Документация

x = rand(10,1);
y = rand(10,1);
dt = delaunayTriangulation(x,y)

triplot(dt);
%
% Display the Vertex and Triangle labels on the plot
hold on
vxlabels = arrayfun(@(n) {sprintf('P%d', n)}, (1:10)');
Hpl = text(x, y, vxlabels, 'FontWeight', 'bold', 'HorizontalAlignment',...
   'center', 'BackgroundColor', 'none');
ic = incenter(dt);
numtri = size(dt,1);
trilabels = arrayfun(@(x) {sprintf('T%d', x)}, (1:numtri)');
Htl = text(ic(:,1), ic(:,2), trilabels, 'FontWeight', 'bold', ...
   'HorizontalAlignment', 'center', 'Color', 'blue');
hold off

X = rand(10,3)

dt = delaunayTriangulation(X)

tetramesh(dt, 'FaceColor', 'cyan');

% To display large tetrahedral meshes use the convexHull method to
% compute the boundary triangulation and plot it using trisurf.
% For example;
% triboundary = convexHull(dt)
% trisurf(triboundary, X(:,1), X(:,2), X(:,3), 'FaceColor', 'cyan')

X = rand(10,2)

dt = delaunayTriangulation(X)

% The triangulation datastructure is;
dt.ConnectivityList

% Indexing is a shorthand way to query the triangulation. The format is
% dt(i, j) where j is the j'th vertex of the i'th triangle, standard
% indexing rules apply.
% The triangulation datastructure is
dt(:,:)

dt(2,:)

dt(2,3)

dt(1:3,:)

% Construct a Delaunay triangulation from
% 10 random points within a unit square
x = rand(10,1);
y = rand(10,1);
dt = delaunayTriangulation(x,y)

% Insert 5 additional random points
dt.Points(end+(1:5),:) = rand(5,2)

dt.Points(5,:) = [0, 0]

dt.Points(4,:) = []

X = [0 0; 16 0; 16 2; 2 2; 2 3; 8 3; 8 5; 0 5];
C = [1 2; 2 3; 3 4; 4 5; 5 6; 6 7; 7 8; 8 1];
dt = delaunayTriangulation(X, C);
subplot(2,1,1);
triplot(dt);
axis([-1 17 -1 6]);
xlabel('Constrained Delaunay triangulation', 'fontweight','b');
% Plot the constrained edges in red
hold on;
plot(X(C'),X(C'+size(X,1)),'-r', 'LineWidth', 2);
hold off;

% Now delete the constraints and plot the unconstrained Delaunay
dt.Constraints = [];
subplot(2,1,2);
triplot(dt);
axis([-1 17 -1 6]);
xlabel('Unconstrained Delaunay triangulation', 'fontweight','b');

clf
load usapolygon
% Define an edge constraint between two successive
% points that make up the polygonal boundary.
nump = numel(uslon);
C = [(1:(nump-1))' (2:nump)'; nump 1];
dt = delaunayTriangulation(uslon, uslat, C);

io = dt.isInterior();
patch('faces',dt(io,:), 'vertices', dt.Points, 'FaceColor','r');
axis equal;
axis([-130 -60 20 55]);
xlabel('Constrained Delaunay Triangulation of usapolygon', 'fontweight','b');

% Create a set of points representing the point cloud
numpts = 192;
t = linspace( -pi, pi, numpts+1 )';
t(end) = [];
r = 0.1 + 5*sqrt( cos( 6*t ).^2 + (0.7).^2 );
x = r.*cos(t);
y = r.*sin(t);
ri = randperm(numpts);
x = x(ri);
y = y(ri);

% Construct a Delaunay Triangulation of the point set.
dt = delaunayTriangulation(x,y);
tri = dt(:,:);

% Insert the location of the Voronoi vertices into the existing
% triangulation
V = dt.voronoiDiagram();
% Remove the infinite vertex
V(1,:) = [];
numv = size(V,1);
dt.Points(end+(1:numv),:) = V;

% The Delaunay edges that connect pairs of sample points represent the
% boundary.
delEdges = dt.edges();
validx = delEdges(:,1) <= numpts;
validy = delEdges(:,2) <= numpts;
boundaryEdges = delEdges((validx & validy), :)';
xb = x(boundaryEdges);
yb = y(boundaryEdges);
clf;
triplot(tri,x,y);
axis equal;
hold on;
plot(x,y,'*r');
plot(xb,yb, '-r');
xlabel('Curve reconstruction from a point cloud', 'fontweight','b');
hold off;

% Construct a constrained Delaunay triangulation of a sample of points
% on the domain boundary.
load trimesh2d
dt = delaunayTriangulation(x,y,Constraints);
inside = dt.isInterior();

% Construct a triangulation to represent the domain triangles.
tr = triangulation(dt(inside, :), dt.Points);

% Construct a set of edges that join the circumcenters of neighboring
% triangles; the additional logic constructs a unique set of such edges.
numt = size(tr,1);
T = (1:numt)';
neigh = tr.neighbors();
cc = tr.circumcenter();
xcc = cc(:,1);
ycc = cc(:,2);
idx1 = T < neigh(:,1);
idx2 = T < neigh(:,2);
idx3 = T < neigh(:,3);
neigh = [T(idx1) neigh(idx1,1); T(idx2) neigh(idx2,2); T(idx3) neigh(idx3,3)]';

% Plot the domain triangles in green, the domain boundary in blue and the
% medial axis in red.
clf;
triplot(tr, 'g');
hold on;
plot(xcc(neigh), ycc(neigh), '-r', 'LineWidth', 1.5);
axis([-10 310 -10 310]);
axis equal;
plot(x(Constraints'),y(Constraints'), '-b', 'LineWidth', 1.5);
xlabel('Medial Axis of a Polygonal Domain', 'fontweight','b');
hold off;

load trimesh2d
clf;
triplot(trife,xfe,yfe);
axis equal;
axis([-10 310 -10 310]);
axis equal;
xlabel('Initial Mesh', 'fontweight','b');

dt = delaunayTriangulation(x,y,Constraints);
clf;
triplot(dt);
axis equal;
axis([-10 310 -10 310]);
axis equal;
xlabel('Background Triangulation', 'fontweight','b');

descriptors.tri = pointLocation(dt,xfe, yfe);
descriptors.baryCoords = cartesianToBarycentric(dt,descriptors.tri, [xfe yfe]);

cc1 = [210 90];
circ1 = (143:180)';
x(circ1) = (x(circ1)-cc1(1))*0.6 + cc1(1);
y(circ1) = (y(circ1)-cc1(2))*0.6 + cc1(2);
tr = triangulation(dt(:,:),x,y);
clf;
triplot(tr);
axis([-10 310 -10 310]);
axis equal;
xlabel('Edited Background Triangulation - Hole Size Reduced', 'fontweight','b');

Xnew = barycentricToCartesian(tr,descriptors.tri, descriptors.baryCoords);
tr = triangulation(trife, Xnew);
clf;
triplot(tr);
axis([-10 310 -10 310]);
axis equal;
xlabel('Morphed Mesh', 'fontweight','b');