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

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

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

This book excerpt is from Mike de la Flor's "The Cararra Studio." ISBN 1-58450-310-6. All rights reserved. Chapter 1: 3D Modeling Concepts and Techniques, is posted with permission from Charles River Media.

 Getting Around in 3D: Cartesian Coordinates Polygonal Modeling Modeling with Curves

Polygons, vertices, curves, normals, edges, and coordinates; this list sounds more like a syllabus from a geometry course instead of tools used by computer graphics (CG) artists. The truth is that behind all 3D programs, there are very complex mathematics and programming. Fortunately, we do not have to be mathematicians to be proficient 3D modelers or animators. All of the mathematics is neatly tucked under a stylized user interface (UI). All we have to do is click on the right buttons to get it to work for us.

An old adage says that you do not have to be an engineer to drive and enjoy a car. However, it’s a very good idea to know something about how your car works to keep it running at its best and avoid expensive repairs. If you plan to be a Formula 1 race car driver, however, you not only have to know how to drive a car, you also need to understand its engineering, aerodynamics, and the physics of moving at 230 mph—your life depends on it. Similarly, with Carrara Studio, you can be content just knowing that by clicking on the right buttons you can create amazing 3D graphics and animations. However, if you plan to make a living as a 3D modeler or animator, consider that once you understand the basic concepts in 3D you can begin to harness the power of Carrara Studio to develop your own style. More important, you can be more creative and make smarter decisions as a professional CG artist.

This chapter was written to help give you a head start in the sometimes complex and always competitive world of 3D computer graphics. If you want to skip this chapter for now, feel free to jump to the tutorials in later chapters and have fun. However, when you feel a bit curious about what is happening under the hood, come back and look at this chapter—it will be worth your time.

### Getting Around in 3D: Cartesian Coordinates

Although some astrophysicists will have us believe that there are possibly more than three dimensions in our universe, our brains, and consequently the computers we design, are wired to deal with only three dimensions. Since all 3D objects have width, height, and depth, there must be some method to describe these 3D attributes. To solve this problem, most 3D programs, including Carrara Studio, use the Cartesian coordinate system to describe the characteristics of a 3D environment and the objects within it (see Figure 1.1).

In Cartesian coordinates, the variables x, y, and z are used to determine the location of any object in space. At the center of Cartesian space is the origin, the point where all dimensions begin. The value of x, y, and z is zero at the origin.

### Translation

In order to move in 3D space an object must follow one, two, or all three of the x, y, and z axes. For example, if the center of a cube is located five units along the z-axis, two units along the y-axis, and three units along the x-axis, the location of the cube can be accurately plotted in 3D space. If the x, y, and z values of the cube change, then the cube has moved or translatedin 3D space as in Figure 1.2.

### Rotation

align="justify" >X, y, and z values can also describe the rotation of an object. Like translation, rotation occurs along one axis or a combination of the x-, y-, and z-axes. If the cube described earlier tilts to the left five degrees, then it is said to have rotated five degrees about the x-axis (see Figure 1.3).

### The Right-Handed Rule

An easy way to remember the Cartesian coordinate system is to use the right-handed rulemodel. Hold up your right hand and make a fist. Now, extend your index finger as if pointing up. Point the middle finger to the left and finally extend your thumb toward you. Your index finger represents the z-axis, the middle represents the x-axis, and the thumb the y-axis (see Figure 1.4).

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

URL: http://webreference.com/3d/cararra/1