Abstract We propose theprimitive tree, a novel and compact space‐partition method that samples and reconstructs a distance field with high accuracy, even for regions far from the surfaces. The primitive tree is based on the octree and stores the indices of the nearest primitives in its leaf nodes. Most previous approaches have involved a trade‐off between accuracy and speed in distance queries, but our method can improve both aspects simultaneously. In addition, our method can sample unsigned distance fields effectively, even for self‐intersecting and nonmanifold models. We present test results showing that our method can sample and represent large scenes, with more than ten million triangles, rapidly and accurately.

We address the computational resource requirements of 3D example-based synthesis with an adaptive synthesis technique that uses a tree-based synthesis map. A signed-distance field (SDF) is determined for the 3D exemplars, and then new models can be synthesized as SDFs by neighborhood matching. Unlike voxel synthesis approach, our input is posed in the real domain to preserve maximum detail. In comparison to straightforward extensions to the existing volume texture synthesis approach, we made several improvements in terms of memory requirements, computation times, and synthesis quality. The inherent parallelism in this method makes it suitable for a multicore CPU. Results show that computation times and memory requirements are very much reduced, and large synthesized scenes exhibit fine details which mimic the exemplars.

This paper presents analytic solutions to the integral moving least squares (MLS) equations originally proposed by Shen et al. by choosing another specific weighting function that renders the numerator in the MLS equation unitless. In addition, we analyze the original method to show that their approximation surfaces (i.e., enveloping surfaces with nonzero values in the weighting function) often form zero isosurfaces near concavities behind the triangle-soup models. This paper also presents error terms for the integral MLS formulations against signed distance fields. Based on our analytic solutions, we show that our method provides both interpolation and approximation surfaces faster and more efficiently. Because our method computes solutions for integral MLS equations directly, it does not rely on numerical steps that might have numerical-accuracy issues. In particular, unlike the original method that deals with incorrect approximation surfaces by iteratively adjusting parameters, this paper proposes faster and more efficient approximations to surfaces without needing iterative routines. We also present computational efficiency comparisons, in which our method is 15-fold faster in computing integrations, even with conservative assumptions. Finally, we show that the surface normal vectors on the implicit surfaces formed by our analytic solutions are identical to the angle-weighted pseudonormal vectors.