Main Content


Query points inside Delaunay triangulation



TF = isInterior(DT) returns a column vector of logical values that indicate whether the triangles in a 2-D constrained Delaunay triangulation are inside a bounded geometric domain. An element of TF is 1 (true) when the corresponding triangle in DT is inside the domain and 0 (false) otherwise.


collapse all

Compute and plot the triangles of a 2-D constrained Delaunay triangulation within a specified boundary.

Create a geometric domain whose shape is a square frame.

outerprofile = [-5 -5; -3 -5; -1 -5;  1 -5; 
                 3 -5;  5 -5;  5 -3;  5 -1; 
                 5  1;  5  3;  5  5;  3  5; 
                 1  5; -1  5; -3  5; -5  5; 
                -5  3; -5  1; -5 -1; -5 -3];
innerprofile = outerprofile.*0.5;
P = [outerprofile; innerprofile];

Define the edge constraints.

outercons = [(1:19)' (2:20)'; 20 1;];
innercons = [(21:39)' (22:40)'; 40 21];
C = [outercons; innercons];

Create the constrained Delaunay triangulation.

DT = delaunayTriangulation(P,C);

Plot the triangulation, highlighting the inner and outer squares in red.

hold on 
plot(DT.Points(innercons',1),DT.Points(innercons',2), ...
plot(DT.Points(outercons',1),DT.Points(outercons',2), ...
axis equal  

Plot only the triangles between the inner and outer squares, highlighting the inner and outer squares in red.

TF = isInterior(DT);
hold on
plot(DT.Points(outercons',1),DT.Points(outercons',2), ...
plot(DT.Points(innercons',1),DT.Points(innercons',2), ...
axis equal

Input Arguments

collapse all

Constrained Delaunay triangulation, specified as a scalar 2-D delaunayTriangulation object with a set of constrained edges that define a bounded geometric domain. A bounded domain is a region enclosed by multiple constrained edges that do not intersect or overlap.

Data Types: delaunayTriangulation


  • isInterior can produce incorrect or inconsistent results when boundary constraints intersect or overlap. To avoid this behavior, use constraints that form one or multiple closed boundaries that do not intersect or overlap. When boundary constraints are nested without intersections or overlaps, the inside or outside status alternates across the boundaries.

Extended Capabilities

Thread-Based Environment
Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

Version History

Introduced in R2013a