MATH 306

Chapter 1

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

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.

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.

• Length: 7 cm• Height: 2 cm• Width: 3 cm

Central projection

• One vanishing point

• Two vanishing points

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.

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.

Two vanishing points

Orthogonal projections

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

Orthogonal projections

• example

Your turn! Front, top, right

Oblique perspective

Axonometric perspective: back, bottom and left.

Coded blue print