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

Surface remeshing is a key component in many geometry processing applications. The typical goal consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application (e.g., the minimum interior angle is above an application-dependent threshold). Our algorithm is designed to address all three optimization goals simultaneously by targeting prescribed bounds on approximation error <inline-formula> <tex-math notation="LaTeX">$\delta$</tex-math><alternatives><inline-graphic xlink:href="hu-ieq1-2632720.gif"/> </alternatives></inline-formula>, minimal interior angle <inline-formula><tex-math notation="LaTeX">$\theta$</tex-math> <alternatives><inline-graphic xlink:href="hu-ieq2-2632720.gif"/></alternatives></inline-formula> and maximum mesh complexity <inline-formula><tex-math notation="LaTeX">$N$</tex-math><alternatives> <inline-graphic xlink:href="hu-ieq3-2632720.gif"/></alternatives></inline-formula> (number of vertices). The approximation error bound <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math><alternatives> <inline-graphic xlink:href="hu-ieq4-2632720.gif"/></alternatives></inline-formula> is a hard constraint, while the other two criteria are modeled as optimization goals to guarantee feasibility. Our optimization framework applies carefully prioritized local operators in order to greedily search for the coarsest mesh with minimal interior angle above <inline-formula><tex-math notation="LaTeX">$\theta$</tex-math><alternatives> <inline-graphic xlink:href="hu-ieq5-2632720.gif"/></alternatives></inline-formula> and approximation error bounded by <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math><alternatives> <inline-graphic xlink:href="hu-ieq6-2632720.gif"/></alternatives></inline-formula>. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that for reasonable angle bounds (<inline-formula><tex-math notation="LaTeX"> $\theta \leq 35^\circ$</tex-math><alternatives><inline-graphic xlink:href="hu-ieq7-2632720.gif"/></alternatives> </inline-formula>) our approach delivers high-quality meshes with implicitly preserved features (no tagging required) and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.

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