# Triangulated Mesh Simplification Using Equidistant Cuts

**Triangulated Mesh Simplification Using Equidistant Cuts**

In our work we are concerned with an application aimed to reduce the
amount of polygons of a triangulated mesh, and thereby simplify 3D
objects with the attempt to minimize the difference between the original
and the new mesh.

Our algorithm consists of four parts:

1. Pre-processing – in this step we insert the triangular mesh into a
data structure, which is quite similar to winged-edge data structure.
This structure will help us optimize the further parts of the algorithm

2. Creation of the polygons – in this part we create a set of axis
aligned equidistant planes. These planes intersect the triangulated
mesh, and their intersection creates a polygon, or in the case of
non-convex meshes, a set of polygons

3. Polygon simplification – the polygons from the previous part are
being simplified. That is, while the number of vertices is decreasing,
we try to preserve the shape and the area of the polygons

4. Creating of a new object – in this part, the simplified polygons are
connected into a triangulated mesh

To verify the functionality of our method we implemented an application
in C++ and some external libraries. Our results indicate that the
particular algorithm is able to reduce the quantity of polygons and, at
the same time, preserve the quality of the given object.