How do I discretize a line using delaunay triangulation

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I want to discretize a line segment using the matlab function X = [0.3 0; 0.3 0.4;0 0.2; 0.6 0.2; 0.7 0.7; 0.7 0.3;0.63 0.40;0.8 0.65]; DT = delaunayTriangulation(X); It does create the triangulation, but I keep getting triangles that pass through the line segment. How can I avoid this please?
Thank you,

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Steven Lord
Steven Lord 2015-8-20
Add constraints to the Delaunay triangulation that forces the triangulation to use the line segments as triangle edges, perhaps?

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