01 Introduction

Generate a realistic drawing of a cube

To draw a cube, we ask

• Modeling: How do we describe the cube
• Rendering: How do we visualize the model

Modeling

Suppose we construct a cube that

• centered at the origin (0, 0, 0)
• has dimensions $2\times 2\times 2$
• edges are aligned with x / y / z axes

One way to think is to list out the coordinates of the cube vertices, but they are just 8 points, we need more information to capture the shape.

Now, we ask the edges, which two points are connected.

Then we have an encoding data, telling us the 3D geometry of the cube

• Vertices: A(1, 1, 1), B(-1, 1, 1), C(1, -1, 1), D(-1, -1, 1), E(1, 1, -1), F(-1, 1, -1), G(1, -1, -1), H(-1, -1, -1)
• Edges connected: AB, CD, EF, GH, AC, BD, EG, FH, AE, CG, BF, DH

Now the question is how do we render it into 2D images? This requires two operations

1. Map 3D vertices into 2D points
2. Connect 2D points

Perspective Projection