1. Week 12 - Thursday
CS361

2. Last time What did we talk about last time? Exam 2
Before that…Kevin Schlipper came to speak
Before that…review
Before that…image based techniques

3. Questions?

4. Project 4

5. Polygonal Techniques

6. Sources of 3D data
As you know, just getting 3D data into a program is tricky
There are a few standard ways
Type in the data (cube examples)
Generate the data procedurally
Visualization of scientific (or other) data as spheres, cubes, or other primitives
Modeling programs
Sampling or scanning the real world
Reconstruction from photographs
Combinations!

7. Video of Scanning Michelangelo's David
And ScanView tool to view the data

8. Motion capture is huge now
Models created by artists
Moving based on motion capture

9. Tessellation
Surfaces often need to be tessellated, broken down into polygons
The surfaces can be
Convex polygons
More complicated polygons
3D surfaces made out of complicated polygons

10. Triangulation
For most graphics hardware, polygons must be triangulated into component triangles
"Bowties" have to be converted into triangles, perhaps making a guess about what the modeler meant
The literature contains many triangulation algorithms including the O(n2) ear clipping algorithm

11. Shading problems Data often arrives as quadrilateral meshes
How we break those into triangles can make a big visual difference, depending on vertex colors and texture mapping
Sometimes no triangulation works for texture mapping
It may be necessary to distort the texture to make it work

12. Splines
A spline is a curve in space that is defined as a piecewise function
Each piece of the curve is often a cubic function
Usually the first and second derivatives of the functions are the same at points where they meet to keep them smooth
Splines are a common tool for defining shapes in 2D and 3D
Artists add control points with handles to change the slope of the curves

13. NURBS
Non-uniform rational basis splines (NURBS) are a very general form of splines
Many 3D modeling program represent surfaces as patches between these splines
Rendering NURBS usually means turning these mathematically precise surfaces into triangles

14. Edge cracking and T-vertices
Turning the splines into polygons can cause two surfaces to have cracks between them, called edge cracking
Edge stitching makes sure all vertices on a shared edge between surfaces are shared as well
Shading is also an issue for T-vertices
Triangles that share edges should share all the same vertices too

15. Consolidation
After generating a polygon mesh, we may want to consolidate it in a few ways
Merging finds shared vertices among faces
Orientation makes sure that all polygons face the same direction
This way, neighboring polygons would not be facing opposite ways from the perspective of culling operations
It may be necessary to generate normals for each vertex based on the surface normals
All the same as the surface for flat surfaces
Interpolated normals on vertices for curving surfaces

16. Triangle fans
In order to reuse data, we can break groups of triangles into fans, strips, and meshes
A triangle fan has a center vertex shared by all triangles
The data sent to the GPU is the center vertex, the second vertex of the first triangle, the third vertex of the first triangle, and then just one additional vertex per triangle

17. Triangle strips
A triangle strip is similar to a triangle fan except that the triangles do not all share a common vertex
As before, only a single new vertex is needed for each triangle after the first one
Note that the clockwiseness of vertex order reverses for each triangle
DirectX (and MonoGame) and OpenGL automatically render the vertices of every other triangle in opposite order to perform backface culling properly

18. Optimizing triangle strips
The previous example showed a sequential triangle strip
Generalized triangle strips are more flexible, but we may need to send a vertex more than once or use some other special command, as in the following example
There are algorithms designed to generate the smallest number of strips possible (though reaching the true optimal is NP-hard)

19. Triangle meshes
For a closed surface, a mesh can be more efficient than either fans or strips
For large closed meshes, on average, each vertex is connected to six triangles
Consequently, we may only need to store as little as 0.5 vertices per triangle
More importantly, we only have to do lighting calculations once for each vertex
To get these advantages, our system has to have a good caching algorithm (and cache size) so that a lit, transformed vertex is still in cache the next time we need it

20. Vertex buffers By now, you're used to vertex buffers
They are a generic way to store model data in a contiguous chunk of memory
The memory could be:
A list of points
A list of line segments
A polyline
A triangle list
A triangle fan
A triangle strip
The size of a vertex is called the stride
If you do not want to repeat information in the vertex buffer, you can use an index buffer to specify which vertices from the vertex buffer to use

21. Simplification
Mesh simplification is a way of reducing polygon count while preserving appearance
Three common kinds:
Static – make several models of different complexity and choose the right one
Dynamic – generate models on the fly, allowing for a continuous spectrum of level of detail (LOD)
View-dependent – change based on the particular view

22. Dynamic simplification
Use edge collapses
Merge two vertices into one
There are different strategies for determining which edge to collapse, but we usually look for a "low cost" edge
There are different strategies for determining cost…
Some edges should not be collapsed
If it causes a surface's normal to flip
If it causes edges to cross

23. View dependent simplification
Terrain is highly view dependent
Close things need a lot of detail
Distant mountains may not
Some techniques are just dynamic simplification applied based on distance from the viewer
Others break the terrain into tiles or other divisions
Some features of a terrain heightfield require more detail to look realistic
Special edges may be added in after the fact to connect low detail tiles to high detail tiles

24. Subdivision We're mostly skipping Chapter 13
It's about curves and curved surfaces
One of its focuses is subdividing simple meshes into more complex ones
There are many techniques to do so
Shapes get smoother and blobbier
There are ways to specify that some edges should remain

25. Quiz

26. Upcoming

27. Next time…
Bounding volumes and intersection tests

28. Reminders
Read Chapter 16
No class on Monday!