1. MATH 306
Chapter 1

2. Projection and perspective
Representing three-dimensional figures in a plane (flat surface).
Parallel Projection
Oblique or Cavalier Perspective
Axonometric Perspective
Central Projection
One vanishing point
Two vanishing points

3. Parallel projection Cavalier or Oblique
1. Draw the front view of the object.
2. Draw an oblique line (vector), called receding line.
3. All measurements drawn backwards are half or smaller than the original measurement.
4. 30 or 45 degrees is the angle for all lines drawn backwards.
5. Lines that should not be seen are dotted.

5. Parallel projection Axonometric X-axis = width Y-axis = length
Z-axis = height
Determine the width, height and length of the solid.
Draw lines parallel to each axis from each determined point or vertex.

6. Length: 7 cm
Height: 2 cm
Width: 3 cm

7. Central projection
One vanishing point
Two vanishing points

8. One vanishing point
The face of the solid is parallel to the plane of the page.
Connect all vertices of the solid to the vanishing point on the horizontal line.

9. One vanishing point
Draw lines parallel to the lines of the original solid (at a distance you think is ok for good depth perception).
Dotted lines are used for any edges that are not normally visible in a solid.

12. Two vanishing points

17. Orthogonal projections
Different views of an object on a plane (flat surface).
Top view
Left view
Right view
Bottom view
Front view
Back view

18. Orthogonal projections
example

19. Your turn! Front, top, right

20. Oblique perspective

21. Axonometric perspective: back, bottom and left.

22. Coded blue print