1. CAP 4703 Computer Graphic Methods Prof. Roy Levow Chapter 9

2. Hierarchical and Object- Oriented Modeling  Problem is how to organize related elements of an object to be rendered  Hierarchical representation –Tree with subtrees representing components –Object-Oriented Model

3. Problems with Linear Models  How to represent dependencies –Wheels of a car move with the car –Position of hand depends on position of arm which depends on position of body, etc.

4. Tree Structure  Shows dependencies but introduces redunancy –All wheels of a car are the same but drawn in different positions or from different views  Can generalize to directed acyclic graph, DAG  Example: Robot Arm

5. Traversal  Can traverse as tree or DAG  Position of components depending on position of other components functions in stack fashion  Can save transform matrix, alter sub components, and then restore matrix when returning to base component  Can add special nodes to save/restore transform matrix

6. Animation  Kinematics –Describe position of parts based on joint angles  Dynamics –Describe changes in terms of forces applied –Physics engine may be used

7. Animation.2  Consider following problem –Start figure in one position –Determine final position  How can we change articulation angles to transform between the two? –Inverse kinematics / dynamics –Generally no simple function

8. Animation.3  Approximate solutions –Key frame animation  design key frames  interpolate angles to transform between, tweening –Morphing  Interpolate shapes

9. Object-Oriented Approach  Define classes for components –Most easily built on class version of OpenGL  Example classes in text, pp437-462  GLT, OpenGL C++ Toolkit GLT