In Computer Graphics, the two main approaches to rendering and visibility involve ray tracing and rasterization. However, a limitation of both approaches is that they essentially use point sampling. This is the source of noise and aliasing, and also leads to significant difficulties for differentiable rendering. In this work, we present a new rendering method, which we call vectorization, that computes 2D point-to-region integrals analytically, thus eliminating point sampling in the 2D integration domain such as for pixel footprints and area lights. Our vectorization revisits the concept of beam tracing, and handles the hidden surface removal problem robustly and accurately. That is, for each intersecting triangle inserted into the viewport of a beam in an arbitrary order, we are able to maintain all the visible regions formed by intersections and occlusions, thanks to our Visibility Bounding Volume Hierarchy structure. As a result, our vectorization produces perfectly anti-aliased visibility, accurate and analytic shading and shadows, and most important, fast and noise-free gradients with Automatic Differentiation or Finite Differences that directly enables differentiable rendering without any changes to our rendering pipeline. Our results are inherently high-quality and noise-free, and our gradients are one to two orders of magnitude faster than those computed with existing differentiable rendering methods.

中文翻译：

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用于快速、分析和可微可见性的矢量化

在计算机图形学中，渲染和可见性的两种主要方法涉及光线追踪和光栅化。然而，这两种方法的一个限制是它们本质上都使用点采样。这是噪声和混叠的来源，也导致了可微渲染的重大困难。在这项工作中，我们提出了一种新的渲染方法，我们称之为矢量化，它通过解析计算 2D 点到区域积分，从而消除了 2D 积分域中的点采样，例如像素足迹和区域光。我们的矢量化重新审视了光束追踪的概念，并稳健而准确地处理了隐藏表面去除问题。也就是说，对于以任意顺序插入光束视口的每个相交三角形，由于我们的 Visibility Bounding Volume Hierarchy 结构，我们能够保持由交叉点和遮挡形成的所有可见区域。因此，我们的矢量化产生了完美的抗锯齿可见性、准确和分析的阴影和阴影，以及最重要的、快速且无噪声的渐变，具有自动微分或有限差分，直接实现可微分渲染，而无需对我们的渲染管道进行任何更改。我们的结果本质上是高质量和无噪声的，我们的梯度比使用现有可微渲染方法计算的梯度快一到两个数量级。具有自动微分或有限差分的快速且无噪声的渐变，可直接启用可微分渲染，而无需对我们的渲染管道进行任何更改。我们的结果本质上是高质量和无噪声的，我们的梯度比使用现有可微渲染方法计算的梯度快一到两个数量级。具有自动微分或有限差分的快速且无噪声的渐变，可直接启用可微分渲染，而无需对我们的渲染管道进行任何更改。我们的结果本质上是高质量和无噪声的，我们的梯度比使用现有可微渲染方法计算的梯度快一到两个数量级。