We present a novel function representation (F-Rep) based geometric modeling kernel tailor-made to support computer aided design (CAD) and fabrication of high resolution volumetric models containing hundreds of billions of voxel grid elements. Our modeling kernel addresses existing limitations associated with evaluating, storing, and accessing volumetric data produced by F-Reps in contexts outside of rendering. The result is an F-Rep modeling kernel well suited for CAD-based applications.

Our kernel utilizes a sparse volume data structure to manage F-Rep data while efficient F-Rep evaluation is achieved through a combination of interval arithmetic (IA), just-in-time (JIT) compilation of user-defined functions, and massively parallel evaluation on the GPU. We employ IA as the basis for local pruning of the function evaluation tree to minimize total function evaluations, we use a novel JIT compilation scheme to optimize function execution, and we take advantage of GPU-parallelism to enhance computational throughput. We illustrate the kernel’s effectiveness in visualizing and slicing models with complex defining functions and detailed geometry, and utilize the geometry kernel to manufacture a physical part. Additionally, we present performance metrics across multiple hardware configurations demonstrating significant performance improvements over existing F-Rep geometry kernels, and we examine how our geometry kernel scales with computing power.

我们提出了一种基于几何建模内核的新颖函数表示（F-Rep），该内核是为支持计算机辅助设计（CAD）和包含数千亿体素网格元素的高分辨率体积模型的制造而定制的。我们的建模内核解决了与评估、存储和访问 F-Reps 在渲染之外的上下文中生成的体积数据相关的现有限制。结果是 F-Rep 建模内核非常适合基于 CAD 的应用程序。

我们的内核利用稀疏体数据结构来管理 F-Rep 数据，同时通过区间算术 (IA)、用户定义函数的即时 (JIT) 编译和大规模并行的组合来实现高效的 F-Rep 评估GPU 上的评估。我们采用 IA 作为函数评估树局部修剪的基础，以最小化总函数评估，我们使用新颖的 JIT 编译方案来优化函数执行，并利用 GPU 并行性来增强计算吞吐量。我们说明了该内核在可视化和切片具有复杂定义函数和详细几何形状的模型方面的有效性，并利用几何内核来制造物理零件。此外，