outline
- was looking for things in houdini, and metaballs was one of
  the things I didn't think I can explain to students, so want
  to look into it and figure out why it is so bad to model with

- what are implicit surfaces
- operations on implicit surfaces
  - blending
  - csg
  - warping
- pretty pictures
- most of the pictures on my slides are stolen from UCalgary
  - saw a neat sketch at Siggraph 2000, so I checked there for info

2 ----------------------------------------------------------------------------

intro
- 2-D gemoetric shapes defined mathematically in 3-D space
- evaluate a point P on function F, 
      if it = 0, it is on the surface
            < 0, it is inside the surface
            > 0, it is outside the surface
  F is the implicit surface function|scalar field|field func|potential func

- explicit express surfaces in height field (z = f(x,y))
- can't represent overhang or vertical slopes, or double back
- parametric is one way, implicit is another
- implicit is easy to determine inside & outside of a surface
- also automatic blending of surfaces

3 ----------------------------------------------------------------------------

field/potential function
- d is a distance function
- h is a blend function
  - domain r affects the primitive's range of influence
  - distance larger than r-max = no influence
  - shape of h affects the primitive radius and blending characteristics 
- t is a threshold
  - surface at F(p) - t = 0

4 ----------------------------------------------------------------------------

modeling with implicit surfaces
- different names for the same thing
- only difference is in potential functions
- blending characteristics e.g. continuity of blend in areas of mutal influence

5 ----------------------------------------------------------------------------

- for the most part, distance from the skeleton defines the primitive
- plane is really a half-plane (has inside and outside

- these are primitives used in the implicit surface modeller at UCalgary
- talk about operations on the primitives next, also at UCalgary

6 ----------------------------------------------------------------------------

blending
- blending first
- basic is adding the potential functions for the primitives
- but still use the same threshold

- did this in houdini.  red sphere is r-max, end of influence
- when the area of overlap adds up to t, we get a blend
- same thing for multiple primitives

7 ----------------------------------------------------------------------------

generalized blending
- for a larger range of blends
- example of n = 1 to 10
- as n goes to infinity, it goes to the union of A and B

8 ----------------------------------------------------------------------------

local vs global blending
- all the primitives in the system influence one another
- houdini implementation only has global blending within each network
  - makes it hard to model with because it is hard to predict when
    and how much primitives influence each other
- local blending gives finer control
- do it as a union of primitive pairs

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csg
- inside is -ve, outside is +ve
- examine each edge to see whether they are part of the surface
  by comparing min or max values at the edge

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warping
- distort shape by changing the space around it
- passed in the warped point to the distance function 
- can do affine transformations such as scaling
- Barr deformation operators

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the blob tree
- the blob tree is built from these operators
- also a good way to visualize the model structure
- all operators are binary except warp, which is unary

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visualizing the model
- not going to say very much
- to preview, use polygon mesh
- to render, raytraced

13 ----------------------------------------------------------------------------

- stamingo = stork + flamingo
- some scene
- sea shell I saw at Siggraph 2000, compared to a real model
  looks really close
- so modeling with metaballs in houdini is very limiting, but
  this stuff from Calgary looks sort of cool