Parallel projections are very useful for engineers, and draftsmen to create working drawings, blueprints, schematics or working drawings of objects that preserve its shape and scale.
Points on an object are projected to the view plane along parallel lines (projectors).
The view plane (projection plane) ax + by + cz + d = 0 is intersected with the projector drawn from the object point along a fixed vector , i.e., All the points on the object are projected to the view plane along parallel lines. For example, in the figure shown below, the projection of is on the view plane whose normal is .
The views formed by parallel projections varies according to the angle that the direction of projection makes with the projection plane. If the projection is perpendicular to the image plane, i.e., is along the same direction as , then that projection is called the orthographic projection.
The projection is oblique when the projection is not perpendicular to the image plane.
provided (what does this mean?)
Find a matrix for parallel projections onto the plane
Substituting the values of in equation 6
Substituting the values of t in equation 18, 19, 20 and solving
The matrix for orthographic parallel projection is then given by