The Cararra Studio. Chapter 1: 3D Modeling Concepts and Techniques | 2 | WebReference

The Cararra Studio. Chapter 1: 3D Modeling Concepts and Techniques | 2

The Cararra Studio. Chapter 1: 3D Modeling Concepts and Techniques

Polygonal Modeling

Polygon models are the most basic and common types of geometric models used in 3D.

Vertices, Polygons, and Normals

A vertex, or point, is the fundamental building block of all 3D objects. Vertices are defined by their x, y, and z coordinates, but by themselves, vertices have no volume or area and cannot be rendered (in other words, they are invisible). However, when three or more vertices are linked by lines, a polygon is formed, as seen in Figure 1.5. A polygon is a type of curve that can either be open or closed (Figure 1.6a), and it can be empty or filled (Figure 1.6b).

FIGURE 1.5 The parts of a polygon. FIGURE 1.6 An empty polygon (a) and a filled
polygon (b).

Polygons can have any number of vertices to define their shape, but in 3D models, it is best if they have three vertices to form a triangle or four vertices to form a quadrangle (quad for short). Polygons with more than four vertices will not subdivide or smooth as well as triangles or quads. Moreover, a polygonal model composed of quads is generally smaller in file size than a polygonal model composed of triangles—assuming that both models have the same number of vertices. Unlike a single vertex, which is always invisible, when a polygon is filled it becomes a visible 3D component that can be rendered. A filled polygon has surface characteristics that will interact with light; it can have color, reflect light, and cast shadows (see Figure 1.7).

FIGURE 1.7. Filled polygons can
interact with digital light.
FIGURE 1.8 A series of connected
polygons build a polymesh.


Although a filled polygon can be rendered, by itself a polygon has no volume, no thickness, and is rigid. However, when several polygons are connected, by sharing their edges and vertices, they form a polymesh—a three-dimensional shape (see Figure 1.8). In Carrara Studio, polygonal models can be directly manipulated by using the Vertex modeler.

All polygons are said to have a backside and a front side. The direction in which a polygon is facing is referred to as the face normal. As polygons are created, they will automatically be front-facing polygons. Polygons that have front-facing normals will render correctly. It is important to be aware of face normals because every now and then, you will find that a dark polygon mysteriously appears in a render or in a preview of a polygonal model. The culprit is almost always a polygon that has had its normal reversed. Reversed normal polygons are also common in imported 3D models, especially with DXF files. It is important to correct reversed normals because they will not accept textures correctly or render correctly (see Figure 1.9).

FIGURE 1.9 A polymesh with a single reversed normal.
FIGURE 1.10 (a) Vertex normals give a faceted polymesh a smooth surface.
(b) Note that the silhouette is not smoothed

By now, we know that a polymesh is composed of flat polygons that share vertices and edges. Therefore, when light reflects off a polymesh, it will appear faceted (like a gem cut) (see Figure 1.10a). In other words, each polygon in the model will appear flat. To overcome this inherent property of a polymesh, vertex normalsare used to give the model a smooth appearance. Simply put, vertex normals average the angles of the polygons that surround a particular vertex and calculate a smooth surface, as seen in Figure 1.10b. When switching from flat shading to Gouraud shading in Carrara Studio, you are turning vertex normals off and on.

Created: March 27, 2003
Revised: February 13, 2003