Vectorization for Fast, Analytic, and Differentiable Visibility

In Computer Graphics, the two main approaches to rendering and visibility involve ray tracing and rasterization. However, a limitation of both approaches is that they essentially use point sampling. This is the source of noise and aliasing, and also leads to significant difficulties for differentiable rendering. In this work, we present a new rendering method, which we call vectorization, that computes 2D point-to-region integrals analytically, thus eliminating point sampling in the 2D integration domain such as for pixel footprints and area lights. Our vectorization revisits the concept of beam tracing, and handles the hidden surface removal problem robustly and accurately. That is, for each intersecting triangle inserted into the viewport of a beam in an arbitrary order, we are able to maintain all the visible regions formed by intersections and occlusions, thanks to our Visibility Bounding Volume Hierarchy structure. As a result, our vectorization produces perfectly anti-aliased visibility, accurate and analytic shading and shadows, and most important, fast and noise-free gradients with Automatic Differentiation or Finite Differences that directly enables differentiable rendering without any changes to our rendering pipeline. Our results are inherently high-quality and noise-free, and our gradients are one to two orders of magnitude faster than those computed with existing differentiable rendering methods.

OLBVH: octree linear bounding volume hierarchy for volumetric meshes

We present a novel bounding volume hierarchy for GPU-accelerated direct volume rendering (DVR) as well as volumetric mesh slicing and inside-outside intersection testing. Our novel octree-based data structure is laid out linearly in memory using space filling Morton curves. As our new data structure results in tightly fitting bounding volumes, boundary markers can be associated with nodes in the hierarchy. These markers can be used to speed up all three use cases that we examine. In addition, our data structure is memory-efficient, reducing memory consumption by up to 75%. Tree depth and memory consumption can be controlled using a parameterized heuristic during construction. This allows for significantly shorter construction times compared to the state of the art. For GPU-accelerated DVR, we achieve performance gain of 8.4$$\times $$ × –13$$\times $$ × . For 3D printing, we present an efficient conservative slicing method that results in a 3$$\times $$ × –25$$\times $$ × speedup when using our data structure. Furthermore, we improve volumetric mesh intersection testing speed by 5$$\times $$ × –52$$\times $$ × .

DESIGN AND APPLICATION OF BOUNDING VOLUME HIERARCHY COLLISION DETECTION ALGORITHM BASED ON VIRTUAL SPHERE

The result of collision detection is closely related to the further deformation or cutting action of soft tissue. In order to further improve the efficiency and stability of collision detection, in this paper, a collision detection algorithm of bounding volume hierarchy based on virtual sphere was proposed. The proposed algorithm was validated and the results show that the detection efficiency of the bounding volume hierarchy algorithm based on virtual sphere is higher than that of the serial hybrid bounding volume hierarchy algorithm and the parallel hybrid bounding volume hierarchy algorithm. Different collision detection algorithms were tested and the results show that the collision detection algorithm based on virtual sphere has high detection efficiency and good stability. As the number of triangular patches increased, the advantage was more and more obvious. Finally, the proposed algorithm was applied to two large and medium-sized virtual scenes to implement the collision detection between the vastus lateralis muscle, thigh and surgical instrument. Based on the virtual sphere, the collision detection algorithm of bounding volume hierarchy can implement efficient and stable collision detection in a virtual surgery system. Meanwhile, the algorithm can be combined with other acceleration algorithms (such as the multithread acceleration algorithm) to further improve detection efficiency.