AI 中文总结
研究如何实现快速且稳健的网格实体造型，核心方法是通过拓扑聚合，利用整数精确谓词局部计算排列，将成对相交分类并保持结果一致，主要贡献是输出有效水密，速度快且能在浏览器中交互。
AI 中文摘要
网格实体造型输出采用浮点数形式：无论计算多么精确，每个输出坐标都会被具体化——舍入到可表示的位置——而下一阶段可能会观察到精确结果中从未出现过的交叉和顺序。只有基于索引的拓扑结构在具体化过程中得以保留。我们保持其精确性：在构建过程中，排列的径向结构由原始输入平面上的精确谓词排序——无需精确构造即可实现精确——当决策跨越面时，通过拓扑聚合恢复预期答案：在其拓扑单元内对不同的几何观测进行多数投票。我们使用整数精确谓词在局部计算排列，每个阶段都是一个从未明确构造的图上的图问题。成对相交被分类为五种规范类型（VV、VE、VF、EE、EF），每个切割面都排列在自己的平面中，并且两级标识使结果在各面之间保持一致，无需全局结构。排列及其域划分构建一次并可任意查询：任何arity的布尔值都是一个逐域位测试，体积区域直接从划分中读取，开放表面——声明为有向片——通过相同代数切割体积。该方法在仅包含头文件的trueform库中实现，用C++编写，并带有Python和TypeScript绑定。与现有技术相比，它能产生有效的、水密的输出，同时运行速度快达两个数量级，并在浏览器中保持交互性。
英文摘要
Mesh CSG output is consumed in floating point: however exact the computation, every emitted coordinate is materialised -- rounded to a representable position -- and the next stage can observe crossings and orderings the exact result never had. Only index-based topology survives materialisation. We keep it exact: within the build, the arrangement's radial structure is ordered by exact predicates on the original input planes -- exact without exact constructions -- and where a decision spans faces, the intended answer is recovered by topological aggregation: a majority vote over the disagreeing geometric observations within their topological unit. We compute the arrangement locally with integer-exact predicates, every stage a graph problem on graphs it never explicitly constructs. Pairwise intersections are classified into five canonical types (VV, VE, VF, EE, EF), each cut face is arranged in its own plane, and a two-level identity keeps the result consistent across faces with no global structure. The arrangement and its domain partition are built once and queried arbitrarily often: a boolean of any arity is a per-domain bit test, volumetric regions read straight off the partition, and open surfaces -- declared as oriented sheets -- cut volumes through the same algebra. The method is implemented in the header-only trueform library, in C++ with Python and TypeScript bindings. Compared to prior art, it produces valid, watertight output while running up to two orders of magnitude faster, and stays interactive in the browser.
