This paper presents a unified differentiable boolean operator for implicit solid shape modeling using Constructive Solid Geometry (CSG). Traditional CSG relies on min, max operators to perform boolean operations on implicit shapes. But because these boolean operators are discontinuous and discrete in the choice of operations, this makes optimization over the CSG representation challenging. Drawing inspiration from fuzzy logic, we present a unified boolean operator that outputs a continuous function and is differentiable with respect to operator types. This enables optimization of both the primitives and the boolean operations employed in CSG with continuous optimization techniques, such as gradient descent. We further demonstrate that such a continuous boolean operator allows modeling of both sharp mechanical objects and smooth organic shapes with the same framework. Our proposed boolean operator opens up new possibilities for future research toward fully continuous CSG optimization.

翻译：本文提出了一种用于隐式实体形状建模的统一可微布尔运算符，该建模基于构造实体几何（CSG）。传统CSG依赖于min、max运算符对隐式形状执行布尔运算。但由于这些布尔运算符在运算选择上具有不连续性和离散性，使得基于CSG表示的优化面临挑战。受模糊逻辑启发，我们提出了一种统一的布尔运算符，该运算符能输出连续函数，且对运算符类型可微。这使得CSG中使用的基元与布尔运算均可通过梯度下降等连续优化技术进行优化。我们进一步证明，这种连续布尔运算符能够在同一框架下对尖锐的机械物体和光滑的有机形状进行建模。我们提出的布尔运算符为未来实现完全连续的CSG优化研究开辟了新的可能性。