- Bolts: length, diameter, thread pitch,

1

• - Bolts length, diameter, thread pitch,
• - A modeling format
• -- Provide software that knows how to draw the
  object given the parameters, or knows how to
  produce a polygonal mesh
• -- How you manage the model depends on the
  rendering style
• -- Can be an exact representation
• Rendering Instances
• A routine takes parameters and produces a
  polygonal representation
• Brings parametric instancing into the rendering
  pipeline
• May include texture maps, normal vectors, colors,
  etc
• OpenGL utility library (GLu) defines routines for
  cubes, cylinders, disks, and other common shapes
• The procedure may be dynamic - For example,
  adjust the polygon resolution according to
  distance from the viewer
• Display List
• The list cannot be modified after it is compiled
• When to use display lists 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 (except
  transformations)

• KeyFrame animation
• Underlying technique is interpolation
• The in-between frames are interpolated from the
  keyframes
• Originally done by armies of underpaid animators
• Interpolating splines are smooth curves that
  interpolate their control points
• Perfect for keyframe animation
• Time is directly associated with the parameter
  value, controlling speed
• Anything can be keyframed and interpolated
  Position, Orientation, Scale, Deformation, Patch
  Control Points (facial animation), Color, Surface
  normal
• Special interpolation schemes for things like
  rotations
• - Use quaternions to represent rotation and
  interpolate between quaternions
• Control of parameterization controls speed of
  animation
• Motion Blur
• Extract data from real-world people acting out a
  scene
• Optical take video and extract motion
• Magnetic/Radio attach magnets, transponders and
  use sensors to get.
• Mechanical methods of extracting motion (for
  small motions)
• all are limited in the complexity of the scenes
  they can capture
• - Solution Break scenes into smaller pieces and
  re-construct later
• Procedural

• Blobs and Metaballs
• Define the location of some points
• May be to define a function on the distance to a
  given point, (x,y,z), Sum these functions up,
  and use them as an implicit function
• Question If I have two special points, in 2D,
  and my function is just the distance, what shape
  results?
• More generally, use Gaussian functions of
  distance, or other forms
• - Various results are called blobs or metaballs
• Rendering Implicit Surfaces
• Some methods can render them directly
• - Raytracing - find intersections with Newtons
  method
• For polygonal renderer, must convert to polygons
• Advantages
• Good for organic looking shapes eg human body
• Reasonable interfaces for design
• Disadvantages
• Difficult to render and control when animating
• Being replaced with subdivision surfaces, it
  appears
• Production rules Model by a set of rules to
  follow to generate it
• Works best for things like plants
• - Start with a stem

• - Interpolate between the two nearest mipmaps
  using nearest or interpolated points from each,
  GL_LINEAR_MIPMAP_LINEAR
• BoundaryglTexParameteri(GL_TEXTURE_2D,GL_TEXTURE_
  WRAP_S, p)
• When Mapping outside the texture image
• - Repeat Assume the texture is tiled GL_REPEAT
• - Clamp to Clamp to Edge the texture
  coordinates are truncated to valid values, and
  then used - GL_CLAMP
• - Can specify a special border color
  GL_TEXTURE_BORDER_COLOR, R,G,B,A
• Procedural Texture Use a function to computes
  the texture value on the fly
• Advantages
• - Near-infinite resolution with small storage
  cost
• - Idea works for many other things
• Disadvantage being slow in many cases
• Other Type
• Environment mapping looks up incoming
  illumination in a map -- Simulates reflections
  from shiny surfaces
• Bump-mapping computes an offset to the normal
  vector at each rendered pixel -- No need to put
  bumps in geometry, but silhouette looks wrong
• Displacement mapping adds an offset to the
  surface at each point -- Like putting bumps on
  geometry, but simpler to model
• Modeling
• Overview
• Modeling is the process of describing an object
• Sometimes the description is an end in itself

• Shading
• Local Shading Models
• Local shading models provide a way to determine
  the intensity and color of a point on a surface
• - Fast and Simple to compute
• - Local and not required the knowledge of the
  entire scene, because not consider other objects
• What they capture Approximate effects of global
  lighting
• - Direct illumination from light sources
• - Diffuse and Specular components
• What they dont do Shadows, Mirrors, Refraction,
  and so on.
• Consists of three terms linearly combined

• Diffuse the amount of incoming light reflected
  equally in all directions
• Specular the amount of light reflected in a
  mirror-like fashion

• Ambient term to approximate light arriving via
  other surfaces
• Shading Interpolation
• Flat shading computes shading at a
  representative point to whole polygon
• - Advantages Fast - one shading computation per
  polygon
• - Disadvantages Inaccurate, What are the
  artifacts?
• Gouraud interpolation
• - Advantages
• 1. Fast - incremental calculations when
  rasterizing
• 2. Much smoother - use one normal per shared
  vertex to get continuity between faces
• - Disadvantages
• 1. What are the artifacts?
• 2. Is it accurate?
• Phong interpolation
• - AdvantagesHigh quality, narrow specularities
• - DisadvantagesExpensive, still an
  approximation for most surfaces
• Consider two sub-problems of illumination
• - Where does the light go? Light transport
• - What happens at surfaces? Reflectance models
• L and I of light sources are important for a
  local shading model

2

• Tensor Product Surface Patches
• Defined over a rectangular domain 0?slt1, 0?tlt1
• Use a rectangular grid of control points to
  specify the surface
• - 4 points in the bi-linear case on the previous
  slide, more in other
• Surface takes the form For some functions Fi,s
  and Fj,t
• Bezier Patches
• Edge curves are Bezier curves
• Any curve of constant s or t is a Bezier curve
• One way to think about it
• Each row of 4 control points defines a Bezier
  curve in s
• Evaluating each of these curves at the same s
  provides 4 virtual control points
• The virtual control points define a Bezier curve
  in t
• Evaluating this curve at t gives the point x(s,t)
• Properties of Bezier patches
• The patch interpolates its corner points from the
  interpolation of the underlying curves
• The tangent plane at each corner interpolates the
  corner vertex and the two neighboring edge
  vertices
• - The tangent plane is the plane that is
  perpendicular to the normal vector at a point,
  the tangent plane property derives from the curve
  tangent properties and the way to compute normal
  vectors
• The patch lies within the convex hull of its
  control vertices
• Matrix form

• Shading Revisited
• To produce photorealistic pictures like a
  photograph
• A better metric is perceptual the image should
  generate a target set of perceptions
• Applications include Film special effects,
  Training simulations, Computer games,
  Architectural visualizations, Psychology
  experiments,
• To achieve the goal of photorealism, we must
  think carefully about light and how it interacts
  with surfaces
• Light Transport concerned with how much light
  arrives at any surface, and from what direction
• The physical quantity is radiance How much light
  is traveling along a line in space per unit
  foreshortened area per unit solid angle
• Similar problems arise in radiated heat transport
  (i.e. satellites) RadiometryThe study of light
  distribution
• Reflectance Modeling concerned with the way in
  which
• light reflects off surfaces
• To deciding what surfaces look like, in solving
• the light transport

• Ray-Plane Intersection
• To do polygons, intersect with plane then do
  point-in-polygon test
• Point-in-Polygon Testing
• Project point and polygon onto a 2D plane
  project to the smaller two normal vector
  elements plane
• Cast a ray from the point to infinity and count
  the number of edges it crosses
• Odd number means point is inside
• Edge crossing tests are very fast - think
  clipping
• More complex tests
• Ray-Polygon test reveals a common strategy
• Intersect with something easy - a superset of the
  actual shape
• Do a bounds check to make sure you have actually
  hit the shape
• Also works for cylinders, disks, cones
• CSG is well suited to raytracing
• Find intersection along ray of all the CSG
  primitives
• Break the ray into intervals according to which
  primitives it is in
• Do set operations to find the first interval that
  is actually inside the CSG
• Ray-Patch Intersection
• Equation in 3 parameters, two for
• surface and one for ray

• Instead of subdivision, view splitting as
  refinement
• Inserting additional control points, and knots,
  between the existing
• Useful not just for rendering - also a user
  interface tool
• By the Oslo algorithm
• Refining Uniform Cubic B-Splines
• Basic idea Generate 2n-3 new control points
• Add a new control point in the middle of each
  curve segment P0,1, P1,2, P2,3 , , Pn-2,n-1
• Modify existing control points P1, P2, ,
  Pn-2
• Throw away the first and last control
• Rules
• If the curve is a loop, generate 2n new control
  points by averaging across the loop
• When drawing, dont draw the control polygon,
  join the X(i) points
• Rational Curves Each point is the ratio of two
  curves
• - NURBS x(t), y(t), z(t) and w(t) are
  non-uniform B-splines
• Advantages
• Perspective invariant, so can be evaluating in
  screen space
• Can perfectly represent conic sections circles,
  ellipses, etc
• --Piecewise cubic curves cannot do this
• NURBS Non-uniform Rational B-splines