FloralSurf: Space-Filling Geodesic Ornaments

We propose a method to generate floral patterns on manifolds without relying on parametrizations. Taking inspiration from the literature on procedural space-filling vegetation, these patterns are made of non-intersecting ornaments that are grown on the surface by repeatedly adding different types of decorative elements, until the whole surface is covered. Each decorative element is defined by a set of geodesic Bézier splines and a set of growth points from which to continue growing the ornaments. Ornaments are grown in a greedy fashion, one decorative element at a time. At each step, we analyze a set of candidates, and retain the one that maximizes surface coverage, while ensuring that it does not intersect other ornaments. All operations in our method are performed in the intrinsic metric of the surface, thus ensuring that the derived decorations have good coverage, with neither distortions nor discontinuities, and can be grown on complex surfaces. In our method, users control the decorations by selecting the size and shape of the decorative elements and the position of the growth points.We demonstrate decorations that vary in the length of the ornaments' lines, and the number, scale and orientation of the placed decorations. We show that these patterns mimic closely the design of hand-drawn objects. Our algorithm supports any manifold surface represented as triangle meshes. In particular, we demonstrate patterns generated on surfaces with high genus, with and without borders and holes, and that can include a mixture of thin and large features.