flipped edge is fixed, remember it
const edge_t flippedEdge(iV1, iV3);
if (fixedEdges.count(flippedEdge))
flippedFixedEdges.push_back(flippedEdge);
do_edgeflip(iT, iTopo);
triStack.push(iT);
triStack.push(iTopo);
}
}
m_nearPtLocator.add_point(iVert, vertices);
return flippedFixedEdges;
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::insert_vertex(const std::uint32_t iVert)
{
const vec2_<T>& v = vertices[iVert];
std::array<std::uint32_t, 2> trisAt = walking_search_triangle_at(v);
std::stack<std::uint32_t> triStack = (trisAt[1] == null_neighbour)
? insert_point_in_triangle(iVert, trisAt[0])
: insert_point_on_edge(iVert, trisAt[0], trisAt[1]);
enforce_delaunay_property_using_edge_flips(v, iVert, triStack);
m_nearPtLocator.add_point(iVert, vertices);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::enforce_delaunay_property_using_edge_flips(
const vec2_<T>& v,
const std::uint32_t iVert,
std::stack<std::uint32_t>& triStack)
{
while (!triStack.empty()) {
const std::uint32_t iT = triStack.top();
triStack.pop();
const triangle_t& t = triangles[iT];
const std::uint32_t iTopo = get_opposite_triangle_index(t, iVert);
if (iTopo == null_neighbour) {
continue;
}
if (check_is_edgeflip_needed(v, iT, iTopo, iVert)) {
do_edgeflip(iT, iTopo);
triStack.push(iT);
triStack.push(iTopo);
}
}
}
/*!
* Handles super-triangle vertices.
* Super-tri points are not infinitely far and influence the input points
* Three cases are possible:
* 1. If one of the opposed vertices is super-tri: no flip needed
* 2. One of the shared vertices is super-tri:
* check if on point is same side of line formed by non-super-tri
* vertices as the non-super-tri shared vertex
* 3. None of the vertices are super-tri: normal circumcircle test
*/
/*
* v3 original edge: (v1, v3)
* /|\ flip-candidate edge: (v, v2)
* / | \
* / | \
* / | \
* new vertex--> v | v2
* \ | /
* \ | /
* \ | /
* \|/
* v1
*/
template <typename T, typename TNearPointLocator>
bool triangulator_t<T, TNearPointLocator>::check_is_edgeflip_needed(
const vec2_<T>& v,
const std::uint32_t iV,
const std::uint32_t iV1,
const std::uint32_t iV2,
const std::uint32_t iV3) const
{
const vec2_<T>& v1 = vertices[iV1];
const vec2_<T>& v2 = vertices[iV2];
const vec2_<T>& v3 = vertices[iV3];
if (m_superGeomType == super_geometry_type_t::SUPER_TRIANGLE) {
// If flip-candidate edge touches super-triangle in-circumference
// test has to be replaced with orient2d test against the line
// formed by two non-artificial vertices (that don't belong to
// super-triangle)
if (iV < 3) // flip-candidate edge touches super-triangle
{
// does original edge also touch super-triangle?
if (iV1 < 3)
return locate_point_wrt_line(v1, v2, v3) == locate_point_wrt_line(v, v2, v3);
if (iV3 < 3)
return locate_point_wrt_line(v3, v1, v2) == locate_point_wrt_line(v, v1, v2);
return false; // original edge does not touch super-triangle
}
if (iV2 < 3) // flip-candidate edge touches super-triangle
{
// does original edge also touch super-triangle?
if (iV1 < 3)
return locate_point_wrt_line(v1, v, v3) == locate_point_wrt_line(v2, v, v3);
if (iV3 < 3)
return locate_point_wrt_line(v3, v1, v) == locate_point_wrt_line(v2, v1, v);
return false; // original edge does not touch super-triangle
}
// flip-candidate edge does not touch super-triangle
if (iV1 < 3)
return locate_point_wrt_line(v1, v2, v3) == locate_point_wrt_line(v, v2, v3);
if (iV3 < 3)
return locate_point_wrt_line(v3, v1, v2) == locate_point_wrt_line(v, v1, v2);
}
return check_is_in_circumcircle(v, v1, v2, v3);
}
template <typename T, typename TNearPointLocator>
bool triangulator_t<T, TNearPointLocator>::check_is_edgeflip_needed(
const vec2_<T>& v,
const std::uint32_t iT,
const std::uint32_t iTopo,
const std::uint32_t iV) const
{
/*
* v3 original edge: (v1, v3)
* /|\ flip-candidate edge: (v, v2)
* / | \
* / | \
* / | \
* new vertex--> v | v2
* \ | /
* \ | /
* \ | /
* \|/
* v1
*/
const triangle_t& tOpo = triangles[iTopo];
const std::uint32_t i = get_opposite_vertex_index(tOpo, iT);
const std::uint32_t iV2 = tOpo.vertices[i];
const std::uint32_t iV1 = tOpo.vertices[cw(i)];
const std::uint32_t iV3 = tOpo.vertices[ccw(i)];
// flip not needed if the original edge is fixed
if (fixedEdges.count(edge_t(iV1, iV3)))
return false;
return check_is_edgeflip_needed(v, iV, iV1, iV2, iV3);
}
template <typename T, typename TNearPointLocator>
std::uint32_t triangulator_t<T, TNearPointLocator>::walk_triangles(
const std::uint32_t startVertex,
const vec2_<T>& pos) const
{
// begin walk in search of triangle at pos
std::uint32_t currTri = vertTris[startVertex][0];
std::unordered_set<std::uint32_t> visited;
bool found = false;
while (!found) {
const triangle_t& t = triangles[currTri];
found = true;
// stochastic offset to randomize which edge we check first
const std::uint32_t offset(detail::randGenerator() % 3);
for (std::uint32_t i_(0); i_ < std::uint32_t(3); ++i_) {
const std::uint32_t i((i_ + offset) % 3);
const vec2_<T>& vStart = vertices[t.vertices[i]];
const vec2_<T>& vEnd = vertices[t.vertices[ccw(i)]];
const point_to_line_location_t::Enum edgeCheck = locate_point_wrt_line(pos, vStart, vEnd);
if (edgeCheck == point_to_line_location_t::RIGHT_SIDE && t.neighbors[i] != null_neighbour && visited.insert(t.neighbors[i]).second) {
found = false;
currTri = t.neighbors[i];
break;
}
}
}
return currTri;
}
/* Flip edge between T and Topo:
*
* v4 | - old edge
* /|\ ~ - new edge
* / | \
* n3 / T' \ n4
* / | \
* / | \
* T -> v1~~~~~~~~~v3 <- Topo
* \ | /
* \ | /
* n1 \Topo'/ n2
* \ | /
* \|/
* v2
*/
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::do_edgeflip(
const std::uint32_t iT,
const std::uint32_t iTopo)
{
triangle_t& t = triangles[iT];
triangle_t& tOpo = triangles[iTopo];
const std::array<std::uint32_t, 3>& triNs = t.neighbors;
const std::array<std::uint32_t, 3>& triOpoNs = tOpo.neighbors;
const std::array<std::uint32_t, 3>& triVs = t.vertices;
const std::array<std::uint32_t, 3>& triOpoVs = tOpo.vertices;
// find vertices and neighbors
std::uint32_t i = get_opposite_vertex_index(t, iTopo);
const std::uint32_t v1 = triVs[i];
const std::uint32_t v2 = triVs[ccw(i)];
const std::uint32_t n1 = triNs[i];
const std::uint32_t n3 = triNs[cw(i)];
i = get_opposite_vertex_index(tOpo, iT);
const std::uint32_t v3 = triOpoVs[i];
const std::uint32_t v4 = triOpoVs[ccw(i)];
const std::uint32_t n4 = triOpoNs[i];
const std::uint32_t n2 = triOpoNs[cw(i)];
// change vertices and neighbors
using detail::arr3;
t = triangle_t::make(arr3(v4, v1, v3), arr3(n3, iTopo, n4));
tOpo = triangle_t::make(arr3(v2, v3, v1), arr3(n2, iT, n1));
// adjust neighboring triangles and vertices
change_neighbour(n1, iT, iTopo);
change_neighbour(n4, iTopo, iT);
// only adjust adjacent triangles if triangulation is not finalized:
// can happen when called from outside on an already finalized triangulation
if (!is_finalized()) {
add_adjacent_triangle(v1, iTopo);
add_adjacent_triangle(v3, iT);
remove_adjacent_triangle(v2, iT);
remove_adjacent_triangle(v4, iTopo);
}
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::change_neighbour(
const std::uint32_t iT,
const std::uint32_t oldNeighbor,
const std::uint32_t newNeighbor)
{
if (iT == null_neighbour) {
return;
}
triangle_t& t = triangles[iT];
t.neighbors[get_neighbour_index(t, oldNeighbor)] = newNeighbor;
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::add_adjacent_triangle(
const std::uint32_t iVertex,
const std::uint32_t iTriangle)
{
vertTris[iVertex].push_back(iTriangle);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::add_adjacent_triangles(
const std::uint32_t iVertex,
const std::uint32_t iT1,
const std::uint32_t iT2,
const std::uint32_t iT3)
{
std::vector<std::uint32_t>& vTris = vertTris[iVertex];
vTris.reserve(vTris.size() + 3);
vTris.push_back(iT1);
vTris.push_back(iT2);
vTris.push_back(iT3);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::add_adjacent_triangles(
const std::uint32_t iVertex,
const std::uint32_t iT1,
const std::uint32_t iT2,
const std::uint32_t iT3,
const std::uint32_t iT4)
{
std::vector<std::uint32_t>& vTris = vertTris[iVertex];
vTris.reserve(vTris.size() + 4);
vTris.push_back(iT1);
vTris.push_back(iT2);
vTris.push_back(iT3);
vTris.push_back(iT4);
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::remove_adjacent_triangle(
const std::uint32_t iVertex,
const std::uint32_t iTriangle)
{
std::vector<std::uint32_t>& tris = vertTris[iVertex];
tris.erase(std::find(tris.begin(), tris.end(), iTriangle));
}
template <typename T, typename TNearPointLocator>
std::uint32_t triangulator_t<T, TNearPointLocator>::triangulate_pseudo_polygon(
const std::uint32_t ia,
const std::uint32_t ib,
const std::vector<std::uint32_t>::const_iterator pointsFirst,
const std::vector<std::uint32_t>::const_iterator pointsLast)
{
if (pointsFirst == pointsLast)
return pseudo_polygon_outer_triangle(ia, ib);
// Find delaunay point
const std::uint32_t ic = find_delaunay_point(ia, ib, pointsFirst, pointsLast);
// Find pseudopolygons split by the delaunay point
std::vector<std::uint32_t>::const_iterator newLast = pointsFirst;
while (*newLast != ic) {
++newLast;
}
const std::vector<std::uint32_t>::const_iterator newFirst = newLast + 1;
// triangulate splitted pseudo-polygons
const std::uint32_t iT2 = triangulate_pseudo_polygon(ic, ib, newFirst, pointsLast);
const std::uint32_t iT1 = triangulate_pseudo_polygon(ia, ic, pointsFirst, newLast);
// add new triangle
const triangle_t t = { { ia, ib, ic }, { null_neighbour, iT2, iT1 } };
const std::uint32_t iT = add_triangle(t);
// adjust neighboring triangles and vertices
if (iT1 != null_neighbour) {
if (pointsFirst == newLast) {
change_neighbour(iT1, ia, ic, iT);
} else {
triangles[iT1].neighbors[0] = iT;
}
}
if (iT2 != null_neighbour) {
if (newFirst == pointsLast) {
change_neighbour(iT2, ic, ib, iT);
} else {
triangles[iT2].neighbors[0] = iT;
}
}
add_adjacent_triangle(ia, iT);
add_adjacent_triangle(ib, iT);
add_adjacent_triangle(ic, iT);
return iT;
}
template <typename T, typename TNearPointLocator>
std::uint32_t triangulator_t<T, TNearPointLocator>::find_delaunay_point(
const std::uint32_t ia,
const std::uint32_t ib,
const std::vector<std::uint32_t>::const_iterator pointsFirst,
const std::vector<std::uint32_t>::const_iterator pointsLast) const
{
MCUT_ASSERT(pointsFirst != pointsLast);
const vec2_<T>& a = vertices[ia];
const vec2_<T>& b = vertices[ib];
std::uint32_t ic = *pointsFirst;
vec2_<T> c = vertices[ic];
for (std::vector<std::uint32_t>::const_iterator it = pointsFirst + 1; it != pointsLast; ++it) {
const vec2_<T> v = vertices[*it];
if (!check_is_in_circumcircle(v, a, b, c))
{
continue;
}
ic = *it;
c = vertices[ic];
}
return ic;
}
template <typename T, typename TNearPointLocator>
std::uint32_t triangulator_t<T, TNearPointLocator>::pseudo_polygon_outer_triangle(
const std::uint32_t ia,
const std::uint32_t ib) const
{
const std::vector<std::uint32_t>& aTris = vertTris[ia];
const std::vector<std::uint32_t>& bTris = vertTris[ib];
for (std::vector<std::uint32_t>::const_iterator it = aTris.begin(); it != aTris.end(); ++it)
{
if (std::find(bTris.begin(), bTris.end(), *it) != bTris.end())
{
return *it;
}
}
return null_neighbour;
}
template <typename T, typename TNearPointLocator>
void triangulator_t<T, TNearPointLocator>::insert_vertices(
const std::vector<vec2_<T>>& newVertices)
{
return insert_vertices(
newVertices.begin(), newVertices.end(), get_x_coord_vec2d<T>, get_y_coord_vec2d<T>);
}
template <typename T, typename TNearPointLocator>
bool triangulator_t<T, TNearPointLocator>::is_finalized() const
{
return vertTris.empty() && !vertices.empty();
}
} // namespace cdt
#endif
#endif // header-guard