Algorithms used for cel edge rendering reflect some of the major themes and techniques of NPR. Our goal here is to present algorithms that give a flavor of the field. Methods used can be roughly categorized as based on surface shading, procedural geometry,image processing, geometric edge detection, or a hybrid of these.
用于cel边缘渲染的算法反映了NPR的一些主要主题和技术。我们在这里的目标是提出算法，给出一个领域的味道。使用的方法可以大致分为基于表面阴影、程序几何、图像处理、几何边缘检测或这些方法的混合。
There are several different types of edges that can be used in toon rendering:
卡通渲染中可以使用几种不同类型的边:
• A boundary or border edge is one not shared by two triangles, e.g., the edge of a sheet of paper. A solid object typically has no boundary edges.
边界或边界边缘不是由两个三角形共享的，例如一张纸的边缘。实体对象通常没有边界边。
• A crease, hard, or feature edge is one that is shared by two triangles, and the angle between the two triangles (called the dihedral angle) is greater than some predefined value. A good default crease angle is 60 degrees [972]. As an example,a cube has crease edges. Crease edges can be further subcategorized into ridge and valley edges.
折痕、硬边或特征边是由两个三角形共享的边，这两个三角形之间的角度(称为二面角)大于某个预定义值。一个好的默认折痕角度是60度[972]。例如，立方体有折痕边。折痕边可以进一步细分为脊边和谷边。
• A material edge appears when the two triangles sharing it differ in material or otherwise cause a change in shading. It also can be an edge that the artist wishes to always have displayed, e.g., forehead lines or a line to separate the same colored pants and shirt.
当共享材质的两个三角形材质不同或导致阴影发生变化时，会出现材质边缘。它也可以是艺术家希望一直显示的边缘，例如前额线或分隔相同颜色的裤子和衬衫的线。
• A contour edge is one in which the two neighboring triangles face in different directions compared to some direction vector, typically one from the eye.
轮廓边是指两个相邻的三角形相对于某个方向向量(通常是一个来自眼睛的方向向量)面向不同的方向。
• A silhouette edge is a contour edge along the outline of the object, i.e., it separates the object from the background in the image plane.
轮廓边缘是沿着对象轮廓的轮廓边缘，即它在图像平面中将对象与背景分开。
See Figure 15.4. This categorization is based on common usage within the literature,but there are some variations, e.g., what we call crease and material edges are sometimes called boundary edges elsewhere.
参见图15.4。这种分类是基于文献中的常见用法，但也有一些变化，例如，我们所说的折痕和材料边缘有时在其他地方也称为边界边缘。
Figure 15.4. A box open on the top, with a stripe on the front. The boundary (B), crease (C),material (M), and silhouette (S) edges are shown. None of the boundary edges are considered silhouette edges by the definitions given, as these edges have only one adjoining polygon.
图15.4。顶部打开的盒子，前面有一条条纹。显示了边界(B)、折痕(C)、材料(M)和剪影(S)边。根据给定的定义，没有边界边被视为剪影边，因为这些边只有一个相邻的多边形。
We differentiate here between contour and silhouette edges. Both are edges along which one part of the surface faces the viewer, the other part faces away. Silhouette edges are a subset of contour edges, those which separate the object from another object or the background. For example, in a side view of a head, the ears form contour edges,even though they appear within the silhouette outline of the head.Other examples in Figure 15.3 include the nose, two bent fingers, and where the hair parts. In some of the early literature, contour edges are referred to as silhouettes, but the full class of contour edges is usually meant. Also, contour edges should not be confused with contour lines used on topographical maps.
我们在这里区分轮廓和剪影边缘。两者都是边缘，表面的一部分面向观察者，另一部分背向观察者。轮廓边缘是轮廓边缘的子集，轮廓边缘将对象与另一个对象或背景分开。例如，在头部的侧视图中，耳朵形成轮廓边，即使它们出现在头部的轮廓内。图15.3中的其他例子包括鼻子、两个弯曲的手指和头发部分。在一些早期文献中，轮廓边缘被称为轮廓，但通常是指轮廓边缘的完整类别。此外，等高线不应与地形图上使用的等高线相混淆。
Note that boundary edges are not the same as contour or silhouette edges. Contour and silhouette edges are defined by a view direction, while boundary edges are view-independent. Suggestive contours [335] are formed by locations that are almost a contour from the original viewpoint. They provide additional edges that help convey the object’s shape. See Figure 15.5. While our focus here is primarily on detecting and rendering contour edges, considerable work has been done for other types of strokes [281, 1014, 1521]. We also focus primarily on finding such edges for polygonal models. B´enard et al. [132] discuss approaches for finding contours of models comprised of subdivision surfaces or other higher-order definitions.
请注意，边界边不同于轮廓或剪影边。轮廓和轮廓边由视图方向定义，而边界边与视图无关。暗示轮廓[335]由几乎是来自原始视点的轮廓的位置形成。它们提供了有助于传达对象形状的附加边缘。参见图15.5。虽然我们在这里的重点主要是检测和渲染轮廓边缘，但对于其他类型的笔画已经做了大量的工作[281，1014，1521]。我们也主要关注于为多边形模型寻找这样的边。B enard等人【132】讨论了寻找由细分表面或其他高阶定义组成的模型轮廓的方法。
Figure 15.5. From left to right: silhouette, contour, and contour together with suggestive contour edges. (Images courtesy of Doug DeCarlo, Adam Finkelstein, Szymon Rusinkiewicz, and Anthony Santella.)
图15.5。从左到右:剪影、轮廓和轮廓以及提示性轮廓边。(图片由Doug DeCarlo、Adam Finkelstein、Szymon Rusinkiewicz和Anthony Santella提供。)