How to get rid off additional triangles on cut sphere with delaunayTriangulation.

Hi,

I have problem with triangulation. I make cut sphere and triangulation for collision check, but i have problem with additional triangles made on "back" of flat surface. It's important for me to get rid of it because I am trying to simulate mirror (including concave mirror) and it's a major obstacle for me.

function obj = ConvexMirror(x, y, z, r, angle, n)
...
% some irrelevant code
...
[obj.x, obj.y, obj.z] = sphere(n);
obj.x = obj.x(ceil(2/3 * n):end,:); % here is cutting sphere       
obj.y = obj.y(ceil(2/3 * n):end,:);       
obj.z = obj.z(ceil(2/3 * n):end,:);
obj.r = r;
obj.s = surf(r.*obj.x + x,r.*obj.y + y,r.*obj.z + z, ...
             'FaceColor', [0.5 0.5 0.5]);
obj = obj.triangulate();
end

function obj = triangulate(obj)
    DT = delaunayTriangulation(obj.s.XData(:), ...
                               obj.s.YData(:), ...
                               obj.s.ZData(:));
    [obj.faces, obj.vertices] = freeBoundary(DT);   % i guess here are made additional triangles
    obj.tris = trisurf(obj.faces, ...
                       obj.vertices(:,1), ...
                       obj.vertices(:,2), ...
                       obj.vertices(:,3), ...
                       'FaceAlpha', 1);
    obj.vert1 = obj.vertices(obj.faces(:,1),:);
    obj.vert2 = obj.vertices(obj.faces(:,2),:);
    obj.vert3 = obj.vertices(obj.faces(:,3),:);
    faceCenter = (obj.vert1+obj.vert2+obj.vert3)/3;
    faceNormal = cross(obj.vert2-obj.vert1, ...
                       obj.vert3-obj.vert1,2);
    obj.q = quiver3(faceCenter(:,1), ...
                     faceCenter(:,2), ...
                     faceCenter(:,3),...
                     faceNormal(:,1), ...
                     faceNormal(:,2), ...
                     faceNormal(:,3), 10, ...
                     'Visible', 'off');
    ...
    % some irrevelant code
    ...
end

I've tried to delete first/last 19 faces, but it's not it.

Collision: TriangleRayIntersection https://www.mathworks.com/matlabcentral/fileexchange/33073-triangle-ray-intersection

Thanks for help!

Answer 1

[Mateusz Szmyd]

Instead of using delaunay easier is to:

[x,y,z] = sphere;
s = surf(x,y,z);
patch(surf2patch(s,'triangles'))