Triangle mesh

Polygon mesh composed of triangles

In computer graphics, a triangle mesh is a type of polygon mesh. It comprises a set of triangles (typically in three dimensions) that are connected by their common edges or vertices. Many graphics software packages and hardware devices can operate more efficiently on triangles that are grouped into meshes than on a similar number of triangles that are presented individually. This is typically because computer graphics do operations on the vertices at the corners of triangles. With individual triangles, the system has to operate on three vertices for every triangle. In a large mesh, there could be eight or more triangles meeting at a single vertex by processing those vertices just once, it is possible to do a fraction of the work and achieve an identical effect. In many computer graphics applications it is necessary to manage a mesh of triangles. The mesh components are vertices, edges, and triangles. An application might require knowledge of the various connections between the mesh components. These connections can be managed independently of the actual vertex positions. This document describes a simple data structure that is convenient for managing the connections. This is not the only possible data structure. Many other types exist and have support for various queries about meshes.

Various methods of storing and working with a mesh in computer memory are possible. With the OpenGL and DirectX APIs there are two primary ways of passing a triangle mesh to the graphics hardware, triangle strips and index arrays.

One way of sharing vertex data between triangles is the triangle strip. With strips of triangles each triangle shares one complete edge with one neighbour and another with the next. Another way is the triangle fan which is a set of connected triangles sharing one central vertex. With these methods vertices are dealt with efficiently resulting in the need to only process N+2 vertices in order to draw N triangles. Triangle strips are efficient, however the drawback is that it may not be obvious how or convenient to translate an arbitrary triangle mesh into strips.

This operation involves identifying an edge hvk, vti where vk is called the keep vertex and vt is called the throw vertex. The triangles that share this edge are removed from the mesh. The vertex vt is also removed from the mesh. Any triangles that shared vt have that vertex replaced by vk. Figure 1 shows a triangle mesh and a sequence of three edge collapses applied to the mesh.

With index arrays, a mesh is represented by two separate arrays, one array holding the vertices, and another holding sets of three indices into that array which define a triangle. The graphics system processes the vertices first and renders the triangles afterwards, using the index sets working on the transformed data. In OpenGL, this is supported by the glDrawElements primitive when using Vertex Buffer Object (VBO). With this method, any arbitrary set of triangles sharing any arbitrary number of vertices can be stored, manipulated, and passed to the graphics API, without any intermediary processing.