/*
* Unstructured triangular grid functions, particularly contouring.
*
* There are two main classes: Triangulation and TriContourGenerator.
*
* Triangulation
* -------------
* Triangulation is an unstructured triangular grid with npoints and ntri
* triangles. It consists of point x and y coordinates, and information about
* the triangulation stored in an integer array of shape (ntri,3) called
* triangles. Each triangle is represented by three point indices (in the
* range 0 to npoints-1) that comprise the triangle, ordered anticlockwise.
* There is an optional mask of length ntri which can be used to mask out
* triangles and has the same result as removing those triangles from the
* 'triangles' array.
*
* A particular edge of a triangulation is termed a TriEdge, which is a
* triangle index and an edge index in the range 0 to 2. TriEdge(tri,edge)
* refers to the edge that starts at point index triangles(tri,edge) and ends
* at point index triangles(tri,(edge+1)%3).
*
* Various derived fields are calculated when they are first needed. The
* triangle connectivity is stored in a neighbors array of shape (ntri,3) such
* that neighbors(tri,edge) is the index of the triangle that adjoins the
* TriEdge(tri,edge), or -1 if there is no such neighbor.
*
* A triangulation has one or more boundaries, each of which is a 1D array of
* the TriEdges that comprise the boundary, in order following the boundary
* with non-masked triangles on the left.
*
* TriContourGenerator
* -------------------
* A TriContourGenerator generates contours for a particular Triangulation.
* The process followed is different for non-filled and filled contours, with
* one and two contour levels respectively. In both cases boundary contour
* lines are found first, then interior lines.
*
* Boundary lines start and end on a boundary. They are found by traversing
* the triangulation boundary edges until a suitable start point is found, and
* then the contour line is followed across the interior of the triangulation
* until it ends on another boundary edge. For a non-filled contour this
* completes a line, whereas a filled contour continues by following the
* boundary around until either another boundary start point is found or the
* start of the contour line is reached. Filled contour generation stores
* boolean flags to indicate which boundary edges have already been traversed
* so that they are not dealt with twice. Similar flags are used to indicate
* which triangles have been used when following interior lines.
*
* Interior lines do not intersect any boundaries. They are found by
* traversing all triangles that have not yet been visited until a suitable
* starting point is found, and then the contour line is followed across the
* interior of the triangulation until it returns to the start point. For
* filled contours this process is repeated for both lower and upper contour
* levels, and the direction of traversal is reversed for upper contours.
*
* Working out in which direction a contour line leaves a triangle uses the
* a lookup table. A triangle has three points, each of which has a z-value
* which is either less than the contour level or not. Hence there are 8
* configurations to deal with, 2 of which do not have a contour line (all
* points below or above (including the same as) the contour level) and 6 that
* do. See the function get_exit_edge for details.
*/
#ifndef MPL_TRI_H
#define MPL_TRI_H
#include <pybind11/pybind11.h>
#include <pybind11/numpy.h>
#include <iostream>
#include <list>
#include <map>
#include <set>
#include <vector>
namespace py = pybind11;
/* An edge of a triangle consisting of an triangle index in the range 0 to
* ntri-1 and an edge index in the range 0 to 2. Edge i goes from the
* triangle's point i to point (i+1)%3. */
struct TriEdge
{
TriEdge();
TriEdge(int tri_, int edge_);
bool operator<(const TriEdge& other) const;
bool operator==(const TriEdge& other) const;
bool operator!=(const TriEdge& other) const;
friend std::ostream& operator<<(std::ostream& os, const TriEdge& tri_edge);
int tri, edge;
};
// 2D point with x,y coordinates.
struct XY
{
XY();
XY(const double& x_, const double& y_);
double angle() const; // Angle in radians with respect to x-axis.
double cross_z(const XY& other) const; // z-component of cross product.
bool is_right_of(const XY& other) const; // Compares x then y.
bool operator==(const XY& other) const;
bool operator!=(const XY& other) const;
XY operator*(const double& multiplier) const;
const XY& operator+=(const XY& other);
const XY& operator-=(const XY& other);
XY operator+(const XY& other) const;
XY operator-(const XY& other) const;
friend std::ostream& operator<<(std::ostream& os, const XY& xy);
double x, y;
};
// 3D point with x,y,z coordinates.
struct XYZ
{
XYZ(const double& x_, const double& y_, const double& z_);
XYZ cross(const XYZ& other) const;
double dot(const XYZ& other) const;
XYZ operator-(const XYZ& other) const;
friend std::ostream& operator<<(std::ostream& os, const XYZ& xyz);
double x, y, z;
};
// 2D bounding box, which may be empty.
class BoundingBox
{
public:
BoundingBox();
void add(const XY& point);
void expand(const XY& delta);
// Consider these member variables read-only.
bool empty;
XY lower, upper;
};
/* A single line of a contour, which may be a closed line loop or an open line
* strip. Identical adjacent points are avoided using push_back(), and a closed
* line loop should also not have identical first and last points. */
class ContourLine : public std::vector<XY>
{
public:
ContourLine();
void push_back(const XY& point);
void write() const;
};
// A Contour is a collection of zero or more ContourLines.
typedef std::vector<ContourLine> Contour;
// Debug contour writing function.
void write_contour(const Contour& contour);
/* Triangulation with npoints points and ntri triangles. Derived fields are
* calculated when they are first needed. */
class Triangulation
{
public:
typedef py::array_t<double, py::array::c_style | py::array::forcecast> CoordinateArray;
typedef py::array_t<double, py::array::c_style | py::array::forcecast> TwoCoordinateArray;
typedef py::array_t<int, py::array::c_style | py::array::forcecast> TriangleArray;
typedef py::array_t<bool, py::array::c_style | py::array::forcecast> MaskArray;
typedef py::array_t<int, py::array::c_style | py::array::forcecast> EdgeArray;
typedef py::array_t<int, py::array::c_style | py::array::forcecast> NeighborArray;
/* A single boundary is a vector of the TriEdges that make up that boundary
* following it around with unmasked triangles on the left. */
typedef std::vector<TriEdge> Boundary;
typedef std::vector<Boundary> Boundaries;
/* Constructor with optional mask, edges and neighbors. The latter two
* are calculated when first needed.
* x: double array of shape (npoints) of points' x-coordinates.
* y: double array of shape (npoints) of points' y-coordinates.
* triangles: int array of shape (ntri,3) of triangle point indices.
* Those ordered clockwise are changed to be anticlockwise.
* mask: Optional bool array of shape (ntri) indicating which triangles
* are masked.
* edges: Optional int array of shape (?,2) of start and end point
* indices, each edge (start,end and end,start) appearing only
* once.
* neighbors: Optional int array of shape (ntri,3) indicating which
* triangles are the neighbors of which TriEdges, or -1 if
* there is no such neighbor.
* correct_triangle_orientations: Whether or not should correct triangle
* orientations so that vertices are
* ordered anticlockwise. */
Triangulation(const CoordinateArray& x,
const CoordinateArray& y,
const TriangleArray& triangles,
const MaskArray& mask,
const EdgeArray& edges,
const NeighborArray& neighbors,
bool correct_triangle_orientations);
/* Calculate plane equation coefficients for all unmasked triangles from
* the point (x,y) coordinates and point z-array of shape (npoints) passed
* in via the args. Returned array has shape (npoints,3) and allows
* z-value at (x,y) coordinates in triangle tri to be calculated using
* z = array[tri,0]*x + array[tri,1]*y + array[tri,2]. */
TwoCoordinateArray calculate_plane_coefficients(const CoordinateArray& z);
// Return the boundaries collection, creating it if necessary.
const Boundaries& get_boundaries() const;
// Return which boundary and boundary edge the specified TriEdge is.
void get_boundary_edge(const TriEdge& triEdge,
int& boundary,
int& edge) const;
/* Return the edges array, creating it if necessary. */
EdgeArray& get_edges();
/* Return the triangle index of the neighbor of the specified triangle
* edge. */
int get_neighbor(int tri, int edge) const;
/* Return the TriEdge that is the neighbor of the specified triangle edge,
* or TriEdge(-1,-1) if there is no such neighbor. */
TriEdge get_neighbor_edge(int tri, int edge) const;
/* Return the neighbors array, creating it if necessary. */
NeighborArray& get_neighbors();
// Return the number of points in this triangulation.
int get_npoints() const;
// Return the number of triangles in this triangulation.
int get_ntri() const;
/* Return the index of the point that is at the start of the specified
* triangle edge. */
int get_triangle_point(int tri, int edge) const;
int get_triangle_point(const TriEdge& tri_edge) const;
// Return the coordinates of the specified point index.
XY get_point_coords(int point) const;
// Indicates if the specified triangle is masked or not.
bool is_masked(int tri) const;
/* Set or clear the mask array. Clears various derived fields so they are
* recalculated when next needed.
* mask: bool array of shape (ntri) indicating which triangles are
* masked, or an empty array to clear mask. */
void set_mask(const MaskArray& mask);
// Debug function to write boundaries.
void write_boundaries() const;
private:
// An edge of a triangulation, composed of start and end point indices.
struct Edge
{
Edge() : start(-1), end(-1) {}
Edge(int start_, int end_) : start(start_), end(end_) {}
bool operator<(const Edge& other) const {
return start != other.start ? start < other.start : end < other.end;
}
int start, end;
};
/* An edge of a boundary of a triangulation, composed of a boundary index
* and an edge index within that boundary. Used to index into the
* boundaries collection to obtain the corresponding TriEdge. */
struct BoundaryEdge
{
BoundaryEdge() : boundary(-1), edge(-1) {}
BoundaryEdge(int boundary_, int edge_)
: boundary(boundary_), edge(edge_) {}
int boundary, edge;
};
/* Calculate the boundaries collection. Should normally be accessed via
* get_boundaries(), which will call this function if necessary. */
void calculate_boundaries();
/* Calculate the edges array. Should normally be accessed via
* get_edges(), which will call this function if necessary. */
void calculate_edges();
/* Calculate the neighbors array. Should normally be accessed via
* get_neighbors(), which will call this function if necessary. */
void calculate_neighbors();
/* Correct each triangle so that the vertices are ordered in an
* anticlockwise manner. */
void correct_triangles();
/* Determine which edge index (0,1 or 2) the specified point index is in
* the specified triangle, or -1 if the point is not in the triangle. */
int get_edge_in_triangle(int tri, int point) const;
bool has_edges() const;
bool has_mask() const;
bool has_neighbors() const;
// Variables shared with python, always set.
CoordinateArray _x, _y; // double array (npoints).
TriangleArray _triangles; // int array (ntri,3) of triangle point indices,
// ordered anticlockwise.
// Variables shared with python, may be unset (size == 0).
MaskArray _mask; // bool array (ntri).
// Derived variables shared with python, may be unset (size == 0).
// If unset, are recalculated when needed.
EdgeArray _edges; // int array (?,2) of start & end point indices.
NeighborArray _neighbors; // int array (ntri,3), neighbor triangle indices
// or -1 if no neighbor.
// Variables internal to C++ only.
Boundaries _boundaries;
// Map used to look up BoundaryEdges from TriEdges. Normally accessed via
// get_boundary_edge().
typedef std::map<TriEdge, BoundaryEdge> TriEdgeToBoundaryMap;
TriEdgeToBoundaryMap _tri_edge_to_boundary_map;
};
// Contour generator for a triangulation.
class TriContourGenerator
{
public:
typedef Triangulation::CoordinateArray CoordinateArray;
typedef Triangulation::TwoCoordinateArray TwoCoordinateArray;
typedef py::array_t<unsigned char> CodeArray;
/* Constructor.
* triangulation: Triangulation to generate contours for.
* z: Double array of shape (npoints) of z-values at triangulation
* points. */
TriContourGenerator(Triangulation& triangulation,
const CoordinateArray& z);
/* Create and return a non-filled contour.
* level: Contour level.
* Returns new python list [segs0, segs1, ...] where
* segs0: double array of shape (?,2) of point coordinates of first
* contour line, etc. */
py::tuple create_contour(const double& level);
/* Create and return a filled contour.
* lower_level: Lower contour level.
* upper_level: Upper contour level.
* Returns new python tuple (segs, kinds) where
* segs: double array of shape (n_points,2) of all point coordinates,
* kinds: ubyte array of shape (n_points) of all point code types. */
py::tuple create_filled_contour(const double& lower_level,
const double& upper_level);
private:
typedef Triangulation::Boundary Boundary;
typedef Triangulation::Boundaries Boundaries;
/* Clear visited flags.
* include_boundaries: Whether to clear boundary flags or not, which are
* only used for filled contours. */
void clear_visited_flags(bool include_boundaries);
/* Convert a non-filled Contour from C++ to Python.
* Returns new python tuple ([segs0, segs1, ...], [kinds0, kinds1...])
* where
* segs0: double array of shape (n_points,2) of point coordinates of first
* contour line, etc.
* kinds0: ubyte array of shape (n_points) of kinds codes of first contour
* line, etc. */
py::tuple contour_line_to_segs_and_kinds(const Contour& contour);
/* Convert a filled Contour from C++ to Python.
* Returns new python tuple ([segs], [kinds]) where
* segs: double array of shape (n_points,2) of all point coordinates,
* kinds: ubyte array of shape (n_points) of all point code types. */
py::tuple contour_to_segs_and_kinds(const Contour& contour);
/* Return the point on the specified TriEdge that intersects the specified
* level. */
XY edge_interp(int tri, int edge, const double& level);
/* Find and follow non-filled contour lines that start and end on a
* boundary of the Triangulation.
* contour: Contour to add new lines to.
* level: Contour level. */
void find_boundary_lines(Contour& contour,
const double& level);
/* Find and follow filled contour lines at either of the specified contour
* levels that start and end of a boundary of the Triangulation.
* contour: Contour to add new lines to.
* lower_level: Lower contour level.
* upper_level: Upper contour level. */
void find_boundary_lines_filled(Contour& contour,
const double& lower_level,
const double& upper_level);
/* Find and follow lines at the specified contour level that are
* completely in the interior of the Triangulation and hence do not
* intersect any boundary.
* contour: Contour to add new lines to.
* level: Contour level.
* on_upper: Whether on upper or lower contour level.
* filled: Whether contours are filled or not. */
void find_interior_lines(Contour& contour,
const double& level,
bool on_upper,
bool filled);
/* Follow contour line around boundary of the Triangulation from the
* specified TriEdge to its end which can be on either the lower or upper
* levels. Only used for filled contours.
* contour_line: Contour line to append new points to.
* tri_edge: On entry, TriEdge to start from. On exit, TriEdge that is
* finished on.
* lower_level: Lower contour level.
* upper_level: Upper contour level.
* on_upper: Whether starts on upper level or not.
* Return true if finishes on upper level, false if lower. */
bool follow_boundary(ContourLine& contour_line,
TriEdge& tri_edge,
const double& lower_level,
const double& upper_level,
bool on_upper);
/* Follow contour line across interior of Triangulation.
* contour_line: Contour line to append new points to.
* tri_edge: On entry, TriEdge to start from. On exit, TriEdge that is
* finished on.
* end_on_boundary: Whether this line ends on a boundary, or loops back
* upon itself.
* level: Contour level to follow.
* on_upper: Whether following upper or lower contour level. */
void follow_interior(ContourLine& contour_line,
TriEdge& tri_edge,
bool end_on_boundary,
const double& level,
bool on_upper);
// Return the Triangulation boundaries.
const Boundaries& get_boundaries() const;
/* Return the edge by which the a level leaves a particular triangle,
* which is 0, 1 or 2 if the contour passes through the triangle or -1
* otherwise.
* tri: Triangle index.
* level: Contour level to follow.
* on_upper: Whether following upper or lower contour level. */
int get_exit_edge(int tri, const double& level, bool on_upper) const;
// Return the z-value at the specified point index.
const double& get_z(int point) const;
/* Return the point at which the a level intersects the line connecting the
* two specified point indices. */
XY interp(int point1, int point2, const double& level) const;
// Variables shared with python, always set.
Triangulation _triangulation;
CoordinateArray _z; // double array (npoints).
// Variables internal to C++ only.
typedef std::vector<bool> InteriorVisited; // Size 2*ntri
typedef std::vector<bool> BoundaryVisited;
typedef std::vector<BoundaryVisited> BoundariesVisited;
typedef std::vector<bool> BoundariesUsed;
InteriorVisited _interior_visited;
BoundariesVisited _boundaries_visited; // Only used for filled contours.
BoundariesUsed _boundaries_used; // Only used for filled contours.
};
/* TriFinder class implemented using the trapezoid map algorithm from the book
* "Computational Geometry, Algorithms and Applications", second edition, by
* M. de Berg, M. van Kreveld, M. Overmars and O. Schwarzkopf.
*
* The domain of interest is composed of vertical-sided trapezoids that are
* bounded to the left and right by points of the triangulation, and below and
* above by edges of the triangulation. Each triangle is represented by 1 or
* more of these trapezoids. Edges are inserted one a time in a random order.
*
* As the trapezoid map is created, a search tree is also created which allows
* fast lookup O(log N) of the trapezoid containing the point of interest.
* There are 3 types of node in the search tree: all leaf nodes represent
* trapezoids and all branch nodes have 2 child nodes and are either x-nodes or
* y-nodes. X-nodes represent points in the triangulation, and their 2 children
* refer to those parts of the search tree to the left and right of the point.
* Y-nodes represent edges in the triangulation, and their 2 children refer to
* those parts of the search tree below and above the edge.
*
* Nodes can be repeated throughout the search tree, and each is reference
* counted through the multiple parent nodes it is a child of.
*
* The algorithm is only intended to work with valid triangulations, i.e. it
* must not contain duplicate points, triangles formed from colinear points, or
* overlapping triangles. It does have some tolerance to triangles formed from
* colinear points but only in the simplest of cases. No explicit testing of
* the validity of the triangulation is performed as this is a computationally
* more complex task than the trifinding itself. */
class TrapezoidMapTriFinder
{
public:
typedef Triangulation::CoordinateArray CoordinateArray;
typedef py::array_t<int, py::array::c_style | py::array::forcecast> TriIndexArray;
/* Constructor. A separate call to initialize() is required to initialize
* the object before use.
* triangulation: Triangulation to find triangles in. */
TrapezoidMapTriFinder(Triangulation& triangulation);
~TrapezoidMapTriFinder();
/* Return an array of triangle indices. Takes 1D arrays x and y of
* point coordinates, and returns an array of the same size containing the
* indices of the triangles at those points. */
TriIndexArray find_many(const CoordinateArray& x, const CoordinateArray& y);
/* Return a reference to a new python list containing the following
* statistics about the tree:
* 0: number of nodes (tree size)
* 1: number of unique nodes (number of unique Node objects in tree)
* 2: number of trapezoids (tree leaf nodes)
* 3: number of unique trapezoids
* 4: maximum parent count (max number of times a node is repeated in
* tree)
* 5: maximum depth of tree (one more than the maximum number of
* comparisons needed to search through the tree)
* 6: mean of all trapezoid depths (one more than the average number of
* comparisons needed to search through the tree) */
py::list get_tree_stats();
/* Initialize this object before use. May be called multiple times, if,
* for example, the triangulation is changed by setting the mask. */
void initialize();
// Print the search tree as text to stdout; useful for debug purposes.
void print_tree();
private:
/* A Point consists of x,y coordinates as well as the index of a triangle
* associated with the point, so that a search at this point's coordinates
* can return a valid triangle index. */
struct Point : XY
{
Point() : XY(), tri(-1) {}
Point(const double& x, const double& y) : XY(x,y), tri(-1) {}
explicit Point(const XY& xy) : XY(xy), tri(-1) {}
int tri;
};
/* An Edge connects two Points, left and right. It is always true that
* right->is_right_of(*left). Stores indices of triangles below and above
* the Edge which are used to map from trapezoid to triangle index. Also
* stores pointers to the 3rd points of the below and above triangles,
* which are only used to disambiguate triangles with colinear points. */
struct Edge
{
Edge(const Point* left_,
const Point* right_,
int triangle_below_,
int triangle_above_,
const Point* point_below_,
const Point* point_above_);
// Return -1 if point to left of edge, 0 if on edge, +1 if to right.
int get_point_orientation(const XY& xy) const;
// Return slope of edge, even if vertical (divide by zero is OK here).
double get_slope() const;
/* Return y-coordinate of point on edge with specified x-coordinate.
* x must be within the x-limits of this edge. */
double get_y_at_x(const double& x) const;
// Return true if the specified point is either of the edge end points.
bool has_point(const Point* point) const;
bool operator==(const Edge& other) const;
friend std::ostream& operator<<(std::ostream& os, const Edge& edge)
{
return os << *edge.left << "->" << *edge.right;
}
void print_debug() const;
const Point* left; // Not owned.
const Point* right; // Not owned.
int triangle_below; // Index of triangle below (to right of) Edge.
int triangle_above; // Index of triangle above (to left of) Edge.
const Point* point_below; // Used only for resolving ambiguous cases;
const Point* point_above; // is 0 if corresponding triangle is -1
};
class Node; // Forward declaration.
// Helper structure used by TrapezoidMapTriFinder::get_tree_stats.
struct NodeStats
{
NodeStats()
: node_count(0), trapezoid_count(0), max_parent_count(0),
max_depth(0), sum_trapezoid_depth(0.0)
{}
long node_count, trapezoid_count, max_parent_count, max_depth;
double sum_trapezoid_depth;
std::set<const Node*> unique_nodes, unique_trapezoid_nodes;
};
struct Trapezoid; // Forward declaration.
/* Node of the trapezoid map search tree. There are 3 possible types:
* Type_XNode, Type_YNode and Type_TrapezoidNode. Data members are
* represented using a union: an XNode has a Point and 2 child nodes
* (left and right of the point), a YNode has an Edge and 2 child nodes
* (below and above the edge), and a TrapezoidNode has a Trapezoid.
* Each Node has multiple parents so it can appear in the search tree
* multiple times without having to create duplicate identical Nodes.
* The parent collection acts as a reference count to the number of times
* a Node occurs in the search tree. When the parent count is reduced to
* zero a Node can be safely deleted. */
class Node
{
public:
Node(const Point* point, Node* left, Node* right);// Type_XNode.
Node(const Edge* edge, Node* below, Node* above); // Type_YNode.
Node(Trapezoid* trapezoid); // Type_TrapezoidNode.
~Node();
void add_parent(Node* parent);
/* Recurse through the search tree and assert that everything is valid.
* Reduces to a no-op if NDEBUG is defined. */
void assert_valid(bool tree_complete) const;
// Recurse through the tree to return statistics about it.
void get_stats(int depth, NodeStats& stats) const;
// Return the index of the triangle corresponding to this node.
int get_tri() const;
bool has_child(const Node* child) const;
bool has_no_parents() const;
bool has_parent(const Node* parent) const;
/* Recurse through the tree and print a textual representation to
* stdout. Argument depth used to indent for readability. */
void print(int depth = 0) const;
/* Remove a parent from this Node. Return true if no parents remain
* so that this Node can be deleted. */
bool remove_parent(Node* parent);
void replace_child(Node* old_child, Node* new_child);
// Replace this node with the specified new_node in all parents.
void replace_with(Node* new_node);
/* Recursive search through the tree to find the Node containing the
* specified XY point. */
const Node* search(const XY& xy);
/* Recursive search through the tree to find the Trapezoid containing
* the left endpoint of the specified Edge. Return 0 if fails, which
* can only happen if the triangulation is invalid. */
Trapezoid* search(const Edge& edge);
/* Copy constructor and assignment operator defined but not implemented
* to prevent objects being copied. */
Node(const Node& other);
Node& operator=(const Node& other);
private:
typedef enum {
Type_XNode,
Type_YNode,
Type_TrapezoidNode
} Type;
Type _type;
union {
struct {
const Point* point; // Not owned.
Node* left; // Owned.
Node* right; // Owned.
} xnode;
struct {
const Edge* edge; // Not owned.
Node* below; // Owned.
Node* above; // Owned.
} ynode;
Trapezoid* trapezoid; // Owned.
} _union;
typedef std::list<Node*> Parents;
Parents _parents; // Not owned.
};
/* A Trapezoid is bounded by Points to left and right, and Edges below and
* above. Has up to 4 neighboring Trapezoids to lower/upper left/right.
* Lower left neighbor is Trapezoid to left that shares the below Edge, or
* is 0 if there is no such Trapezoid (and similar for other neighbors).
* To obtain the index of the triangle corresponding to a particular
* Trapezoid, use the Edge member variables below.triangle_above or
* above.triangle_below. */
struct Trapezoid
{
Trapezoid(const Point* left_,
const Point* right_,
const Edge& below_,
const Edge& above_);
/* Assert that this Trapezoid is valid. Reduces to a no-op if NDEBUG
* is defined. */
void assert_valid(bool tree_complete) const;
/* Return one of the 4 corner points of this Trapezoid. Only used for
* debugging purposes. */
XY get_lower_left_point() const;
XY get_lower_right_point() const;
XY get_upper_left_point() const;
XY get_upper_right_point() const;
void print_debug() const;
/* Set one of the 4 neighbor trapezoids and the corresponding reverse
* Trapezoid of the new neighbor (if it is not 0), so that they are
* consistent. */
void set_lower_left(Trapezoid* lower_left_);
void set_lower_right(Trapezoid* lower_right_);
void set_upper_left(Trapezoid* upper_left_);
void set_upper_right(Trapezoid* upper_right_);
/* Copy constructor and assignment operator defined but not implemented
* to prevent objects being copied. */
Trapezoid(const Trapezoid& other);
Trapezoid& operator=(const Trapezoid& other);
const Point* left; // Not owned.
const Point* right; // Not owned.
const Edge& below;
const Edge& above;
// 4 neighboring trapezoids, can be 0, not owned.
Trapezoid* lower_left; // Trapezoid to left that shares below
Trapezoid* lower_right; // Trapezoid to right that shares below
Trapezoid* upper_left; // Trapezoid to left that shares above
Trapezoid* upper_right; // Trapezoid to right that shares above
Node* trapezoid_node; // Node that owns this Trapezoid.
};
// Add the specified Edge to the search tree, returning true if successful.
bool add_edge_to_tree(const Edge& edge);
// Clear all memory allocated by this object.
void clear();
// Return the triangle index at the specified point, or -1 if no triangle.
int find_one(const XY& xy);
/* Determine the trapezoids that the specified Edge intersects, returning
* true if successful. */
bool find_trapezoids_intersecting_edge(const Edge& edge,
std::vector<Trapezoid*>& trapezoids);
// Variables shared with python, always set.
Triangulation& _triangulation;
// Variables internal to C++ only.
Point* _points; // Array of all points in triangulation plus corners of
// enclosing rectangle. Owned.
typedef std::vector<Edge> Edges;
Edges _edges; // All Edges in triangulation plus bottom and top Edges of
// enclosing rectangle.
Node* _tree; // Root node of the trapezoid map search tree. Owned.
};
#endif