Polygon Object

多边形对象

Polygon Object

多边形对象

This creates an empty polygon object. Initially, all you will see in the view is its origin and axes.

这将创建一个空多边形对象。最初，您将在视图中看到的只是它的原点和轴。

You can later fill this object with points and polygons.

稍后您可以用点和多边形填充这个对象。

The polygon object can also be used as an alternative to the null object for grouping objects together.

多边形对象也可以作为空对象的替代，用于将对象分组在一起。

Polygon fundamentals

多边形的基本原理

A polygon is a triangle or a quadrangle. A triangle has the points A, B and C; a quadrangle has the points A, B, C and D.

多边形是三角形或四边形。三角形有点 a，b 和 c; 四边形有点 a，b，c 和 d。

Perfect polygons, like the one in Figure 1, are not that common, since the points may lie anywhere in 3D space. This is not a problem if the points are planar — i.e., if they all lie on the same plane, as in Figure 2.

完美的多边形，比如图1中的多边形，并不常见，因为这些点可能位于三维空间的任何位置。如果这些点是平面的，那么这就不是问题了，即，如果它们都位于同一个平面上，如图2所示。

If the quadrangle’s points are not on the same plane, the quadrangle is said to be non-planar. In Figure 3, point B has been moved into the depth plane. Now, Cinema 4D must render this polygon as two triangles. This happens internally and usually has no negative effects. However, non-planar polygons can occasionally lead to unexpected effects and are generally best avoided.

如果四边形的点不在同一平面上，那么这个四边形就是非平面的。在图3中，点 b 已经移动到深度平面中。现在，Cinema 4D 必须将这个多边形渲染成两个三角形。这种情况发生在内部，通常没有负面影响。然而，非平面多边形偶尔会导致意想不到的效果，通常最好避免这种情况。

For planar quadrangles, if the interior angle at points B or D is greater than 180°, problems can occur when rendering — this is because the polygon overlaps itself, as in Figure 4.

对于平面四边形，如果点 b 或 d 的内角大于180 ° ，绘制时就会出现问题ーー这是因为多边形本身重叠，如图4所示。

Another problem arises if all of the polygon’s points are on the same line. In this case, a surface normal cannot exist and the polygon is called a degenerated polygon, illustrated in Figure 5.

如果多边形的所有点都在同一条线上，就会出现另一个问题。在这种情况下，表面法线不存在，多边形被称为退化多边形，如图5所示。

Polygon coordinate system

多边形坐标系

Polygons in Cinema 4D have their own coordinate system, as illustrated in Figure 6. You cannot see this system in the viewports, but it is important to be aware of it when using modeling tools such as Matrix Extrude.

C4D中的多边形有它们自己的坐标系，如图6所示。你不能在视图中看到这个系统，但是在使用矩阵挤压这样的建模工具时注意它是很重要的。

The origin of the polygon coordinate system is located at the center of the polygons. The X axis is along the line between A and B. The Z axis is the normal. The Y axis is perpendicular to the XZ plane.

多边形坐标系的原点位于多边形的中心。X 轴在 a 和 b 之间。Z 轴是法线。Y 轴垂直于 XZ 平面。

N-gons

An n-gon (pronounced en-gon) is simply a polygon that has more than four corner points. N-gons can help to simplify the polygon modeling process.

N-gon (发音为 en-gon)是一个多边形，它有四个以上的角点。N-gons 可以简化多边形的建模过程。

Before n-gons were implemented in Cinema 4D, almost every time you cut a polygon, new edges would be created automatically on the neighboring polygons. These extra edges could make the object difficult to work with and slow down your workflow, because a manual rebuilding would often be required in order to clean up the mesh.

在C4D 中实现 n-gons 之前，几乎每次你切割一个多边形，邻近的多边形上都会自动生成新的边。这些额外的边缘可能会使物体难以处理，并减慢您的工作流程，因为通常需要手动重建以清理网格。

The following example demonstrates the advantage of using n-gons.

下面的示例演示了使用 n-gons 的优点。

Suppose you want to bevel an area. First you cut around the area that you want to bevel (the inset picture marks the cut line). Above you can see the result of making the cut in an older version of Cinema 4D (left) and in the current version of Cinema 4D (right).

假设您希望将一个区域削成斜面。首先，在需要斜切的区域周围进行切割(插入图片标记了切割线)。上面你可以看到在老版本的 Cinema 4D (左)和当前版本的 Cinema 4D (右)中进行剪辑的结果。

With the older version of Cinema 4D, notice how unwanted triangles have been created in the areas around the cut. These triangles will make it difficult, if not impossible, to select and bevel the desired area. A substantial rebuilding of the mesh would be required.

随着老版本的C4D，注意如何不必要的三角形已经创建周围的地区削减。这些三角形将使它很难，如果不是不可能，选择和斜面所需的面积。需要对网格进行实质性重建。

Thanks to n-gons (right picture), it is now much easier to recognize, select and work with the actual cuts.

多亏了 n-gons (右图) ，现在更容易识别，选择和工作与实际的削减。

N-gons change your workflow. Instead of having to clean up the mesh after each cut, you can now leave the cleanup stage until the end of the modeling process. But why do you still need to clean up the mesh if n-gons are so wonderful?

N-gons 改变你的工作流程。不必在每次切割后清理网格，您现在可以离开清理阶段直到建模过程结束。但是为什么你仍然需要清理网格，如果 n-gons 是如此美妙？

N-gons are one of the most powerful features in the 3D modeler’s toolbox. However, a perfect mesh should ideally be made up of triangles and quadrangles only, especially if the mesh is to be deformed or animated. Internally, n-gons will be triangulated automatically when you render, animate and so on. Because automatic triangulation is unlikely to produce the triangles in the best places, it’s up to you to ensure that the mesh is correctly structured.

N-gons 是3D 建模工具箱中最强大的特性之一。然而，一个完美的网格应该理想地只由三角形和四边形组成，特别是如果网格是变形或动画。在内部，n-gons 将被自动三角测量当您渲染，动画等。因为自动三角测量不太可能在最好的地方产生三角形，所以你要确保网格结构正确。

Only you can ensure that the points and polygons of, say, a character’s elbow are in exactly the right places to allow the arm to bend cleanly.

只有你才能确保，比如说，一个角色的肘部的点和多边形恰好在正确的位置，使得手臂能够弯曲得干净利落。

Making parametric objects editable

使参数对象可编辑

Cinema 4D works mainly with parametric objects – objects that can be defined mathematically. Such objects include the primitives, spline primitives and Generators. These objects have neither polygons nor points. Instead, the surface is defined mathematically and is only converted to polygons when rendered.

C4D 主要使用参数化对象——可以用数学方法定义的对象。这些对象包括基元、样条基元和生成器。这些对象既没有多边形也没有点。相反，曲面是用数学方法定义的，只有在渲染时才转换为多边形。

To make parametric objects editable, i.e., to convert them into polygons or points, choose Mesh/Conversion/ Make Editable.

要使参数对象可编辑，即，将其转换为多边形或点，选择 Mesh/Conversion/Make Editable。

Make Editable

制作可编辑的

Polygon Object

多边形对象

Spline Object

样条对象

Quadrangles for modeling

用于建模的四边形

You are free to use triangles, but be particularly careful when using them with Subdivision Surfaces — triangles can cause irregularities. Only quadrangles generate a totally clean Subdivision Surfaces .

你可以随意使用三角形，但是在细分曲面使用时要特别小心---- 三角形可能会导致不规则。只有四边形产生一个完全干净的细分曲面。