More Object Representations

1
More Object Representations

• Parametric instancing
• Hierarchical modeling
• Constructive Solid Geometry
• Sweep Objects
• Octrees
• Blobs and Metaballs and other such things
• Production rules

2
Parametric Instancing

• Many things, called primitives, are conveniently
  described by a label and a few parameters
• Cylinder Radius, length, does it have end-caps,
  
• Bolts length, diameter, thread pitch,
• Almost anything you buy from a catalogue
• This is a modeling format
• Provide something that knows how to draw the
  object given the parameters
• Depends on the rendering style
• Can be an exact representation

3
Rendering Instances

• Generally, provide a routine that takes the
  parameters and produces a polygonal
  representation
• May include texture maps, normal vectors, colors,
  etc
• OpenGL utility library (GLu) defines routines for
  cubes, cylinders, disks, and other common shapes
• Renderman does similar things, so does POVray,
• The procedure may be dynamic
• Adjust the polygon resolution according to
  distance from the viewer

4
OpenGL Support

• OpenGL defines display lists for encapsulating
  commands that are executed frequently

list_id glGenLists(1) glNewList(list_id,
GL_COMPILE) glBegin(GL_TRIANGLES) draw some
stuff glEnd() glEndList() And
later glCallList(list_id)
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Display Lists (2)

• The list can be
• GL_COMPILE things dont get drawn, just stored
• GL_COMPILE_AND_EXECUTE things are drawn, and
  also stored
• The list can contain almost anything
• Useful for encapsulating lighting set-up commands
• The list cannot be modified after it is compiled
• The whole point is that the list may be
  internally optimized, which precludes
  modification
• For example, sequences of transformations may be
  composited into one transformation

6
Display Lists (3)

• When should you use display lists
• When you do the same thing over and over again
• Advantages
• Cant be much slower than the original way
• Can be much much faster
• Disadvantages
• Doesnt support real parameterized instancing,
  because you cant have any parameters!
• Cant use various commands that would offer other
  speedups
• For example, cant use glVertexPointer()

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Hierarchical Modeling

• A hierarchical model unites several parametric
  instances into one object
• For example a desk is made up of many cubes
• Generally represented as a tree, with
  transformations and instances at any node
• Rendered by traversing the tree, applying the
  transformations, and rendering the instances
• Particularly useful for rigid-body animation
• Human is a hierarchy of body, head, upper arm,
  lower arm, etc
• Animate by changing the transformations at the
  nodes

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Hierarchical Model Example
body

• Vitally Important Point
• Every node has its own local coordinate system.
• This makes specifying transformations much much
  easier.

left arm
xarm
rotate about shoulder upper arm
l
translate (l,0,0) rotate about (0,0,0) lower arm
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OpenGL Support

• OpenGL defines glPushMatrix() and glPopMatrix()
• Takes the current matrix and pushes it onto a
  stack, or pops the matrix off the top of the
  stack and makes it the current matrix
• Note Pushing does not change the current matrix
• Rendering a hierarchy (recursive)

RenderNode(tree) glPushMatrix() Apply node
transformation Draw node contents RenderNode(chi
ldren) glPopMatrix()
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Regularized Set Operations

• Hierarchical modeling is not good enough if
  objects in the hierarchy intersect each other
• Transparency will reveal internal surfaces that
  should not exist
• Computing properties like mass counts the same
  volume twice
• Solution is to define regularized set operations
• Just a fancy name
• Every object must be a closed volume
  (mathematically closed)
• Define mathematical set operations (union,
  intersection, difference, complement) to the sets
  of points within the volume

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Constructive Solid Geometry (CSG)

• Based on a tree structure, like hierarchical
  modeling, but now
• The internal nodes are set operations union,
  intersection or difference (sometimes complement)
• The edges of the tree have transformations
  associated with them
• The leaves contain only geometry
• Motivated by computer aided design and
  manufacture
• Difference in particular is like drilling or
  milling
• Other operations reduce the number of primitives
  required
• A common format in CAD products

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CSG Example
Fill it in!
-
-
scale translate
cube
?
scale translate
scale translate
?
cylinder
cylinder
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Rendering CSG

• Normals and texture coordinates typically come
  from underlying primitives (not a big deal with
  CAD)
• Some rendering algorithms can render CSG directly
• Raytracing (later in the course)
• Scan-line with an A-buffer
• Can do 2D with tesselators in OpenGL
• For OpenGL and other polygon renderers, must
  convert CSG to polygonal representation
• Must remove redundant faces, and chop faces up
• Basic algorithm Split polygons until they are
  inside, outside, or on boundary. Then choose
  appropriate set for final answer.
• Generally difficult, messy and slow
• Numerical imprecision is the major problem

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CSG Summary

• Advantages
• Good for describing many things, particularly
  machined objects
• Better if the primitive set is rich
• Early systems used quadratic surfaces
• Moderately intuitive and easy to understand
• Disadvantages
• Not a good match for polygon renderers
• Some objects may be very hard to describe, if at
  all
• Geometric computations are sometimes easy,
  sometimes hard
• A volume representation (hence solid in the name)
• Boundary (surface representation) can also work

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Sweep Objects

• Define a polygon by its edges
• Sweep it along a path
• The path taken by the edges form a surface - the
  sweep surface
• Special cases
• Surface of revolution Rotate edges about an axis
• Extrusion Sweep along a straight line

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General Sweeps

• The path maybe any curve
• The polygon that is swept may be transformed as
  it is moved along the path
• Scale, rotate with respect to path orientation,
• One common way to specify is
• Give a poly-line (sequence of line segments) as
  the path
• Give a poly-line as the shape to sweep
• Give a transformation to apply at the vertex of
  each path segment
• Difficult to avoid self-intersection

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Rendering Sweeps

• Convert to polygons
• Break path into short segments
• Create a copy of the sweep polygon at each
  segment
• Join the corresponding vertices between the
  polygons
• May need things like end-caps on surfaces of
  revolution and extrusions
• Normals come from sweep polygon and path
  orientation
• Sweep polygon defines one texture parameter,
  sweep path defines the other

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Spatial Enumeration

• Basic idea Describe something by the space it
  occupies
• For example, break the volume of interest into
  lots of tiny cubes, and say which cubes are
  inside the object
• Works well for things like medical data
• The process itself, like MRI or CAT scans,
  enumerates the volume
• Data is associated with each voxel (volume
  element)
• Problem to overcome
• For anything other than small volumes or low
  resolutions, the number of voxels explodes
• Note that the number of voxels grows with the
  cube of linear dimension

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Octrees (and Quadtrees)

• Build a tree where successive levels represent
  better resolution (smaller voxels)
• Large uniform spaces result in shallow trees
• Quadtree is for 2D (four children for each node)
• Octree is for 3D (eight children for each node)

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Quadtree Example
top left
top right
bot left
bot right
Octree principle is the same, but there are 8
children
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Rendering Octrees

• Volume rendering renders octrees and associated
  data directly
• A special area of graphics, visualization, not
  covered in this class
• Can convert to polygons by a few methods
• Just take faces of voxels that are on the
  boundary
• Find iso-surfaces within the volume and render
  those
• Typically do some interpolation (smoothing) to
  get rid of the artifacts from the voxelization
• Typically render with colors that indicate
  something about the data, but other methods exist

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Spatial Data Structures

• Octrees are an example of a spatial data
  structure
• A data structure specifically designed for
  storing information of a spatial nature
• eg Storing the location of fire hydrants in a
  city
• In graphics, octrees are frequently used to store
  information about where polygons, or other
  primitives, are located in a scene
• Speeds up many computations by making it fast to
  determine when something is relevant or not
• Just like BSP trees speed up visibility
• Other spatial data structures include BSP trees,
  KD-Trees, Interval trees,