Molecular Animation

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Molecular Animation

• Bajaj, Pascucci, Holt, Netravali

Computer Sciences T I C A M University of Texas
at Austin, TX Bell Laboratories, Murray Hill
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Input Data weighted points
Nutrasweet molecule
Atoms represented by balls with Van Der Walls
radii (different colors correspond to different
radii)
Atoms Centers
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Basic Data-Structures

• Union of balls
• Delaunay triangulation
• 0-shape

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Basic Data-Structures

• Union of balls
• Power Diagram
• 0-shape

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Rolling Ball Blend

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Rolling Ball Blend

• The Rolling Ball Blend has the topological
  structure of the OFFSET

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OFFSET vs ?-SHAPE

Tunnel
OFFSET
Possible topological differences
?-SHAPE
Cavity
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OFFSET vs ?-SHAPE

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OFFSET vs ?-SHAPE

Linear growing can induce flips in the Regular
Triangulation
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OFFSET vs ?-SHAPE

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OFFSET vs ?-SHAPE

l1 const
(efficient)
(exact)
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Efficient Linear Growing

Preprocessing

• Build in the (d1)-dimensional space the power
  diagram of the cones.
• The intersection with the horizontal
  hyperplane rr0 is the power diagram of the
  OFFSET of distance r0.
• Sweeping an horizontal plane one can record in an
  array all the flips that occur in the Regular
  Triangulation.

Power Diagram Hyperplane
Ball
Cone
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Efficient Linear Growing

Run Time
Initial r0
?

• Maintain the Regular Triangulation relative to
  the current OFFSET distance r0.
• To increase the OFFSET distance to r1 perform
  sequentially all the flips following r0 until r1
  is found.

Flips Performed
Flips Array
Target r1
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Efficient Linear Growing
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NURBS Representation
2D Domain
(s,t)
(x,y,z)
3D Range
x2s/(s2t21)
y2t/(s2t21)
z(s2t2-1)/(s2t21)
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Trimming Curves

• Each plane of the Power Diagram is mapped onto a
  circle in domain space

• The topological structure of the trimming
  circles of the sphere S is given by the
  topological structure of the convex cell C
  relative to S in the Power Diagram.

• A vertex of C inside S corresponds to a triple of
  intersecting trimming circles
• An edge of C intersecting S corresponds to a
  pair of intersecting trimming circles.