Feature based volumes for implicit intersections.

The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or feature based volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualization of feature curves and modeling of surface based structures including microstructures

Implicitization of curves and (hyper)surfaces using predicted support

We reduce implicitization of rational planar parametric curves and (hyper)surfaces to linear algebra, by interpolating the coefficients of the implicit equation. For predicting the implicit support, we focus on methods that exploit input and output structure in the sense of sparse (or toric) elimination theory, namely by computing the Newton polytope of the implicit polynomial, via sparse resultant theory. Our algorithm works even in the presence of base points but, in this case, the implicit equation shall be obtained as a factor of the produced polynomial. We implement our methods on Maple, and some on Matlab as well, and study their numerical stability and efficiency on several classes of curves and surfaces. We apply our approach to approximate implicitization, and quantify the accuracy of the approximate output, which turns out to be satisfactory on all tested examples; we also relate our measures to Hausdorff distance. In building a square or rectangular matrix, an important issue is (over)sampling the given curve or surface: we conclude that unitary complexes offer the best tradeoff between speed and accuracy when numerical methods are employed, namely SVD, whereas for exact kernel computation random integers is the method of choice. We compare our prototype to existing software and find that it is rather competitive

Shape from Shading through Shape Evolution

In this paper, we address the shape-from-shading problem by training deep networks with synthetic images. Unlike conventional approaches that combine deep learning and synthetic imagery, we propose an approach that does not need any external shape dataset to render synthetic images. Our approach consists of two synergistic processes: the evolution of complex shapes from simple primitives, and the training of a deep network for shape-from-shading. The evolution generates better shapes guided by the network training, while the training improves by using the evolved shapes. We show that our approach achieves state-of-the-art performance on a shape-from-shading benchmark

Interactive GPU-based generation of solvent-excluded surfaces

The solvent-excluded surface (SES) is a popular molecular representation that gives the boundary of the molecular volume with respect to a specific solvent. SESs depict which areas of a molecule are accessible by a specific solvent, which is represented as a spherical probe. Despite the popularity of SESs, their generation is still a compute-intensive process, which is often performed in a preprocessing stage prior to the actual rendering (except for small models). For dynamic data or varying probe radii, however, such a preprocessing is not feasible as it prevents interactive visual analysis. Thus, we present a novel approach for the on-the-fly generation of SESs, a highly parallelizable, grid-based algorithm where the SES is rendered using ray-marching. By exploiting modern GPUs, we are able to rapidly generate SESs directly within the mapping stage of the visualization pipeline. Our algorithm can be applied to large time-varying molecules and is scalable, as it can progressively refine the SES if GPU capabilities are insufficient. In this paper, we show how our algorithm is realized and how smooth transitions are achieved during progressive refinement. We further show visual results obtained from real-world data and discuss the performance obtained, which improves upon previous techniques in both the size of the molecules that can be handled and the resulting frame rate.Peer ReviewedPostprint (author's final draft

A generalization of tangent-based implicit curves

An approach to defining quadratic implicit curves is to prescribe two tangent lines and a secant line going through the points of tangency. This paper will show that this method can be generalized to a higher number of tangents, resulting in higher degree curves