What demand ?

Theory:

• basic representations(digitally encode shape)
• sampling & aliasing(acquire & reproduce a signal)
• numerical methods (manipulate signals)
• radiometry & light transport(how light behave)
• perception(how to relate to people)

Systems:

• parallel hetergenous processing
• graphics-specific programming languages
• ...

Activity:

modeling:

Use the coordinates to discribe

Drawing the cube:

How to draw 3D cube to 2D iamge?

1. map 3D to 2D
2. connect 2D points with straight lines

perspective projection:

From the similar triangle,we can get that,$v={\frac{y}{z}}$.Similarly,like our eyes: objects close looks bigger,frr away is bigger.

algorithm:

Generally,z is bigger,iamge is smaller,thus get that :

• camera is at $c=(2,3,5)$
• Convert $(X,Y,Z)$ to $(u,v)$
  1. subtract c from $(X,Y,Z)$ to $(x,y,z)$
  2. divide $(x,y)$ by z to get $(u,v)$

Algorithm details:

1. $c{\ne}(0,0,0)$,we can get the shifting from origin.It's a way to represent relativity
2. if $c=(0,0,0)$,It's the orthogonal projection
3. divide (x,y) by z: inverse ratio about z(distance)
4. c is camera,we can move it ,just like move the camera to get different views of objects

How to draw lines?

Rasterization:

convert continous object to a discrete representation on a raster grid

What pixels should we color ?

Diamond rule:light up pixel if line passes through

• If check every single pixel in the image

  • $O(n^2)$
  • try$O(n)$

• Incremental line rasterization:

v=v1;
for(u=u1;u<=u2;u++)
{
    v+=s
    draw(u,round(v))
}