Perspective Projection

field-of-view and aspect ratio

由fovY和距离、高度之间相互换算

Canonical cube to screen

1. What's a screen ?

• An array of pixels
• Size of the array : resolution(分辨率)
• A typical kind of raster display

2. Raster==screen in German

• Rasterize==drawing on the screen

3. Pixel

• A pixel is a square with uniform color
• color is a mixture of red,green and blue

Defining the screen space

indeces are from $(0,0)$ to$(width-1, height-1)$

Transform

1. Irrelevant to z
2. Transform in xy plane
3. Viewport transform matrix:

Rasterization:

Triangles-Fundamental Shape Primitives

Why triangles?

• Basic polygen
• Break up other polygens
• Guaranteed to planar
• Well defined for interpolating

Sampling

Evaluating a function at a point is sampling.
We can discretize a function by sampling.

Define Binary Function

for(int x=0; x< x_max;x++)
    for(int y=0; y< y_max; y++ )
        inside(triangle , x+0.5 , y+0.5 )

Using a Bounding Box

No need to check all pixels

Incremental Triangle Traversal

suitable for thin and rotated triangles