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CS 352: Computer Graphics. Hierarchical Graphics, Modeling, And Animation. Overview. Modeling Animation Data structures for interactive graphics CSG-tree BSP-tree Quadtrees and Octrees Visibility precomputation

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cs 352 computer graphics

CS 352: Computer Graphics

Hierarchical

Graphics,

Modeling,

And Animation

overview
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
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
representing objects
Representing objects
  • Objects represented as symbols
  • Defined in model coordinates; transformed into world coordinates (M = TRS)

glMatrixMode(GL_MODELVIEW);

glLoadIdentity(); glTranslatef(…);

glRotatef(…); glScalef(…);

glutSolidCylinder(…);

primitives
Primitives
  • The basic sort of primitive is the polygon
  • Number of polygons: tradeoff between render time and model accuracy
spline curves
SplineCurves
  • Linear spline
  • Cardinal spline
  • B-spline
  • Bezier curve
  • NURBS (non-uniform rational b-spline)
sweep
Sweep
  • Sweep a shape over a path to form a generalized cylinder
revolution
Revolution
  • Revolve a shape around an axis to create an object with rotational symmetry
extrusion
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
joining primitives
Joining Primitives
  • Stitching, blending
subdivision surfaces
Subdivision Surfaces
  • Can set level of polygon subdivision
skin and bones
Skin and Bones
  • Skeleton with joined “bones”
  • Can add “skin” on top of bones
  • Automatic or hand-tunedskinning
algorithmic primitives
Algorithmic Primitives

Algorithms for trees, mountains, grass, fur, lightning, fire, …

geometric model file formats
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…
hierarchical models
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)
dag models
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
example robot
Example: Robot
  • Traverse DAG using DFS (or BFS)
  • Push and pop matrices along the way (e.g. left-child right-sibling) (joint position parameters?)
modeling programs
Modeling Programs
  • Moray
    • Shareware
    • Limited functionality
    • Easy
  • Lightwave, Maya
    • NOT shareware
    • Very full-featured
    • Difficult to learn and use
  • Moray, Maya demos; Lightwave video
animation
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)
inverse kinematics
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.
using inverse kinematics
Using Inverse Kinematics
  • Specify joint constraintsand priorities
  • Move end effector(or object pose)
  • Let the system figureout joint positions
  • [IK demo]
keyframe animation
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]
motion capture
Motion Capture
  • More realistic motion sequences can be generated by Motion Capture
  • Attach joint position indicatorsto real actors
  • Record live action
morphing
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
3d morphing
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
example virtual puppetry
Example: virtual puppetry
  • Suppose you want to display virtual puppet shows
    • How could you animate puppet movements?
    • How could you control the animations externally?
character animation
Character Animation
  • To make computer graphics(or cartoon drawings) come alive…
object oriented graphics
Object-oriented Graphics
  • Higher in the programming hierarchy: control models with object-oriented programs

robot robbie;

robbie.smile();

robbie.walk(270, 5, 3);

data structures for modeling
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
application 2 hsr
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.
bsp tree
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?)
bsp tree figures
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)
traversing a bsp tree
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?
building a bsp tree
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…
bsp tree summary
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]
application 3 handling large spatial data sets
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
quadtree
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!
octrees
Octrees
  • Generalize to cutting up a cube into 8 sub-cubes, each of which may be E, F, or P (and subdivided)
  • Much more efficientthan a 3D array ofcells for 3Dvolumetric data
quadtree algorithms
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?
applications of octrees
Applications of Octrees
  • Contour finding in MRI data
  • 3D scanning and rendering
  • Efficient ray tracing
  • Intersection, collision testing
research in visibility
Research in Visibility
  • Can we figure out in advance what will be visible from each viewpoint?
viewer centered representation
Viewer-centered representation
  • Viewer-centered object representations: representation not of volume of space filled but appearance from all viewpoints
occlusion in view space
Occlusion in view space
  • Occlusion in view space is subtraction
events
Events
  • Events: boundaries in viewpoint space where faces appear or disappear
aspect graph
Aspect Graph
  • Aspect graph: a graph with a node for every topologically distinct view of an object, with edges connecting adjacent views
aspect graph varieties
Aspect graph varieties
  • Aspect graphs can be constructed for
    • 3D: space
    • 2D: multiple axis rotations or planar motions
    • 1D: single-axis rotations
1d aspect graph results
1D Aspect Graph Results
  • Useful for rotations without Z-buffer hardware!
  • Not so useful for more viewer freedom, modern graphics hardware
conservative visibility preprocessing
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
weak visibility subdivision
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
conservative visibility preprocessing on a grid
Conservative Visibility Preprocessing on a Grid
  • Divide viewing space into a 3D (or 2D) grid
  • Compute a conservative display list for each cell
conservative visibility algorithm
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!)
perspective
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
summary
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