CS 352: Computer Graphics

1. CS 352: Computer Graphics Hierarchical Graphics, Modeling, And Animation

2. Overview • Modeling • Animation • Data structures for interactive graphics • CSG-tree • BSP-tree • Quadtrees and Octrees • Visibility precomputation • Many figures and examples in this set of lectures are from The Art of 3D Computer Animation and Imaging, by I. Kerlow

3. Modeling • The modeling problem • Modeling primitives • Polygon • Sphere, ellipsoid, torus, superquadric • NURBS, surfaces of revolutions, smoothed polygons • Particles • Skin & bones • Approaches to modeling complex shapes • Tools such as extrude, revolve, loft, split, stitch, blend • Constructive solid geometry (CSG) • Hierarchy; kinematic joints • Inverse kinematics • Keyframes

4. Representing objects • Objects represented as symbols • Defined in model coordinates; transformed into world coordinates (M = TRS) glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glTranslatef(…); glRotatef(…); glScalef(…); glutSolidCylinder(…);

5. Primitives • The basic sort of primitive is the polygon • Number of polygons: tradeoff between render time and model accuracy

7. SplineCurves • Linear spline • Cardinal spline • B-spline • Bezier curve • NURBS (non-uniform rational b-spline)

8. Mesh

9. Mesh deformations

10. Sweep • Sweep a shape over a path to form a generalized cylinder

11. Revolution • Revolve a shape around an axis to create an object with rotational symmetry

12. Extrusion • Extrude: grow a 2D shape in the third dimension • Shape is created with a (1D)b-spline curves • Hole was created by subtracting a cylinder

14. Joining Primitives • Stitching, blending

15. Modifying Primitives

16. Subdivision Surfaces • Can set level of polygon subdivision

20. Skin and Bones • Skeleton with joined “bones” • Can add “skin” on top of bones • Automatic or hand-tunedskinning

22. Particles

23. Algorithmic Primitives Algorithms for trees, mountains, grass, fur, lightning, fire, …

25. Geometric model file formats • .obj: Alias Wavefront • .dxf: Autocad • .vrml: Inventor • Dozens more • Can convert between formats • Converting to a common format may lose info…

26. Hierarchical models • When animation is desired, objects may have parts that move with respect to each other • Object represented as hierarchy • Often there are joints with motion constraints • E.g. represent wheels of car as sub-objects with rotational motion (car moves 2 pi r per rotation)

28. DAG models • Could use tree torepresent object • Actually, a DAG (directed acyclicgraph) is better: can re-use objects • Note that each arrow needs aseparate modeling transform • In object-oriented graphics, alsoneed motion constraints with eacharrow

29. Example: Robot • Traverse DAG using DFS (or BFS) • Push and pop matrices along the way (e.g. left-child right-sibling) (joint position parameters?)

31. Modeling Programs • Moray • Shareware • Limited functionality • Easy • Lightwave, Maya • NOT shareware • Very full-featured • Difficult to learn and use • Moray, Maya demos; Lightwave video

32. Animation • Suppose you want the robot to pick up a can of oil to drink. How? • You could set the joint positions at each moment in the animation (kinematics)

33. Inverse Kinematics • You can’t just invert the joint transformations • Joint settings aren’t even necessarily unique for a hand position! • Inverse kinematics: figure out from the hand position where the joints should be set.

34. Using Inverse Kinematics • Specify joint constraintsand priorities • Move end effector(or object pose) • Let the system figureout joint positions • [IK demo]

35. Keyframe Animation • In traditional key frame animation the animator draws several important frames, and helpers do the “inbetweening” or “tweening” • Computer animation is also key-frame based • At key frames, animator positions objects and lights, sets parameters, etc. • The system interpolates parameter values linearly or along a curve • To get from one object pose to the next, inverse kinematics determine joint motions • [Keyframe animation demo]

36. Motion Capture • More realistic motion sequences can be generated by Motion Capture • Attach joint position indicatorsto real actors • Record live action

38. Morphing • Morphing: smoothly shifting from one image to another • First popularized in a Michael Jackson video • Method: a combination of • Warping both images, gradually moving control points from location in first image to location in the second • Cross-fading from first image sequence to second

39. 3D Morphing • Define 3D before andafter shapes as e.g. NURBS surfaces with same number ofcontrol points • Gradually move control points fromfirst setting to second • Specify key poses: e.g. smile, frown, 12 frames of walking motion

40. Combined approaches

41. Example: virtual puppetry • Suppose you want to display virtual puppet shows • How could you animate puppet movements? • How could you control the animations externally?

42. Character Animation • To make computer graphics(or cartoon drawings) come alive…

43. Personality through Pose, Expression, Motion, Timing

45. Object-oriented Graphics • Higher in the programming hierarchy: control models with object-oriented programs robot robbie; robbie.smile(); robbie.walk(270, 5, 3);

46. Data Structures for Modeling • This part of chapter: how some example applications be done efficiently (i.e. topics without a better home…) • Tree-based subdivisions of space • Example 1: how to represent complex objects made up of union, intersection, difference of other objects

47. CSG Tree

48. Application 2: HSR • How to render in 3D with hidden surface removal when you don’t have a hardware depth-buffer? • Can you think of any other ways of removing hidden surfaces quickly? • Principle: a polygon can’t be occluded by another polygon that is behind it.

49. BSP-tree • The painter’s algorithm for hidden surface removal works by drawing all faces, from back to front • How to get a listing of the faces in back-to-front order? • Put them into a binary tree and traverse the tree (but in what order?)

50. BSP Tree Figures • Right is “front” of polygon; left is “back” • In and Out nodes show regions of space inside or outside the object • (Or, just store split pieces of polygons at leaves)