Realization of triangulated surface with planar sheets

When it comes to realization of triangulated surfaces with planar sheets such as wood panels one common problem is that when more that three faces are meeting at one vertex there is a chance of intersection between the panels which do not share an edge. That’s one reason to choose hexagonal panels instead of triangular, hence there are only 3 faces at one vertex the assembly holds no intersection. However it is not always possible to choose honeycomb pattern therefore I came up with an algorithm to cut the corners of the panels where the intersection occurs. The algorithm implements a modified Lagrangian constrained optimization with non linear constraints. The objective is to minimize the surface area of triangle or trapezoid region which is result of trimming the solid panels near the vertex. The constraints are the signed distance of the corners in each part from the Trimming plane of the opposite side . As you can see in the video after applying the corner cutting algorithm the panels no longer intersect.