Mathieu Desbrun

Figure 1: A brief overview of our remeshing process: The input surface patch (top left) is first parameterized; Then geometric quantities are computed over the parameterization and stored in several 2D maps; These maps are combined to produce a control map, indicating the desired sampling distribution; The control map is then sampled using a halftoning technique, and the samples are triangulated, optimized and finally output as a new 3D mesh. A few examples of the various types of meshes our system can produce are shown (top, from left to right): uniform, increased sampling on higher curvature, the next with a smoother gradation, regular quads, and semi-regular triangles. After an initial pre-processing stage (∼1s), each of these meshes was produced in less than 2 seconds on a low-end PC. We present a novel technique, both flexible and efficient, for interactive remeshing of irregular geometry. First, the original (arbitrary genus) mesh is substituted by a series of 2D maps in parameter space. Using these maps, our algorithm is then able to take advantage of established signal processing and halftoning tools that offer real-time interaction and intricate control. The user can easily combine these maps to create a control map – a map which controls the sampling density over the surface patch. This map is then sampled at interactive rates allowing the user to easily design a tailored resampling. Once this sampling is complete, a Delaunay triangulation and fast optimization are performed to perfect the final mesh. As a result, our remeshing technique is extremely versatile and general, being able to produce arbitrarily complex meshes with a variety of properties including: uniformity, regularity, semiregularity, curvature sensitive resampling, and feature preservation. We provide a high level of control over the sampling distribution allowing the user to interactively custom design the mesh based on their requirements thereby increasing their productivity in creating a wide variety of meshes. 2D Mesh