Constructing Hierarchies for Triangle Meshes

• Authors: Tran S. Gieng;Bernd Hamann;Kenneth I. Joy;Gregory L. Schussman;Issac J. Trotts
• Venue: IEEE Transactions on Visualization and Computer Graphics
• Year: 1998

We present a method to produce a hierarchy of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithm produces a sequence of meshes ${\cal M}_0, {\cal M}_1, {\cal M}_2, ..., {\cal M}_n,$ where each mesh ${\cal M}_i$ can be transformed to mesh ${\cal M}_{i+1}$ through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of the triangle, and this function serves as a basis for assigning a weight to the triangle in the ordering operation and for supplying the points to which the triangles are collapsed. The algorithm produces a limited number of intermediate meshes by selecting, at each step, a number of triangles that can be collapsed simultaneously. This technique allows us to view a triangulated surface model at varying levels of detail while insuring that the simplified mesh approximates the original surface well.