CS488 - Introduction to Computer Graphics - Lecture 16

Comments and Questions

Review

  1. Hidden surface removal
  2. Mouse interaction

Hierarchical Models

Suppose you are modelling classical temples. How do you do it?

  1. Open up Vitruvius. You will find that all temples are assumbled from a few basic parts, such as
  2. You don't know the words, but there are drawings with dimensions.
  3. There are rules for making them bigger and smaller, so you think of scaling matrices.
  4. There are rules for putting them in different orientations, so you think of rotation matrices.
  5. There are rules for placing them in different locations, so you think of translation matrices.

At this point you can make a temple, but it's a lot of work. To make it easier, divide and conquer

  1. Column = base + shaft + capital. Reuse this as a unit.
  2. Entablature = architrave + frieze + cornice. Reuse this as a unit.

You get the idea. The result is

What does this look like?

Scene -> First temple -> Stylobate
                      -> First column -> Generic column -> Base
                                                        -> Shaft
                                                        -> Capital
                      -> Second column
                      -> ...
                      -> Entablature
      -> Second temple /
                       -> First column /

Make a scene

proc scene
  multMatrix(P)
  multMatrix(V)
  pushMatrix( )
    multMatrix(T1)
    temple( )
  popMatrix( )
  pushMatrix( )
    multMatrix(T2)
    temple( )
  popMatrix( )
  etc.

Make a temple

proc temple( )
  pushMatrix( )
    multMatrix(SB)
    stylobate( )
  popMatrix( )
  pushMatrix( )
    multMatrix(C1)
    column( )
  popMatrix( )
  pushMatrix( )
    multMatrix(C2)
    column( )
  popMatrix( )
  ...
  pushMatrix( )
    multMatrix(En)
    entablature( )
  popMatrix( )

We don't want always to write a program, so we encapsulate the program as data.

Traverse a DAG

traverse( root )

proc traverse( node ) {
  if ( primitve( node ) ) {
    draw( node )
  } else { for each child {
    traverse( child )
  }
}

Build a DAG 

scene = gr.transform( )

temple1 = gr.transform( )
gr.add_child( temple1, scene )
gr.set_transform( temple1, gr.translation(...)*gr.rotation(...)
gr.set_material( temple1, marble )
...

stylobate1 = gr.transform( )
floor = gr.cube( )
gr.add_child( stylobate, floor )
gr.add_child( temple1, stylobate )
gr.set_transform( stylobate, gr.scaling(...) )
column1 = gr.transform( )
gr.add_child( temple1, column1 )
gr.set_transform( column1, gr.translation(...)*gr.scaling(...)
...

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