Perspective in Two Dimensions for Computer Graphics

Abstract

Computer graphics perspective is based on photography, the pin-hole camera model. This thesis examines the perspective as practiced by artists, who develop the picture geometry within the planar surface of the canvas. Their approach is flexible, depth is simulated with planar composition as the primary geometry. Renaissance artists discovered construction methods to draw the foreshortening of realistic pictures: the construction of a tiled floor in perspective was fundamental.

This thesis presents the framework, a computer program, I developed to create the perspective of pictures based on the geometry practices of artists. Construction lines on the image plane simulate the 3D geometry of the pictorial space; cartoons of foreground elements are manipulated in 2D within the picture perspective; projected shadows, examples of double projection, are also included. A formalism, reformulating algebraically the straight-edge and compass evaluations, generalizes the planar geometry that solves the challenge of depicting 3D. A revised Painter’s algorithm produces the occlusions between the picture elements from sequencing them from their definitions on the canvas.