Part II - 3D Geometric Transformations

Hearn and Baker – Chapter 5

Right Handed

Left Handed

### Rotation

• Convention => counterclockwise rotation
• Three axes to rotate about
• Axes convention: look down axis’s positive direction

• Rz

• Rx

• Ry

### Composite transformations

e.g. Fixed-point Scaling

### Object Creation

·       Extrusion

o      Begin with points in xz plane (x , 0 , z)

o      Create second set of points by adding a value to y – in effect – translating y coordinates.

e.g create a cube from a square in xy plane by adding 1 to z coordinate

 Starting x y z 1 0 0 0 2 0 1 0 3 1 1 0 4 1 0 0 Extruded 5 0 0 1 6 0 1 1 7 1 1 1 8 1 0 1

·       Surface-of-Revolution

o      Begin with points in plane (e.g. xy plane)

o      Rotate points about an axis (e.g. y-axis) at angle intervals, say 20 degrees

Data for above Figure

Angle

x1

y1

z1

x2

y2

z2

0

0.750

0.250

0.000

0.25

0.750

0.000

60

0.375

0.250

-0.650

0.125

0.750

-0.217

120

-0.375

0.250

-0.650

-0.125

0.750

-0.217

180

-0.750

0.250

0.000

-0.25

0.750

0.000

240

-0.375

0.250

0.650

-0.125

0.750

0.217

300

0.375

0.250

0.650

0.125

0.750

0.217

360

0.750

0.250

0.000

0.25

0.750

0.000