We introduce Segment Tracing, a new algorithm that accelerates the classical Sphere Tracing method for computing the intersection between a ray and an implicit surface. Our approach consists in computing the Lipschitz bound locally over a segment to improve the marching step computation and accelerate the overall process. We describe the computation of the Lipschitz bound for different operators and primitives. We demonstrate that our algorithm significantly reduces the number of field function queries compared to previous methods, without the need for additional accelerating data‐structures. Our method can be applied to a vast variety of implicit models ranging from hierarchical procedural objects built from complex primitives, to simulation‐generated implicit surfaces created from many particles.

中文翻译：

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使用局部 Lipschitz 边界进行分段跟踪

我们介绍了分段跟踪，这是一种新算法，可加速经典球体跟踪方法，用于计算光线和隐式表面之间的交集。我们的方法包括在一个段上本地计算 Lipschitz 边界，以改进行进步骤计算并加速整个过程。我们描述了不同算子和原语的 Lipschitz 界限的计算。我们证明，与以前的方法相比，我们的算法显着减少了字段函数查询的数量，而无需额外的加速数据结构。我们的方法可以应用于各种各样的隐式模型，从由复杂基元构建的分层程序对象，到由许多粒子创建的模拟生成的隐式表面。