Metric-Driven RoSy Fields Design
نویسندگان
چکیده
Designing rotational symmetries on surfaces is an important task for a wide range of graphics applications. This work introduces a rigorous and practical algorithm for automatic N-RoSy design on arbitrary surfaces with user defined field topologies. The user has full control of the number, positions and indices of the singularities, the turning numbers of the loops, and is able to edit the field interactively. We formulate N-RoSy field construction as designing a Riemannian metric, such that the global symmetry of the metric is compatible with the local symmetry of N-RoSy. We prove the compatibility condition using discrete parallel transportation. The complexity of N-RoSy field design is caused by curvatures. In our work, we propose to simplify the Riemannian metric to make it flat almost everywhere. This approach greatly simplifies the process and improves the flexibility, such that, it can design N-RoSy fields with single singularity, and mixed-RoSy. This approach can also be generalized to construct regular remeshing on surfaces. To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sktetching and geometry remeshing. Furthermore, based on our remeshing results with high global symmetry, we generate Celtic knots on surfaces directly. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations
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