Abstract: Based on the analysis of the extension methods for quadrilateral surface, the extension methods for compound triangular surfaces are proposed by the ways of calculating the extension direction, steps and points. The triangular mesh of extension surface is appended with the extension points and border points. By analyzing the relation of adjacent triangular mesh, a process is given to avoid twist or overlapping of extension surfaces. The triangular shape factor is applied to distinguish the strait triangles from the mesh. The extension mesh can be optimized by inserting or incorporating the extension points. The extension surface may be further created by constructing a global compound triangular surface interpolating with the original and extended mesh. The method is applied in a sample and the result shows that the extension procedure is effective and robust.

Key words: Extension, Overlapping, Triangular surface, Twist