1. Honours Graphics 2008 Session 9

2. Today’s focus Physics in graphics Understanding:

3. Physics in graphics The most common application of physics in graphics is a Newtonian physics model for rigid body dynamics Sufficient for a wide variety of problems, including rag-doll physics Others physics systems include: springs, elastics, caustics, fluids, etc.

4. Intermediate: the ~ operator

5. Rigid body dynamics: orientation Use special orthonormal matrix 3 x 3 matrix where each row is of unit length and perpendicular to each other row “Special” means the matrix is not a reflection This matrix represents a rotation (and thus orientation) Use “A” to denote orientation

6. Rigid body dynamics: inertia Objects have volume and mass (and some density distribution) The inertia is described by an inertia tensor, we make use of an inverse inertia tensor in this lecture For a box with mass M and dimensions x, y, and z

7. Rigid body physics: inertia, cont. The inertia of an object in world space is dynamic Simplify the process by working in object space and using a similarity transform to get into world space

8. Rigid body dynamics: initialization Body constants Initial conditions Initial auxiliaries

9. Rigid body dynamics: simulation Compute forces and points of application Compute resultant forces and torques

10. Rigid body dynamics: simulation cont. Integrate quantities

11. Rigid body dynamics: simulation cont. Reorthogonalize Compute auxiliary quantities

12. Intermediate: reorthogonalization

13. Collision response On collision an instantaneous impulse is applied to the object The impulse acts from the point of collision

14. Homework Implement the physics equations described in this session Should be able to model a cube falling onto a flat surface For next session Additional help: http://chrishecker.com/images/b/bb/Gdmphys4.pdf http://chrishecker.com/images/b/bb/Gdmphys4.pdf