# Chapter 6: Rotating Shapes

# Table Of Contents

## Chapter 6: Rotating Shapes

### Understanding Rotated Coordinate Systems

#### Figure 6.1

An airplane and its coordinate system

#### Figure 6.2a

An airplane's coordinate system tilted up. Compare with Figures 6.2b and c

#### Figure 6.2b

An airplane's coordinate system turned to the side. Compare with Figures 6.2a and c

#### Figure 6.2c

An airplane's coordinate system banked on its side. Compare with Figures 6.2a and b

#### Specifying Rotation Angles

#### Figure 6.3a

The right-hand rule to determine a positive/negative rotation angle around the X axis. Compare with Figures 6.3b and c

#### Figure 6.3b

The right-hand rule to determine a positive/negative rotation angle around the Y axis. Compare with Figures 6.3a and c

#### Figure 6.3c

The right-hand rule to determine a positive/negative rotation angle around the Z axis. Compare with Figures 6.3a and b

#### Specifying a Rotation Center

### The Transform Node Syntax

### Experimenting with Rotation

#### Rotating in Different Directions

#### Figure 6.4b

Rotating 45.0 degrees about the X axis and building a cone

#### Figure 6.5b

Rotating -45.0 degrees about the X axis and building a cone

#### Figure 6.6b

Rotating 45.0 degrees about the Y axis and building a cone

#### Figure 6.7b

Rotating -45.0 degrees about the Z axis and building a box

#### Constructing Multiple Rotated Coordinate Systems

#### Figure 6.8

A 3-D asterisk created with cylinders built within one vertical and two rotated coordinate systems

#### Nesting Rotated Coordinate Systems

#### Figure 6.9

A 3-D asterisk ball built with cylinders in rotated coordinate systems

#### Translating and Rotating Coordinate Systems

#### Figure 6.10

An archway with pieces of the roof built within translated, rotated coordinate systems

#### Rotating About a Center Point

#### Figure 6.11

The lower arm of a desk lamp, rotated using a center of rotation at the lower end of the arm

#### Figure 6.12

The first and second arms of the desk lamp, each rotated using a center of rotation at the lower end of each arm