Chapter 3 - Simplification Error Metrics

Abstract

This chapter examines some of the key elements of measuring simplification quality at a high level, looking to several of the published algorithms to see the range of possible approaches to the problem. It investigates the reasons to measure simplification error, the key elements common to many simplification error metrics, and several metrics themselves from the literature. It classifies these metrics into vertex-vertex, vertex-plane, vertex-surface, and surface-surface distance measures. These different classes provide a range of characteristic performance in terms of speed, quality, robustness, and ease of implementation. The vertex-vertex measures are the fastest and most robust, followed by the vertex-plane measures. The vertex-plane measures produce much higher-quality models overall. The vertex-vertex measures are easy to implement, and the vertex-plane measures are only slightly harder, requiring a few more functions in your algebraic toolbox. The vertex-surface and surface-surface measures tend to be somewhat slower than the first two classifications. The surface-surface measures provide guaranteed error bounds on their output, making them useful for both fidelity-based and budget-based simplification systems. For the highest-quality simplifications, systems based on these measures generally assume a clean, manifold mesh as input and preserve the topology of that mesh throughout the process. The three major components for simplification are optimization algorithms, simplification operators, and error metrics.