Conversion of a World Coordinate Point:

Oblique projections are further described as either cavalier or cabinet projections. Figure shows the projection of a point (x, y, z) to the point (x_p, y_p) onto the view plane. Cavalier and cabinet projections differ by the value utilized for the angle α. Angle α is described as the angle among the oblique projection lines from (x, y, z) to (x_p, y_p) and the line on the view plane from (x, y) to (x_p, y_p). Two commonly utilized values for α = 45°, and α = 63.4°.

Figure: Conversion of a World Coordinate Point (x, y, z) to the Position (x_p, y_p) on the View plane for an Oblique Projection   

While α = 45°, as in Figure, the projection is a cavalier projection. In this projection, a cube shall be displayed with all sides maintaining equal lengths. In a cavalier projection, the foreshortening factor for all of the three principal directions is equal. This property is frequently advantageous since edges may be measured directly. Though, the cavalier projection may make an object look too elongated.