Ch9. Polygonal Techniques

1
Ch9. Polygonal Techniques

• 2001? 7? 13?
• ???

2
Main topics

• Tessellation
• - Split into more tractable primitives
• Consolidation
• - process which encompasses merging and linking
  polygonal data
• Simplification
• taking linked data and attempting to remove
  unnecessary features
• Improve speed

3
Sources of 3D data

• Solid-based modelers
• - usually seen in the area of CAD
• - faceter turns the internal model
  representation into polygons which can be
  displayed
• Surface-based modelers
• - all objects are thought of in terms of their
  surfaces.
• - allow direct manipulation of surfaces

4
Tessellation

• Definition
• - Process of splitting a polygon into a set of
• polygons
• Reason
• Many graphics APIs and H/W are optimized for
  triangles.
• The renderer may only handle convex polygons.
• In order to catch shadows and reflected light
  using radiosity techniques

5
Tessellation

• Figure 9.1

6
Tessellation

• How best to project a 3D polygon into 2D
• to determine which one of the xyz coordinates to
  discard in order to leave just two
• The best plane is the one in which the polygon
  has the largest projected area.
• Self-intersection problem badly warped.
• comparison among the polygons edges is called
  for.

7
Bowtie quadrilateral

• Figure 9.2

8
Tessellation

• Polygons are not always made of a single outline.
• Figure 9.3

9
Shading Problems

• Data as quadrilateral meshes must be converted
  into triangles for display.
• How to split a quadrilateral
• to minimize differences
• ( shortest diagonal, smaller difference between
  the colors)

10
Triangles cannot capture the intent of designer

• If a texture is applied to a warped
  quadrilateral, neither triangulation preserves
  the intent, neither does Gouraud shading.
• Figure 9.6
• This problem arises because the image being
  applied to the surface is to be warped when
  displayed.

11
Figure 9.6
12
Edge Cracking

• Edge cracking can occur where spline surfaces
  meet. The points generated for one spline curve
  will not match those generated by its neighbor.
• Edge stitching
• - the process of fixing these cracks

13
T-Vertices

• A problem encountered
• when joining flat surfaces
• When radiosity solutions are used
• When model surfaces meet but do not share all
  vertices

14
T-Vertices

• Fig 9.8

15
Consolidation

• To find and adjust the links between polygons
• Efficiency
• Forming polygon meshes
• - fewer transformation, more efficient clipping,
  saving on memory
• 2. Backface culling

16
Overall approach

• Form edge-face structures for all polygons and
  sort these.
• Find groups of polygons that touch each other
  determine solidity.
• For each group, flip faces to gain consistency.
• Determine what the inside of the mesh is, and
  flip all faces if needed.

17
Overall approach

• 5. Find smoothing groups and compute vertex
  normals.
• 6. Find boundaries.
• 7. Create polygonal meshes.

18
Overall approach
19
Simplification

• Process of taking a complex model and reducing
  its complexity
• Advantage quicker to render
• Common Method Edge collapse
• edge is removed by moving its two vertices to one
  spot.

20
Subset placement strategy

• Advantage if we limit the possibilities, we may
  encode the choice actually made. Faster but
  low-quality.
• Fig 9.12

21
Optimal placement strategy

• We examine a wider range of possibilities.
• Both vertices for an edge are contracted to a new
  location.
• Advantage higher quality meshes
• Disadvantage extra processing, code, and memory
  for recording wider range of possible placement

22
Optimal placement strategy

• To determine the best point placement, we perform
  an analysis on the local neighborhood.
• If the cost of an edge collapse depends on just a
  few local variables, the cost function is easy to
  compute, and each collapse affects only a few of
  its neighbors.

23
Example of bad collapse

• Some edge collapses must be avoided regardless of
  cost.
• Whether a neighboring polygon flips its normal
  direction from a collapse

24
Figure 9.13
25
Cost function

• The sum of the squared distances between each of
  the planes and the new location.
• C(v) ?(niv di)2
• Figure 9.14

26
Features

• Reversibility
• - start with the simplified model and reconstruct
  the complex model from it. It is useful for
  network transmission of models.
• Simplification can produce a large number of
  level-of-detail models from a single complex
  model.

27
Simplification

• Polygon reduction techniques can be useful, but
  they are not a panacea. Because they know nothing
  about visually important elements.