Direct slicing NURBS objects: A numerically dependable form

In additive manufacturing, a three-dimensional model is constructed by sequentially adding material layers. Digitally, complex objects are typically modeled using parametric representations, with Non-Uniform Rational B-Splines (NURBS) surfaces being among the most prominent. Slicing NURBS surfaces—a critical operation in the additive manufacturing workflow—has long been a challenge for 3D modelers due to the complexities inherent in their free-form geometries when intersecting with a plane. Traditionally, this challenge is addressed by converting NURBS representations into meshes composed of approximating triangles. While this approach simplifies the intersection process, it often comes at the expense of accuracy or requires significant computational resources to maintain precision. Although direct slicing methods exist, they encounter various limitations. In this work, we introduce an efficient, numerically robust, conversion-free method for sampling points at the intersection of cutting planes and NURBS objects, termed IsoSlicer. This approach supports NURBS surfaces of any degree while achieving arbitrary accuracy requirements with guaranteed numerical stability.