Surface displacement, tessellation, and subdivision

1
Surface displacement, tessellation,and
subdivision

• Ikrima Elhassan

2
Overview

• The Reyes image rendering architecture", Cook et
  al.,SIGGRAPH 1987
• Curved PN triangles", Vlachos, Peters, Boyd, and
  Mitchell,Symposium on Interactive 3D Graphics,
  2001

3
Reyes Architecture Support Goals

• Speed (render high quality film in less than a
  year)
• Shading/Model Complexity Diversity
• Minimal Raytracing
• Image Quality
• Flexibility

4
Design Goals

• Natural Coordinates
• Vectorization
• Common underlying representation
• Locality
• Linearity
• Large Models
• Back door

5
Geometric Locality Sampling

• Raytracing can cause model and texture paging to
  dominate rendering time as model complexity
  increases
• Uses stochastic sampling called jittering

6
MicroPolygons

• ½ pixel in length for Nyquist limit
• Dice primitives along natural boundaries
• Done in eyespace
• Results in a grid with shared vertices

7
Micropolygons Adv vs. Disadvantages

• Vectorizable
• Texture locality filtering
• Subdivision coherence
• Ease of Clipping Displacement maps
• No perspective

• Shading occurs on nonvisible micropolygons
• Rendering time becomes tied to depth complexity

8
Texture Locality

• 2 Classes of Textures CATs RATs
• Sequential access with CATs
• Can eliminate filtering

9
Description Algorithm

• Bounded primitives (not necessarily tight)
• Primitives must be able to break down into
  diceable primitives
• Must be able to split primitives
• Diceability test returns diceable or not
  diceable

10
Algorithm Description (Continued)

• Does not require clipping
• Use e plane to avoid invalid perspective
  calculation
• Primitives with 0ltz lt e are split until no
  primitives span the e plane

11
Extensions

• Constructive Solid Geometry
• Transparency
• Depth of field
• Motion Blur

12
Implementation

• Bucket Rendering
• Each primitive is diced or split and put into
  corresponding bucket
• Only one bucket is needed at a time
• Lowers memory requirements

13
Final Thoughts on Reyes

• No inverse calculations
• No clipping calculations
• Very vectorized
• No texture thrashing and can eliminate run time
  filtering

• Sampling occurs after shading
• Difficult to handle metaballs
• Hard to bound primitives such as particle systems
  for bucket sort
• Polygons dont have natural coordinate system

14
N-Patches
15
Issues with new geometric primitives

• Must be compatible with work already in progress
• Must be backward compatible
• Fit existing hardware designs

16
N-patches Advantages

• Curved surfaces
• Improved visual quality (smooth silhouettes and
  better vertex shading)
• Do not require developers to store geometry
  differently (triangles)
• Minimize change to APIs
• Minimize bandwidth

17
Goals

• Isolation (cannot access mesh neighbors)
• Fast Evaluation (including normal)
• Modeling range (smoother contours and better
  shading)

18
Interpolation

• Use barycentric coordinates for triangular domain
• Consider a set of points P0, P1,, Pn, and
  consider the set of all affine combinations taken
  from these points. That is all points that can be
  written as
•                                                 
       
• for some
•                                                 
     
• This set of points forms an affine space, and the
  coordinates
•                                              
• are called the barycentric coordinates of the
  points of the space.
• Recall that a point within a triangle ?p0p1p2,
  can be described as p(u,v) p0 u(p1-p0)
  v(p2-p0) (1-u-v)p0 up1 vp2, where (u,v)
  are the barycentric coordinates
• Bicubic interpolation results in C2 surfaces

• Given a tabulated function yi y(xi), i 1...N
  , focus attention on one particular interval,
  between xj and xj1. Linear interpolation in that
  interval gives the interpolation formulay Ayj
  By(j1)
• If we have yi, we can add to the right-hand side
  of equation a cubic polynomial whose second
  derivative varies linearly from a value y j on
  the left to a value y (j1) on the right.

19
Geometry cubic Bezier

• Bijk control points coefficients
• Makes up the control net
• Cubic interpolation

20
Normal quadratic Bezier

• Linear or Quadratic Interpolation

21
Algorithm

• LOD vertices -2 on an edge
• Tangent coefficients determined by planer
  projection

22
Algorithm (Continued)

• Quadratic interpolation allows for inflection
  between vertices

23
Examples of N-patches
24
Sharp Edges

• Proven that you cant have creases with purely
  local information
• More than distinct normal per vertex causes holes
  or cracks
• Not really discussed in detail, solution is to
  add more triangles

25
Hardware Performance

• Operations are dot products, addition of two
  vectors, scaling, and per-component multiply of
  two vectors
• Uses 6.8 to 11.6 vector operations per generated
  vertex
• Fill rate is not a bottleneck, since screen area
  is unchanged
• Key limiting factor, most of time, is bandwidth
• Overhead in additional transformation of vertices
• Reduces calculation for key-frame interpolation
  and collision detection
• Might be able to shift pixel shading to vertex
  shading

26
Advantages

• Generated on-chip
• Saves bandwidth and memory
• Curved surfaces and better shading

• Cant control curvature
• No sharp edges