3D Projections

CSC-214 · Semester III · Computer Graphics

intermediate25 minAvailable

3D Projections

Rotate a cube in 3D and project it onto the 2D grid.

rotate X: 30°rotate Y: 40° perspective projection

Orthographic vs perspective

Orthographic: parallel projectors — depth has no effect on size, used in engineering drawings. Perspective: projectors converge on the eye; distant edges shrink, giving depth cues. Both share the same rotation stage: yaw (Y) then pitch (X).

Pipeline

model coords → rotate → project → rasterize 93 pixels

Lab brief

Objective

Project a 3D wireframe object onto a 2D view plane with parallel and perspective projections and compare the results.

Theory & concepts

Projection maps 3D camera coordinates to 2D view coordinates. Orthographic projection drops the depth coordinate and keeps object sizes constant; perspective projection divides by depth so distant parts shrink. The visualization renders a wireframe object with both projections and lets you orbit the camera.

Rendering diagram…

Parallel and perspective projection paths

# orthographic:  (x, y) -> screen, z discarded
screen = (x, y)

# perspective with center of projection at origin, d = focal distance
screen = (x * d / z, y * d / z)
# far points have large z, so they shrink

Orthographic keeps parallel edges parallel - used for engineering drawings
Perspective produces foreshortening and vanishing points - realistic views
The perspective divide x * d / z is what makes depth compress distance

Prerequisites

Lesson: The 3D viewing pipeline
Lesson: 3D rotation about coordinate axes

Instructions

1Load a wireframe object (cube or house) into the 3D scene.
2Switch between parallel and perspective projection and compare the two images.
3Orbit the camera and watch the projected wireframe change.
4Zoom the camera in perspective mode and observe the change in foreshortening.
5Rotate the object and confirm that parallel edges stay parallel only in orthographic view.
6Overlay the perspective image on the orthographic one and mark where they diverge.

Tasks

Cube both ways
Project a cube with both projections and describe the visual differences.
Convergence test
Confirm that parallel rails converge toward a vanishing point only in perspective.
Focal length
Change d and describe how the perspective distortion changes.

Self-check

The student distinguishes parallel and perspective projection correctly.
The student explains the perspective divide and why far objects shrink.
The student describes when each projection is appropriate.

Environment

wireframe sceneparallel/perspective togglecamera orbitfocal length controloverlay comparison