Abstract I-patches represent a family of implicit multi-sided surfaces. Similarly to functional splines, each boundary curve of the patch is defined as the intersection of a primary and a bounding surface, both given in implicit form, and the patch can connect to the primaries with arbitrary geometric continuity. Following the publication of Varady et al. [1], this paper elaborates the basic formulation in more detail, and introduces several interesting features, including a distance-based surface interpretation, consistent orientation of the primaries, setting shape parameters, and handling various special cases. Implicit multi-sided patches are primarily used for connecting simple implicit surfaces, such as planes, cylinders, spheres etc., however, I-patches are also capable of modeling complex free-form shapes. We show constructions for producing setback vertex blends with conic boundaries and patchworks defined by control polyhedra. We discuss the benefits and limitations of the representation through several examples.

中文翻译：

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带 I 型补丁的多边隐式曲面

摘要 I-patch 表示一系列隐式多边曲面。与函数样条相似，补丁的每条边界曲线都定义为主曲面和边界曲面的交点，两者都以隐式形式给出，补丁可以连接到具有任意几何连续性的主曲面。在 Varady 等人发表之后。[1]，本文更详细地阐述了基本公式，并介绍了几个有趣的功能，包括基于距离的表面解释、原色的一致方向、设置形状参数以及处理各种特殊情况。隐式多边面片主要用于连接简单的隐式曲面，例如平面、圆柱体、球体等，然而，I-面片也能够对复杂的自由形状进行建模。我们展示了用于生成具有圆锥边界和由控制多面体定义的拼凑而成的后退顶点混合的构造。我们通过几个例子讨论了这种表示的好处和局限性。