1. 1 Scene Graphs Week 4.2 ©Anthony Steed 1999-2002

2. 2 Scene Graph Overview n Building Scene Structures n Traversal n Examples n Instancing and Re-Use n More Transformations

3. 3 Concept of Scene Graph n Objects placed relative to one another n Objects made of similar components n Directed acyclic graph root

4. 4 Use for Animation/Modelling

5. 5 n One object has a local transformation relative to its parent shoulder is translation (0 1 0) from base upper arm is translation (0 3 0) from shoulder elbow is translation (0 3 0) from upper arm fore arm is rotation Z by 90 then translation (0 2 0)

6. 6 Rendering Traverse n Must get object definitions in WC before passing to camera n For object under Base p.B is in WC n “inherit” matrices down stack n So for object under shoulder p.SB is in WC (p.S is in base coordinates)

7. 7 In general n On traverse “push” on graph descend “pop” on graph ascend n Combined matrix is current transform (CTM)

8. 8 Sharing Nodes n E.G. One table many places n Table1 has CTM T1T0 n Table1 has CTM T2T0 table table2 table1 T1 T2 T0

9. 9 Spherical Coordinates n Represent a point on a using two angles and . Where r = length(x,y,z) Z P(x,y,z)   X Y Q O Q is projection of P onto XY plane is angle between X axis and OQ  is angle between OP and Z axis

10. 10 Spherical Coordinates n Length OQ = r sin(  ) n So x = r sin(  )cos( ) y = r sin(  )sin( ) z = r cos(  )

11. 11 Rotation About an Arbitrary Axis Z X Y O p1 p2 

12. 12 … 1. Translate p1 so it is at the origin 2. Let p3 = p2-p1 (new position of p2) find spherical co-ordinate of p3 (r, , ) 3. Rotate about Z by - to bring p3 into ZX plane 4. Rotate about Y by -  to bring p3 onto Z axis 5. Now rotate about Z by  6. Invert steps 4-1

13. 13 … Z Y O p1 p2 Z Y O p3 StartTranslate

14. 14 … Z Y p3 Rotate1 Z Y p3 Rotate2 

15. 15 … Z Y p3 After Steps 1-4 n Now we apply the transformation we are after n Invert steps 4-1

16. 16 Scene Graph Recap n Use of scene graph to model environments n Notion of render traversal and the current transformation matrix n Instancing and sharing of nodes n Rotation of objects around an arbitrary axis