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$$\times $$
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–25$$\times $$
×
speedup when using our data structure. Furthermore, we improve volumetric mesh intersection testing speed by 5$$\times $$
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–52$$\times $$
×
.
Mesh optimization is essential to enable sufficient element quality for numerical methods such as the finite element method (FEM). Depending on the required accuracy and geometric detail, a mesh with many elements is necessary to resolve small-scale details. Sequential optimization of large meshes often imposes long run times. This is especially an issue for Delaunay-based methods. Recently, the notion of harmonic triangulations [1] was evaluated for tetrahedral meshes, revealing significantly faster run times than competing Delaunay-based methods. A crucial aspect for efficiency and high element quality is boundary treatment. We investigate directional derivatives for boundary treatment and massively parallel GPUs for mesh optimization. Parallel flipping achieves compelling speedups by up to $$318\times $$
318
×
. We accelerate harmonic mesh optimization by $$119\times $$
119
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for boundary preservation and $$78\times $$
78
×
for moving every boundary vertex, while producing superior mesh quality.
The cycle of computer aided design and verification via physics simulation is often burdened by the use of separate tools for modeling and simulation, which requires conversion between formats, e.g. meshing for finite element simulation. This separation is often unavoidable because the tools contain specific domain knowledge which is mandatory for the task, for example a specific CAD modeling suite. We propose a distributed application that allows interactive modification of tetrahedral meshes, derived from existing CAD models. It provides immediate simulation feedback by offloading resource-intensive tasks onto multiple machines thereby enabling fast design cycles for individualized versions of mass-produced parts.
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