Implicit Surface Representations
Representing
objects and their surfaces implicitly with a mathematical function has
a number of advantages.
- Mesh independent
representation - generate the desired mesh when you require
it
- Compact
representation to within any desired
precision
- A solid model is
guaranteed to produce manifold (manufacturable)
surface
- Tangent planes
and normals can be determined analytically from the gradient of
the RBF function
- Smoothing and anti-alias filtering can be acheived analytically
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An RBF model
fitted to a laser scan of a scapular evaluated at different
resolutions
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Compression
A consequence of the RBF fitting process
is that the fitted function compactly represents the raw data.
There are generally fewer terms in the function than vertices in
the raw surface data. Furthermore, there is no geometry (mesh)
information to be stored, which usually accounts for the majority
of storage.
- The dragon below,
originally consisting 473,000 vertices and 871,000 facets was
compactly represented by 32,000 terms in the fitted function
while achieving an accuracy of 0.1mm over
200mm.
- The point cloud laser scan
of the hand below (27,000 points) was modelled by 2668
terms.
- The Buddha figure (543,000 vertices) was modelled by 82,000 terms to within .1mm
accuracy
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| Laser
scanned point cloud (27,000 points) |
Fitted
surface described by an RBF function consisting of 2,600
terms |
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A dragon consisting of 473,000 vertices &
871,000 facets (left) is modelled with ARANZ's
FastRBFTMengine by
a single function consisting of 32,000 terms
(right) |
Noisy data
New RBF
fitting techniques and RBF filters allow
smooth surfaces to be reconstructed from very noisy data.
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