Blobby Modelling

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Blobby Modelling

• Alex Benton

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What is it?

• Metaball, or Blobby, Modelling is a technique
  which uses implicit surfaces to produce models
  which seem more organic or blobby than
  conventional models built from flat planes and
  rigid angles.
  --me

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Examples--
Paul Bourke (1997)
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Examples--
New Train - Wyvill
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Examples--
Cabrit Model - Wyvill
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Uses of Blobby Modelling

• Organic forms and nonlinear shapes
• Scientific modelling (electron orbitals, some
  medical imaging)
• Muscles and joints with skin
• Rapid prototyping
• CAD/CAM solid geometry

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How does it work?

• Each point in space generates a field of force,
  which drops off as a function of distance from
  the point.
• A blobby model is formed from the shells of these
  force fields, the implicit surface which they
  define in space.

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How does it work? (Bourke 1997)

• Several force functions work well. Examples
• Blobby Molecules - Jim Blinn
• F(r) a e-br2
• Here b is related to the standard deviation of
  the curve, and a to the height.

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How does it work? (Bourke 1997)

• Several force functions work well. Examples
• Metaballs - Blinn again (I think)
• F(r) a(1- 3r2 / b2) 0 lt r lt b/3
  (3a/2)(1-r/b)2 b/3 lt r lt b 0 b lt r
• Here a is a scaling factor and b bounds the
  radius of effect.

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How does it work? (Bourke 1997)

• Several force functions work well. Examples
• Soft Objects - Wyvill Wyvill
• F(r) a(1 - 4r6/9b6 17r4/9b4 - 22r2 / 9b2)
• This function is basically the first few terms in
  the series expansion of an exponential function.
• a scales the function, and b determines
  radius of influence.
• Advantage rapid computation.

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How does it work? (Bourke 1997)

• Force functions comparison

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How does it REALLY work?

• Once you have your force function, the next task
  is to actually find the implicit surface.
• You already know one technique for this
  Marching Cubes.
• However, marching cubes is very accurate and
  detailed working at lower levels of precision is
  difficult.

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How does it REALLY work?

• Introducing OCTREES.
• An Octree is a recursive subdivision of space
  which homes in on the surface, from larger to
  finer detail, and then uses similar techniques to
  Marching Cubes approximate the implicit surface
  with polygons.
• Octrees can display initial approximations of the
  surface immediately.

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How does it REALLY work?

• Because the octree is a cube in space, you
  evaluate the force function F(r) at each vertex
  of the cube.
• This allows you to polygonalize the cube, in the
  same manner as Marching Cubes.
• To refine the polygonalization, you subdivide the
  cube into eight subcubes, discarding any child
  whose vertices are all hot or all cold.

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How does it REALLY work?

• Recursive subdivision

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How does it REALLY work?

• Recursive subdivision

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How does it REALLY work?

• Recursive subdivision

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How does it REALLY work?

• Find the edges, separating hot from cold

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How does it REALLY work?

• For each Octree with hot and cold corners, you
  can find the best-fitting polygons that
  approximate that surface. The edges of the
  polygons pass through points linearly
  interpolated along the edges of the cube.
• T (0.5 - F(P1)) / (F(P2) - F(P1))
• P P1 T (P2 - P1)

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Pros and Cons

• Benefits
• Very rapid general shapes
• Allows rapid manipulation at multiple levels of
  detail
• Surface complexity is not a function of data
  complexity
• Enables a poor mans solid geometry

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Pros and Cons

• Downsides
• Flat surfaces, sharp angles, etc. are difficult
• Difficult to precisely achieve targetted features
• popping between levels can be misleading

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What else?

• Complex primitives!
• Why settle for a point when you could have a
  line? Or a spline?
• Colors and textures
• The same math that blends forces can blend
  textures and colors as well.
• Many other avenues of research currently open...

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YAMM (Yet Another Metaball Modeller)

• YAMM is my hobby and research work.
• Its not polished software. Its home made.
• Available from J\Staff Folders\Alex Benton\YAMM

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Sources for more info...

• http//astronomy.swin.edu.au/pbourke/modelling/im
  plicitsurf/
• http//pages.cpsc.ucalgary.ca/blob/
• http//www.cs.wisc.edu/schenney/courses/cs638-f20
  01/lectures/cs638-11.ppt - Octrees
• D. RicciA Constructive Geometry for Computer
  GraphicsComputer Journal, May 1973
• Jules BloomenthalPolygonization of Implicit
  SurfacesComputer Aided Geometric Design, Issue
  5, 1988
• Brian Wyvill, Craig McPheeters, Geoff
  WyvillAnimating Soft ObjectsThe Visual
  Computer, Issue 4 1986
• Brian Wyvill, Craig McPheeters, Geoff WyvillSoft
  ObjectsAdvanced Computer Graphics (Proc. CG
  Tokyo 1986)