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The typical goal of surface remeshing consists in finding a mesh that is (1)geometrically faithful to the original geometry, (2) as coarse as possible toobtain a low-complexity representation and (3) free of bad elements that wouldhamper the desired application. In this paper, we design an algorithm toaddress all three optimization goals simultaneously. The user specifies desiredbounds on approximation error {\delta}, minimal interior angle {\theta} andmaximum mesh complexity N (number of vertices). Since such a desired mesh mightnot even exist, our optimization framework treats only the approximation errorbound {\delta} as a hard constraint and the other two criteria as optimizationgoals. More specifically, we iteratively perform carefully prioritized localoperators, whenever they do not violate the approximation error bound andimprove the mesh otherwise. In this way our optimization framework greedilysearches for the coarsest mesh with minimal interior angle above {\theta} andapproximation error bounded by {\delta}. Fast runtime is enabled by a localapproximation error estimation, while implicit feature preservation is obtainedby specifically designed vertex relocation operators. Experiments show that ourapproach delivers high-quality meshes with implicitly preserved features andbetter balances between geometric fidelity, mesh complexity and element qualitythan the state-of-the-art.

Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement