This paper presents a new method for polygonization of implicit surfaces. Our method put emphasis on the shape of triangles of the resulting polygonal mesh. The main advantages of the triangulation presented are simplicity and the stable features that can be used for next expanding. The implementation is not complicated and only the standard data structures are used. This algorithm is based on ...

We introduce a geometrical diagram to study the improvement in shape of triangles generated by iterative application of triangle subdivision. The four Triangles Longest Edge (4TLE) subdivision pattern and a new hybrid 4T Longest-Edge/Self-Similar (hybrid 4TLE-SS) scheme are investigated in this way. The map diagram provides a convenient way to visualize the evolution and migration of element sh...

A contact representation by triangles of a graph is a set of triangles in the plane such that two triangles intersect on at most one point, each triangle represents a vertex of the graph and two triangles intersects if and only if their corresponding vertices are adjacent. De Fraysseix, Ossona de Mendez and Rosenstiehl proved that every planar graph admits a contact representation by triangles....