{

if (x == other.x)

return y > other.y;

else

return x > other.x;

{

return XYZ(y*other.z - z*other.y,

z*other.x - x*other.z,

x*other.y - y*other.x);

{

if (empty) {

empty = false;

lower = upper = point;

} else {

if (point.x < lower.x) lower.x = point.x;

else if (point.x > upper.x) upper.x = point.x;

if (point.y < lower.y) lower.y = point.y;

else if (point.y > upper.y) upper.y = point.y;

}

{

if (!empty) {

lower -= delta;

upper += delta;

}

{

if (empty() || point != back())

std::vector<XY>::push_back(point);

{

std::cout << "ContourLine of " << size() << " points:";

for (const auto & it : *this) {

std::cout << ' ' << it;

}

std::cout << std::endl;

{

std::cout << "Contour of " << contour.size() << " lines." << std::endl;

for (const auto & it : contour) {

it.write();

}

const CoordinateArray& y,

const TriangleArray& triangles,

const MaskArray& mask,

const EdgeArray& edges,

const NeighborArray& neighbors,

bool correct_triangle_orientations)

: _x(x),

_y(y),

_triangles(triangles),

_mask(mask),

_edges(edges),

_neighbors(neighbors)

{

if (_x.ndim() != 1 || _y.ndim() != 1 || _x.shape(0) != _y.shape(0))

throw std::invalid_argument("x and y must be 1D arrays of the same length");

if (_triangles.ndim() != 2 || _triangles.shape(1) != 3)

throw std::invalid_argument("triangles must be a 2D array of shape (?,3)");

// Optional mask.

if (_mask.size() > 0 &&

(_mask.ndim() != 1 || _mask.shape(0) != _triangles.shape(0)))

throw std::invalid_argument(

"mask must be a 1D array with the same length as the triangles array");

// Optional edges.

if (_edges.size() > 0 &&

(_edges.ndim() != 2 || _edges.shape(1) != 2))

throw std::invalid_argument("edges must be a 2D array with shape (?,2)");

// Optional neighbors.

if (_neighbors.size() > 0 &&

(_neighbors.ndim() != 2 || _neighbors.shape() != _triangles.shape()))

throw std::invalid_argument(

"neighbors must be a 2D array with the same shape as the triangles array");

if (correct_triangle_orientations)

correct_triangles();

{

get_neighbors(); // Ensure _neighbors has been created.

// Create set of all boundary TriEdges, which are those which do not

// have a neighbor triangle.

typedef std::set<TriEdge> BoundaryEdges;

BoundaryEdges boundary_edges;

for (int tri = 0; tri < get_ntri(); ++tri) {

if (!is_masked(tri)) {

for (int edge = 0; edge < 3; ++edge) {

if (get_neighbor(tri, edge) == -1) {

boundary_edges.insert(TriEdge(tri, edge));

}

}

}

}

// Take any boundary edge and follow the boundary until return to start

// point, removing edges from boundary_edges as they are used. At the same

// time, initialise the _tri_edge_to_boundary_map.

while (!boundary_edges.empty()) {

// Start of new boundary.

auto it = boundary_edges.cbegin();

int tri = it->tri;

int edge = it->edge;

Boundary& boundary = _boundaries.emplace_back();

while (true) {

boundary.emplace_back(tri, edge);

boundary_edges.erase(it);

_tri_edge_to_boundary_map[TriEdge(tri, edge)] =

BoundaryEdge(_boundaries.size()-1, boundary.size()-1);

// Move to next edge of current triangle.

edge = (edge+1) % 3;

// Find start point index of boundary edge.

int point = get_triangle_point(tri, edge);

// Find next TriEdge by traversing neighbors until find one

// without a neighbor.

while (get_neighbor(tri, edge) != -1) {

tri = get_neighbor(tri, edge);

edge = get_edge_in_triangle(tri, point);

}

if (TriEdge(tri,edge) == boundary.front())

break; // Reached beginning of this boundary, so finished it.

else

it = boundary_edges.find(TriEdge(tri, edge));

}

}

{

assert(!has_edges() && "Expected empty edges array");

// Create set of all edges, storing them with start point index less than

// end point index.

typedef std::set<Edge> EdgeSet;

EdgeSet edge_set;

for (int tri = 0; tri < get_ntri(); ++tri) {

if (!is_masked(tri)) {

for (int edge = 0; edge < 3; edge++) {

int start = get_triangle_point(tri, edge);

int end = get_triangle_point(tri, (edge+1)%3);

edge_set.insert(start > end ? Edge(start,end) : Edge(end,start));

}

}

}

// Convert to python _edges array.

py::ssize_t dims[2] = {static_cast<py::ssize_t>(edge_set.size()), 2};

_edges = EdgeArray(dims);

auto edges = _edges.mutable_data();

int i = 0;

for (const auto & it : edge_set) {

edges[i++] = it.start;

edges[i++] = it.end;

}

{

assert(!has_neighbors() && "Expected empty neighbors array");

// Create _neighbors array with shape (ntri,3) and initialise all to -1.

py::ssize_t dims[2] = {get_ntri(), 3};

_neighbors = NeighborArray(dims);

auto* neighbors = _neighbors.mutable_data();

int tri, edge;

std::fill(neighbors, neighbors+3*get_ntri(), -1);

// For each triangle edge (start to end point), find corresponding neighbor

// edge from end to start point. Do this by traversing all edges and

// storing them in a map from edge to TriEdge. If corresponding neighbor

// edge is already in the map, don't need to store new edge as neighbor

// already found.

typedef std::map<Edge, TriEdge> EdgeToTriEdgeMap;

EdgeToTriEdgeMap edge_to_tri_edge_map;

for (tri = 0; tri < get_ntri(); ++tri) {

if (!is_masked(tri)) {

for (edge = 0; edge < 3; ++edge) {

int start = get_triangle_point(tri, edge);

int end = get_triangle_point(tri, (edge+1)%3);

const auto it = edge_to_tri_edge_map.find(Edge(end, start));

if (it == edge_to_tri_edge_map.end()) {

// No neighbor edge exists in the edge_to_tri_edge_map, so

// add this edge to it.

edge_to_tri_edge_map[Edge(start,end)] = TriEdge(tri,edge);

} else {

// Neighbor edge found, set the two elements of _neighbors

// and remove edge from edge_to_tri_edge_map.

neighbors[3*tri + edge] = it->second.tri;

neighbors[3*it->second.tri + it->second.edge] = tri;

edge_to_tri_edge_map.erase(it);

}

}

}

}

// Note that remaining edges in the edge_to_tri_edge_map correspond to

// boundary edges, but the boundaries are calculated separately elsewhere.

const CoordinateArray& z)

{

if (z.ndim() != 1 || z.shape(0) != _x.shape(0))

throw std::invalid_argument(

"z must be a 1D array with the same length as the triangulation x and y arrays");

int dims[2] = {get_ntri(), 3};

Triangulation::TwoCoordinateArray planes_array(dims);

auto planes = planes_array.mutable_unchecked<2>();

auto triangles = _triangles.unchecked<2>();

auto x = _x.unchecked<1>();

auto y = _y.unchecked<1>();

auto z_ptr = z.unchecked<1>();

int point;

for (int tri = 0; tri < get_ntri(); ++tri) {

if (is_masked(tri)) {

planes(tri, 0) = 0.0;

planes(tri, 1) = 0.0;

planes(tri, 2) = 0.0;

}

else {

// Equation of plane for all points r on plane is r.normal = p

// where normal is vector normal to the plane, and p is a

// constant. Rewrite as

// r_x*normal_x + r_y*normal_y + r_z*normal_z = p

// and rearrange to give

// r_z = (-normal_x/normal_z)*r_x + (-normal_y/normal_z)*r_y +

// p/normal_z

point = triangles(tri, 0);

XYZ point0(x(point), y(point), z_ptr(point));

point = triangles(tri, 1);

XYZ side01 = XYZ(x(point), y(point), z_ptr(point)) - point0;

point = triangles(tri, 2);

XYZ side02 = XYZ(x(point), y(point), z_ptr(point)) - point0;

XYZ normal = side01.cross(side02);

if (normal.z == 0.0) {

// Normal is in x-y plane which means triangle consists of

// colinear points. To avoid dividing by zero, we use the

// Moore-Penrose pseudo-inverse.

double sum2 = (side01.x*side01.x + side01.y*side01.y +

side02.x*side02.x + side02.y*side02.y);

double a = (side01.x*side01.z + side02.x*side02.z) / sum2;

double b = (side01.y*side01.z + side02.y*side02.z) / sum2;

planes(tri, 0) = a;

planes(tri, 1) = b;

planes(tri, 2) = point0.z - a*point0.x - b*point0.y;

}

else {

planes(tri, 0) = -normal.x / normal.z; // x

planes(tri, 1) = -normal.y / normal.z; // y

planes(tri, 2) = normal.dot(point0) / normal.z; // constant

}

}

}

return planes_array;

{

auto triangles = _triangles.mutable_data();

auto neighbors = _neighbors.mutable_data();

for (int tri = 0; tri < get_ntri(); ++tri) {

XY point0 = get_point_coords(triangles[3*tri]);

XY point1 = get_point_coords(triangles[3*tri+1]);

XY point2 = get_point_coords(triangles[3*tri+2]);

if ( (point1 - point0).cross_z(point2 - point0) < 0.0) {

// Triangle points are clockwise, so change them to anticlockwise.

std::swap(triangles[3*tri+1], triangles[3*tri+2]);

if (has_neighbors())

std::swap(neighbors[3*tri+1], neighbors[3*tri+2]);

}

}

int& boundary,

int& edge) const

{

get_boundaries(); // Ensure _tri_edge_to_boundary_map has been created.

const auto it = _tri_edge_to_boundary_map.find(triEdge);

assert(it != _tri_edge_to_boundary_map.end() && "TriEdge is not on a boundary");

boundary = it->second.boundary;

edge = it->second.edge;

{

assert(tri >= 0 && tri < get_ntri() && "Triangle index out of bounds");

assert(point >= 0 && point < get_npoints() && "Point index out of bounds.");

auto triangles = _triangles.data();

for (int edge = 0; edge < 3; ++edge) {

if (triangles[3*tri + edge] == point)

return edge;

}

return -1; // point is not in triangle.

{

assert(tri >= 0 && tri < get_ntri() && "Triangle index out of bounds");

assert(edge >= 0 && edge < 3 && "Edge index out of bounds");

if (!has_neighbors())

const_cast<Triangulation&>(*this).calculate_neighbors();

return _neighbors.data()[3*tri + edge];

{

int neighbor_tri = get_neighbor(tri, edge);

if (neighbor_tri == -1)

return TriEdge(-1,-1);

else

return TriEdge(neighbor_tri,

get_edge_in_triangle(neighbor_tri,

get_triangle_point(tri,

(edge+1)%3)));

{

assert(point >= 0 && point < get_npoints() && "Point index out of bounds.");

return XY(_x.data()[point], _y.data()[point]);

{

assert(tri >= 0 && tri < get_ntri() && "Triangle index out of bounds");

assert(edge >= 0 && edge < 3 && "Edge index out of bounds");

return _triangles.data()[3*tri + edge];

{

assert(tri >= 0 && tri < get_ntri() && "Triangle index out of bounds.");

return has_mask() && _mask.data()[tri];

{

if (mask.size() > 0 &&

(mask.ndim() != 1 || mask.shape(0) != _triangles.shape(0)))

throw std::invalid_argument(

"mask must be a 1D array with the same length as the triangles array");

_mask = mask;

// Clear derived fields so they are recalculated when needed.

_edges = EdgeArray();

_neighbors = NeighborArray();

_boundaries.clear();

{

const Boundaries& boundaries = get_boundaries();

std::cout << "Number of boundaries: " << boundaries.size() << std::endl;

for (const auto & boundary : boundaries) {

std::cout << " Boundary of " << boundary.size() << " points: ";

for (const auto & point : boundary) {

std::cout << point << ", ";

}

std::cout << std::endl;

}

const CoordinateArray& z)

: _triangulation(triangulation),

_z(z),

_interior_visited(2*_triangulation.get_ntri()),

_boundaries_visited(0),

_boundaries_used(0)

{

if (_z.ndim() != 1 || _z.shape(0) != _triangulation.get_npoints())

throw std::invalid_argument(

"z must be a 1D array with the same length as the x and y arrays");

{

// Clear _interiorVisited.

std::fill(_interior_visited.begin(), _interior_visited.end(), false);

if (include_boundaries) {

if (_boundaries_visited.empty()) {

const Boundaries& boundaries = get_boundaries();

// Initialise _boundaries_visited.

_boundaries_visited.reserve(boundaries.size());

for (const auto & boundary : boundaries) {

_boundaries_visited.emplace_back(boundary.size());

}

// Initialise _boundaries_used.

_boundaries_used = BoundariesUsed(boundaries.size());

}

// Clear _boundaries_visited.

for (auto & it : _boundaries_visited) {

std::fill(it.begin(), it.end(), false);

}

// Clear _boundaries_used.

std::fill(_boundaries_used.begin(), _boundaries_used.end(), false);

}

{

// Convert all of the lines generated by a call to create_contour() into

// their Python equivalents for return to the calling function.

// A line is either a closed line loop (in which case the last point is

// identical to the first) or an open line strip. Two NumPy arrays are

// created for each line:

// vertices is a double array of shape (npoints, 2) containing the (x, y)

// coordinates of the points in the line

// codes is a uint8 array of shape (npoints,) containing the 'kind codes'

// which are defined in the Path class

// and they are appended to the Python lists vertices_list and codes_list

// respectively for return to the Python calling function.

py::list vertices_list(contour.size());

py::list codes_list(contour.size());

for (Contour::size_type i = 0; i < contour.size(); ++i) {

const ContourLine& contour_line = contour[i];

py::ssize_t npoints = static_cast<py::ssize_t>(contour_line.size());

py::ssize_t segs_dims[2] = {npoints, 2};

CoordinateArray segs(segs_dims);

double* segs_ptr = segs.mutable_data();

py::ssize_t codes_dims[1] = {npoints};

CodeArray codes(codes_dims);

unsigned char* codes_ptr = codes.mutable_data();

for (const auto & point : contour_line) {

*segs_ptr++ = point.x;

*segs_ptr++ = point.y;

*codes_ptr++ = LINETO;

}

if (npoints > 0) {

*codes.mutable_data(0) = MOVETO;

}

// Closed line loop has identical first and last (x, y) points.

if (contour_line.size() > 1 &&

contour_line.front() == contour_line.back())

*(codes_ptr-1) = CLOSEPOLY;

vertices_list[i] = segs;

codes_list[i] = codes;

}

return py::make_tuple(vertices_list, codes_list);

{

// Convert all of the polygons generated by a call to

// create_filled_contour() into their Python equivalents for return to the

// calling function. All of the polygons' points and kinds codes are

// combined into single NumPy arrays for each; this avoids having

// to determine which polygons are holes as this will be determined by the

// renderer. If there are ntotal points in all of the polygons, the two

// NumPy arrays created are:

// vertices is a double array of shape (ntotal, 2) containing the (x, y)

// coordinates of the points in the polygons

// codes is a uint8 array of shape (ntotal,) containing the 'kind codes'

// which are defined in the Path class

// and they are returned in the Python lists vertices_list and codes_list

// respectively.

// Find total number of points in all contour lines.

py::ssize_t n_points = 0;

for (const auto & line : contour) {

n_points += static_cast<py::ssize_t>(line.size());

}

// Create segs array for point coordinates.

py::ssize_t segs_dims[2] = {n_points, 2};

TwoCoordinateArray segs(segs_dims);

double* segs_ptr = segs.mutable_data();

// Create kinds array for code types.

py::ssize_t codes_dims[1] = {n_points};

CodeArray codes(codes_dims);

unsigned char* codes_ptr = codes.mutable_data();

for (const auto & line : contour) {

for (auto point = line.cbegin(); point != line.cend(); point++) {

*segs_ptr++ = point->x;

*segs_ptr++ = point->y;

*codes_ptr++ = (point == line.cbegin() ? MOVETO : LINETO);

}

if (line.size() > 1) {

*(codes_ptr-1) = CLOSEPOLY;

}

}

py::list vertices_list(1);

vertices_list[0] = segs;

py::list codes_list(1);

codes_list[0] = codes;

return py::make_tuple(vertices_list, codes_list);

{

clear_visited_flags(false);

Contour contour;

find_boundary_lines(contour, level);

find_interior_lines(contour, level, false);

return contour_line_to_segs_and_kinds(contour);

const double& upper_level)

{

if (lower_level >= upper_level)

throw std::invalid_argument("filled contour levels must be increasing");

clear_visited_flags(true);

Contour contour;

find_boundary_lines_filled(contour, lower_level, upper_level);

find_interior_lines(contour, lower_level, false);

find_interior_lines(contour, upper_level, true);

return contour_to_segs_and_kinds(contour);

{

return interp(_triangulation.get_triangle_point(tri, edge),

_triangulation.get_triangle_point(tri, (edge+1)%3),

level);

const double& level)

{

// Traverse boundaries to find starting points for all contour lines that

// intersect the boundaries. For each starting point found, follow the

// line to its end before continuing.

const Triangulation& triang = _triangulation;

const Boundaries& boundaries = get_boundaries();

for (const auto & boundary : boundaries) {

bool startAbove, endAbove = false;

for (auto itb = boundary.cbegin(); itb != boundary.cend(); ++itb) {

if (itb == boundary.cbegin())

startAbove = get_z(triang.get_triangle_point(*itb)) >= level;

else

startAbove = endAbove;

endAbove = get_z(triang.get_triangle_point(itb->tri,

(itb->edge+1)%3)) >= level;

if (startAbove && !endAbove) {

// This boundary edge is the start point for a contour line,

// so follow the line.

ContourLine& contour_line = contour.emplace_back();

TriEdge tri_edge = *itb;

follow_interior(contour_line, tri_edge, true, level, false);

}

}

}

const double& lower_level,

const double& upper_level)

{

// Traverse boundaries to find starting points for all contour lines that

// intersect the boundaries. For each starting point found, follow the

// line to its end before continuing.

const Triangulation& triang = _triangulation;

const Boundaries& boundaries = get_boundaries();

for (Boundaries::size_type i = 0; i < boundaries.size(); ++i) {

const Boundary& boundary = boundaries[i];

for (Boundary::size_type j = 0; j < boundary.size(); ++j) {

if (!_boundaries_visited[i][j]) {

// z values of start and end of this boundary edge.

double z_start = get_z(triang.get_triangle_point(boundary[j]));

double z_end = get_z(triang.get_triangle_point(

boundary[j].tri, (boundary[j].edge+1)%3));

// Does this boundary edge's z increase through upper level

// and/or decrease through lower level?

bool incr_upper = (z_start < upper_level && z_end >= upper_level);

bool decr_lower = (z_start >= lower_level && z_end < lower_level);

if (decr_lower || incr_upper) {

// Start point for contour line, so follow it.

ContourLine& contour_line = contour.emplace_back();

TriEdge start_tri_edge = boundary[j];

TriEdge tri_edge = start_tri_edge;

// Traverse interior and boundaries until return to start.

bool on_upper = incr_upper;

do {

follow_interior(contour_line, tri_edge, true,

on_upper ? upper_level : lower_level, on_upper);

on_upper = follow_boundary(contour_line, tri_edge,

lower_level, upper_level, on_upper);

} while (tri_edge != start_tri_edge);

// Close polygon.

contour_line.push_back(contour_line.front());

}

}

}

}

// Add full boundaries that lie between the lower and upper levels. These

// are boundaries that have not been touched by an internal contour line

// which are stored in _boundaries_used.

for (Boundaries::size_type i = 0; i < boundaries.size(); ++i) {

if (!_boundaries_used[i]) {

const Boundary& boundary = boundaries[i];

double z = get_z(triang.get_triangle_point(boundary[0]));

if (z >= lower_level && z < upper_level) {

ContourLine& contour_line = contour.emplace_back();

for (auto edge : boundary) {

contour_line.push_back(triang.get_point_coords(

triang.get_triangle_point(edge)));

}

// Close polygon.

contour_line.push_back(contour_line.front());

}

}

}

const double& level,

bool on_upper)

{

const Triangulation& triang = _triangulation;

int ntri = triang.get_ntri();

for (int tri = 0; tri < ntri; ++tri) {

int visited_index = (on_upper ? tri+ntri : tri);

if (_interior_visited[visited_index] || triang.is_masked(tri))

continue; // Triangle has already been visited or is masked.

_interior_visited[visited_index] = true;

// Determine edge via which to leave this triangle.

int edge = get_exit_edge(tri, level, on_upper);

assert(edge >= -1 && edge < 3 && "Invalid exit edge");

if (edge == -1)

continue; // Contour does not pass through this triangle.

// Found start of new contour line loop.

ContourLine& contour_line = contour.emplace_back();

TriEdge tri_edge = triang.get_neighbor_edge(tri, edge);

follow_interior(contour_line, tri_edge, false, level, on_upper);

// Close line loop

contour_line.push_back(contour_line.front());

}

TriEdge& tri_edge,

const double& lower_level,

const double& upper_level,

bool on_upper)

{

const Triangulation& triang = _triangulation;

const Boundaries& boundaries = get_boundaries();

// Have TriEdge to start at, need equivalent boundary edge.

int boundary, edge;

triang.get_boundary_edge(tri_edge, boundary, edge);

_boundaries_used[boundary] = true;

bool stop = false;

bool first_edge = true;

double z_start, z_end = 0;

while (!stop)

{

assert(!_boundaries_visited[boundary][edge] && "Boundary already visited");

_boundaries_visited[boundary][edge] = true;

// z values of start and end points of boundary edge.

if (first_edge)

z_start = get_z(triang.get_triangle_point(tri_edge));

else

z_start = z_end;

z_end = get_z(triang.get_triangle_point(tri_edge.tri,

(tri_edge.edge+1)%3));

if (z_end > z_start) { // z increasing.

if (!(!on_upper && first_edge) &&

z_end >= lower_level && z_start < lower_level) {

stop = true;

on_upper = false;

} else if (z_end >= upper_level && z_start < upper_level) {

stop = true;

on_upper = true;

}

} else { // z decreasing.

if (!(on_upper && first_edge) &&

z_start >= upper_level && z_end < upper_level) {

stop = true;

on_upper = true;

} else if (z_start >= lower_level && z_end < lower_level) {

stop = true;

on_upper = false;

}

}

first_edge = false;

if (!stop) {

// Move to next boundary edge, adding point to contour line.

edge = (edge+1) % (int)boundaries[boundary].size();

tri_edge = boundaries[boundary][edge];

contour_line.push_back(triang.get_point_coords(

triang.get_triangle_point(tri_edge)));

}

}

return on_upper;

TriEdge& tri_edge,

bool end_on_boundary,

const double& level,

bool on_upper)

{

int& tri = tri_edge.tri;

int& edge = tri_edge.edge;

// Initial point.

contour_line.push_back(edge_interp(tri, edge, level));

while (true) {

int visited_index = tri;

if (on_upper)

visited_index += _triangulation.get_ntri();

// Check for end not on boundary.

if (!end_on_boundary && _interior_visited[visited_index])

break; // Reached start point, so return.

// Determine edge by which to leave this triangle.

edge = get_exit_edge(tri, level, on_upper);

assert(edge >= 0 && edge < 3 && "Invalid exit edge");

_interior_visited[visited_index] = true;

// Append new point to point set.

assert(edge >= 0 && edge < 3 && "Invalid triangle edge");

contour_line.push_back(edge_interp(tri, edge, level));

// Move to next triangle.

TriEdge next_tri_edge = _triangulation.get_neighbor_edge(tri,edge);