We present an efficient polygonization approach for tree trunks modeled by line skeleton-based convolution surfaces. A quad-dominated non-convex bounding polyhedron is firstly created along the skeleton, which is then tetrahedralized and subdivided into the pre-defined resolution. After that, the iso-surface within each tetrahedron is extracted using marching tetrahedra. Our algorithm can generate polygons with adaptive edge lengths according to the thickness of the trunk. In addition, we present an efficient CUDA-based parallel algorithm utilizing the high parallelism of the tetrahedron subdivision, the potential field calculation, and the iso-surface extraction.

No abstract

Several applications in shape modeling and exploration require identification and extraction of a 3D shape part matching a 2D sketch. We present CustomCut, an on‐demand part extraction algorithm. Given a sketched query, CustomCut automatically retrieves partially matching shapes from a database, identifies the region optimally matching the query in each shape, and extracts this region to produce a customized part that can be used in various modeling applications. In contrast to earlier work on sketch‐based retrieval of predefined parts, our approach can extract arbitrary parts from input shapes and does not rely on a prior segmentation into semantic components. The method is based on a novel data structure for fast retrieval of partial matches: the randomized compound k‐NN graph built on multi‐view shape projections. We also employ a coarse‐to‐fine strategy to progressively refine part boundaries down to the level of individual faces. Experimental results indicate that our approach provides an intuitive and easy means to extract customized parts from a shape database, and significantly expands the design space for the user. We demonstrate several applications of our method to shape design and exploration.