Surface Maps via Adaptive Triangulations
نویسندگان
چکیده
We present a new method to compute continuous and bijective maps (surface homeomorphisms) between two or more genus-0 triangle meshes. In contrast previous approaches, we decouple the resolution at which map is represented from of input discretize via common triangulations that approximate meshes while remaining in correspondence them. Both geometry connectivity these are optimized with respect single objective function simultaneously controls mapping distortion, triangulation quality, approximation error. A discrete-continuous optimization algorithm performs both energy-based remeshing as well global second-order vertex positions, parametrized sphere. With this, combine disciplines compatible surface unified formulation make contribution fields. While existing algorithms often operate on fixed pre-computed map, can now globally update this during remeshing. On other hand, surface-to-surface previously required computing costly overlay inherently tied mesh resolution. achieve significant complexity reduction by instead assessing distortion approximating triangulations. This representation robust than overlay-based less intricate implement, naturally supports surfaces. Moreover, it enables adaptive multi-resolution schemes that, e.g., first align corresponding regions coarse resolutions before refining where needed. demonstrate speedups increased flexibility over state-of-the art similar also provide reference implementation method.
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ژورنال
عنوان ژورنال: Computer Graphics Forum
سال: 2023
ISSN: ['1467-8659', '0167-7055']
DOI: https://doi.org/10.1111/cgf.14747