Hierarchical Models

Leran about hierarchical models!

tree-based representation

each repeated symbol is represented by a separate node

DAG representation

trees are a special case of DAG, we can allow multiple edges leading to the same node as long as there are no cycles

articulated object θ

rotation of base platform

articulated object φ

angle between lower arm and x axis

articulated object ψ

angle between upper arm and x axis

scene graph

complete description of all the geometry (vertices, normals, transformations)

benefit of scene graph 1

defines a complete scene so can be useful for reasoning about the scene

benefit of scene graph 2

hides implementation detail from programmer

benefit of scene graph 3

decouples scene representation from the renderer

CSG

constructive solid geometry

CSG model

based on operations on primitives

bsp tree

binary space partition tree

what does a bsp tree do

describes spatial relationships between objects by partitioning the space using a series of planes

bsp tree note 1

hyperplanes do not need to be parallel to image plane

bsp tree note 2

tree traversal tests against plane at each node to check whether the viewer is in front of or behind the plane

quadtree

a special case of 2d bsp tree that splits an image into rectangles

what are quadtrees often used for

bitmap compression

octrees

extension of quadtrees to 3d space

octrees 2

a special case of bsp trees with axis-parallel planes