Procedural implicit surfaces are a popular representation for shape modeling. They provide a simple framework for complex geometric operations such as Booleans, blending and deformations. However, their editability remains a challenging task: as the definition of the shape is purely implicit, direct manipulation of the shape cannot be performed. Thus, parameters of the model are often exposed through abstract sliders, which have to be nontrivially created by the user and understood by others for each individual model to modify. Further, each of these sliders needs to be set one by one to achieve the desired appearance. To circumvent this laborious process while preserving editability, we propose to directly manipulate the implicit surface in the viewport. We let the user naturally interact with the output shape, leveraging points on a co-parameterization we design specifically for implicit surfaces, to guide the parameter updates and reach the desired appearance faster. We leverage our automatic differentiation of the procedural implicit surface to propagate interactions made by the user in the viewport to the shape parameters themselves. We further design a solver that uses such information to guide an intuitive and smooth user workflow. We demonstrate different editing processes across multiple implicit shapes and parameters that would be tedious by tuning sliders.

中文翻译：

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程序隐式曲面的直接操作


程序隐式曲面是形状建模的常用表示形式。它们为复杂的几何运算（如布尔运算、混合和变形）提供了一个简单的框架。但是，它们的可编辑性仍然是一项具有挑战性的任务：由于形状的定义是完全隐式的，因此无法直接操作形状。因此，模型的参数通常通过抽象滑块公开，这些滑块必须由用户非平凡地创建并被其他人理解，以便每个单独的模型进行修改。此外，这些滑块中的每一个都需要逐个设置才能获得所需的外观。为了在保留可编辑性的同时避免这个费力的过程，我们建议直接在视口中操纵隐式表面。我们让用户自然地与输出形状交互，利用我们专门为隐式曲面设计的协参数化上的点来指导参数更新并更快地达到所需的外观。我们利用程序隐式表面的自动微分，将用户在视区中进行的交互传播到形状参数本身。我们进一步设计了一个求解器，该求解器使用此类信息来指导直观、流畅的用户工作流程。我们演示了跨多个隐式形状和参数的不同编辑过程，这些过程在调整滑块时会很乏味。