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

2. Overview Modeling Animation Data structures for interactive graphics
Interactive Computer Graphics
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
Modeling is getting good enough that whole movies can be made with virtual actors

3. Modeling The modeling problem Modeling primitives
Interactive Computer Graphics
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
Interactive Computer Graphics
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
Interactive Computer Graphics
Primitives
The basic sort of primitive is the polygon
Number of polygons: tradeoff between render time and model accuracy

6. Interactive Computer Graphics
For real-time graphics, you may have to limit model size

7. Spline Curves Linear spline Cardinal spline B-spline Bezier curve
Interactive Computer Graphics
Spline Curves
Linear spline
Cardinal spline
B-spline
Bezier curve
NURBS (non-uniform rational b-spline)

8. Interactive Computer Graphics
Mesh

9. Mesh deformations Interactive Computer Graphics
Used for fractal landscapes, mountains, etc.

10. Sweep Sweep a shape over a path to form a generalized cylinder
Interactive Computer Graphics
Sweep
Sweep a shape over a path to form a generalized cylinder

11. Interactive Computer Graphics
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
Interactive Computer Graphics
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

13. Interactive Computer Graphics
This model was created by duplicating, scaling, and extruding an arc. Then texture mapping was applied.

14. Interactive Computer Graphics
Joining Primitives
Stitching, blending

15. Interactive Computer Graphics
Modifying Primitives

16. Subdivision Surfaces Can set level of polygon subdivision
Interactive Computer Graphics
Subdivision Surfaces
Can set level of polygon subdivision
Relatively new type of primitive, subdivision surface, gives you the advantages of working with polygons and the smoothness of parameterized surfaces. Set subdivision level

17. Interactive Computer Graphics

18. Interactive Computer Graphics
This short video – Geri’s Game – a testbed for subdivision surfaces and clothing dynamics in Pixar’s Renderman software

19. Interactive Computer Graphics

20. Skin and Bones Skeleton with joined “bones”
Interactive Computer Graphics
Skin and Bones
Skeleton with joined “bones”
Can add “skin” on top of bones
Automatic or hand-tuned skinning

21. Interactive Computer Graphics
Automatic vs. manual skinning

22. Particles Interactive Computer Graphics
Particle systems emit particles at certain rates, can apply gravity or other forces, can have collectors, etc. Used for smoke, waterfalls, fire, tornadoes, etc.

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

24. Interactive Computer Graphics

25. Geometric model file formats
Interactive Computer Graphics
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…
In this DXF export, first the holes are connected to the border. Then the concave shape is decomposed into several concave parts, which are cut into squares and then triangles.

26. Interactive Computer Graphics
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)

27. Interactive Computer Graphics
One object with several mirrored, rotated instances

28. DAG models Could use tree to represent object
Interactive Computer Graphics
DAG models
Could use tree to represent object
Actually, a DAG (directed acyclic graph) is better: can re-use objects
Note that each arrow needs a separate modeling transform
In object-oriented graphics, also need motion constraints with each arrow

29. Example: Robot Traverse DAG using DFS (or BFS)
Interactive Computer Graphics
Example: Robot
Traverse DAG using DFS (or BFS)
Push and pop matrices along the way (e.g. left-child right-sibling) (joint position parameters?)
How would traversal work? What would a node visit do?

30. Interactive Computer Graphics

31. Modeling Programs Moray Lightwave, Maya
Interactive Computer Graphics
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. Interactive Computer Graphics
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
Interactive Computer Graphics
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
Interactive Computer Graphics
Using Inverse Kinematics
Specify joint constraints and priorities
Move end effector (or object pose)
Let the system figure out joint positions
[IK demo]

35. Interactive Computer Graphics
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. Interactive Computer Graphics
Motion Capture
More realistic motion sequences can be generated by Motion Capture
Attach joint position indicators to real actors
Record live action

37. Interactive Computer Graphics

38. Morphing Morphing: smoothly shifting from one image to another
Interactive Computer Graphics
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. Interactive Computer Graphics
3D Morphing
Define 3D before and after shapes as e.g. NURBS surfaces with same number of control points
Gradually move control points from first setting to second
Specify key poses: e.g. smile, frown, 12 frames of walking motion

40. Combined approaches Interactive Computer Graphics
The expressions on the face of this virtual actress were created with a combination of facial motion capture and biomedical simulations of muscle and tissue

41. Example: virtual puppetry
Interactive Computer Graphics
Example: virtual puppetry
Suppose you want to display virtual puppet shows
How could you animate puppet movements?
How could you control the animations externally?
Animate movements with IK or pose setting and 3D morphing
Control animations: manual settings inputs and keyframe animation – or puppet input device

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

43. Personality through Pose, Expression, Motion, Timing
Interactive Computer Graphics
Personality through Pose, Expression, Motion, Timing
Drunken pig: boring, little structure, blank stare, monotonous body poses, erratic timing
Perky girl: well-defined, many shapes, long limbs, lots of mobility, ample motions, varied and distinct facial expressions, wide-ranging, sculptural body oses; alive, rhythmic, gracious timing
Paranoid guy: outer shape simple but varied; outer shape cartoony; internal structure rubbery; facial expression limited to eyes; body poses expressive but small repertoire; timing quick, ahead of the beat

44. Interactive Computer Graphics

45. Object-oriented Graphics
Interactive Computer Graphics
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
Interactive Computer Graphics
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. Interactive Computer Graphics
CSG Tree

48. Interactive Computer Graphics
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. Interactive Computer Graphics
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”
Interactive Computer Graphics
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)

51. Interactive Computer Graphics
Traversing a BSP tree
Binary Space Partition tree: a binary tree with a polygon at each node
Children in left subtree are behind polygon
Children in right subtree are in front of polygon
Traversing a BSP-tree:
If null pointer, do nothing
Else, draw far subtree, then polygon at current node, then near subtree
Far and near are determined by location of viewer
Runtime of traversal?
Drawbacks?

52. Building a BSP tree Inserting a polygon:
Interactive Computer Graphics
Building a BSP tree
Inserting a polygon:
If tree is empty make it the root
If polygon to be inserted intersects plane of polygon of current node, split and insert half on each side recursively.
Else insert on appropriate side recursively
Problem: the number of faces could grow dramatically
Worst case (O(n2))…but usually it doesn’t grow too badly in practice…

53. Interactive Computer Graphics
BSP-tree Summary
Returns polygons not necessarily in sorted order, but in an order that is correct for back-to-front rendering
Widely used when Z-buffer hardware may not be available (e.g. game engines)
Guarantees back-to-front rendering for alpha blending
Works well (linear-time traversals) in the number of split polygons
[And we hope the number of polygons doesn’t grow too much through splitting]

54. Application 3: Handling Large Spatial Data Sets
Interactive Computer Graphics
Application 3: Handling Large Spatial Data Sets
Example application: image-based rendering
Suppose you have many digital images of a scene, with depth information for pixels
How to find efficiently the points that are in front?
Other applications:
Speeding up ray-tracing with many objects
Rendering contours of 3D volumetric data such as MRI scans

55. Interactive Computer Graphics
Quadtree
Quadtree: divide space into four quadrants. Mark as Empty, Full, or Partially full.
Recursively subdivide partially full regions
Saves much time, space over 2D pixel data!

56. Interactive Computer Graphics
Quadtree Structure

57. Interactive Computer Graphics
Octrees
Generalize to cutting up a cube into 8 sub-cubes, each of which may be E, F, or P (and subdivided)
Much more efficient than a 3D array of cells for 3D volumetric data

58. Quadtree Algorithms How would you render a quadtree shape?
Interactive Computer Graphics
Quadtree Algorithms
How would you
render a quadtree shape?
find the intersection of a ray with a quadtree shape?
Take the union of two quadtrees?
Intersection?
Find the neighbors of a cell?

59. Applications of Octrees
Interactive Computer Graphics
Applications of Octrees
Contour finding in MRI data
3D scanning and rendering
Efficient ray tracing
Intersection, collision testing

60. Research in Visibility
Interactive Computer Graphics
Research in Visibility
Can we figure out in advance what will be visible from each viewpoint?

61. Viewer-centered representation
Interactive Computer Graphics
Viewer-centered representation
Viewer-centered object representations: representation not of volume of space filled but appearance from all viewpoints

62. Occlusion in view space
Interactive Computer Graphics
Occlusion in view space
Occlusion in view space is subtraction

63. Interactive Computer Graphics
Events
Events: boundaries in viewpoint space where faces appear or disappear

64. Interactive Computer Graphics
Aspect Graph
Aspect graph: a graph with a node for every topologically distinct view of an object, with edges connecting adjacent views

65. Aspect graph varieties
Interactive Computer Graphics
Aspect graph varieties
Aspect graphs can be constructed for
3D: space
2D: multiple axis rotations or planar motions
1D: single-axis rotations

66. 1D Aspect Graph for Rotation
Interactive Computer Graphics
1D Aspect Graph for Rotation

67. Interactive Computer Graphics
1D Aspect Graph Results
Useful for rotations without Z-buffer hardware!
Not so useful for more viewer freedom, modern graphics hardware

68. Conservative Visibility Preprocessing
Interactive Computer Graphics
Conservative Visibility Preprocessing
Q. can we take advantage of z-buffer?
Definition: weak visibility. A polygon is weakly visible from a region if any part of the polygon is visible from any viewpoint in the region
Conservative visibility preprocessing: computing in advance a (super-)set of the polygons that are weakly visible from some region
Rendering with Z-buffer yields correct image, but it’s faster since fewer polygons are drawn

69. Weak Visibility Subdivision
Interactive Computer Graphics
Weak Visibility Subdivision
Given an object and a wall, find the region of space from which the wall occludes the object
Divide space into regions, where each edge represents some object appearing or disappearing

70. Conservative Visibility Preprocessing on a Grid
Interactive Computer Graphics
Conservative Visibility Preprocessing on a Grid
Divide viewing space into a 3D (or 2D) grid
Compute a conservative display list for each cell

71. Conservative visibility algorithm
Interactive Computer Graphics
Conservative visibility algorithm
Initialize a display list for each grid cell
Algorithm: for each object, wall, and cell
If the object is not weakly visible from the cell, remove from cell’s display list
You can churn away at this computation as long as you like, increasing runtimes, but you can stop at any time with usable results. (Results improve over time!)

72. Perspective What good did this visibility research do for the world?
Interactive Computer Graphics
Perspective
What good did this visibility research do for the world?
It wasn’t enough for me
I left graphics research and went into digital libraries
Left University of Pittsburgh and went to Wheaton College

73. Interactive Computer Graphics
Summary
3D modeling uses advanced primitives and ways of cutting, joining them
Inverse kinematics determines joint position from end effector motions
Keyframe animation involves important poses and inbetweening
3D morphing animates surface control points
3D spatial subdivision trees include CSG-trees, BSP-trees, Quadtrees, and Octrees
Visibility preprocessing speeds walkthrough