Basic 3D

Project a Cube

Project all eight cube vertices with one exact perspective divide and connect the projected edges.

Example

Project an eight-vertex cube with one perspective divide.

highlighted = computed this step

Step 1 — Cube vertices

Set up the exact input values.

cube vertices{’A’: (Fraction(1, 1), Fraction(1, 1), Fraction(1, 1)), ’B’: (Fraction(3, 1), Fraction(1, 1), Fraction(1, 1)), ’C’: (Fraction(3, 1), Fraction(3, 1), Fraction(1, 1)), ’D’: (Fraction(1, 1), Fraction(3, 1), Fraction(1, 1)), ’E’: (Fraction(1, 1), Fraction(1, 1), Fraction(2, 1)), ’F’: (Fraction(3, 1), Fraction(1, 1), Fraction(2, 1)), ’G’: (Fraction(3, 1), Fraction(3, 1), Fraction(2, 1)), ’H’: (Fraction(1, 1), Fraction(3, 1), Fraction(2, 1))}\begin{array}{c|c}\text{cube vertices}&\text{\{'A': (Fraction(1, 1), Fraction(1, 1), Fraction(1, 1)), 'B': (Fraction(3, 1), Fraction(1, 1), Fraction(1, 1)), 'C': (Fraction(3, 1), Fraction(3, 1), Fraction(1, 1)), 'D': (Fraction(1, 1), Fraction(3, 1), Fraction(1, 1)), 'E': (Fraction(1, 1), Fraction(1, 1), Fraction(2, 1)), 'F': (Fraction(3, 1), Fraction(1, 1), Fraction(2, 1)), 'G': (Fraction(3, 1), Fraction(3, 1), Fraction(2, 1)), 'H': (Fraction(1, 1), Fraction(3, 1), Fraction(2, 1))\}}\end{array}

Step 2 — Front face

Compute the highlighted value.

front projection((1, 1), (3, 1), (3, 3), (1, 3))\begin{array}{c|c}\text{front projection}&\hlmath{\text{((1, 1), (3, 1), (3, 3), (1, 3))}}\end{array}
Projected cubeEach cube vertex is projected by dividing x and y by z.ABCD

Step 3 — Back face

Compute the highlighted value.

back projection((1/2, 1/2), (3/2, 1/2), (3/2, 3/2), (1/2, 3/2))\begin{array}{c|c}\text{back projection}&\hlmath{\text{((1/2, 1/2), (3/2, 1/2), (3/2, 3/2), (1/2, 3/2))}}\end{array}
Projected cubeEach cube vertex is projected by dividing x and y by z.ABCDEFGH

Step 4 — Edges

Compute the highlighted value.

projected edges((A, B), (B, C), (C, D), (D, A), (E, F), (F, G), (G, H), (H, E), (A, E), (B, F), (C, G), (D, H))\begin{array}{c|c}\text{projected edges}&\hlmath{\text{((A, B), (B, C), (C, D), (D, A), (E, F), (F, G), (G, H), (H, E), (A, E), (B, F), (C, G), (D, H))}}\end{array}
Projected cubeEach cube vertex is projected by dividing x and y by z.ABCDEFGH
project-a-cube A cube projection repeats the same perspective divide for each vertex, then draws the edges between the projected points.