Contour plot of an acoustic pressure function defined on the head.
Smooth iso-countours show that both the shell and the function on the shell are smooth.
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Middle surface and multiple layers of a shell:
inner surface and trwo layers are presented.
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Several naturally occurring as well as manufactured objects have shell-like structures,
that is, their boundaries consist of surfaces with thinckness. We present an adaptive,
hierarchical hi-multiresolution reconstruction algorithm to model fat survace
objects form a matched trianulation pair. Fat surfaces are constructed by the contours of trivariate functions defined as prism scaffolds.
In the H-direction, a hierarchical representation of the scaffold is constructed. For
any adaptively extracted scaffold from the hierarchy, a sequence of functions in the h-direction (regularly subdivided mesh) is constructed so that their contours approximate the input shell to within a given error. The fat surfaceds can be made to cature sharp creases of whe shell while being smoothe everywhere else. We also allow function vlaues to be attached to the input vertices of the shell triangulations, so that physical data fields defined on the shell can be bisualized and texture mapping can be performed. Using an interval of isocontours of smoothe trivariate spline functions, rather than a pair of inner and outer surface spline, one avoids the need for interference checks between the inner and outer surface boundaries.
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25561 fat triangles
13141 fat triangles
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6765 fat triangles |
6765 fat triangles | |
5069 fat triangles with cutaway |
smoothing |
40912 fat triangles |
smooth fat surface |
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Most manufactured (airfoils) and several naturally occurring objects (sea shells)
have shell like structures, that is the boundary consists of surfaces with thickness. We call such surfaces as "fat
surfaces" or "fat boundaries". We have a multi-resolution reconstruction algorithm to model the
boundary of such fat surface objects from twin clouds of points (unorganized scattered data)
or nested boundary triangulation (organized data collection). The novelty of our scheme is an adaptive
decimation scheme of fat boundaries, coupled to fat surfaces data approximation
using an interval of isocontours of smooth trivariate polynomial spline functions, rather than a pair of inner and outer surface splines.
This single spline representation of fat surfaces allows for interactive
deformations of the boundary without worry of interference checks between inner and outer surface boundaries,
a serious concern in the case when individual inner and outer surface splines are modified.
Our fat surface reconstructions are easily evaluated for rapid display, and additionally the approximation has quadratic precision.
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(a1) 14672 fat triangles
(a2) smoothing (7528 fat triangles)
(a3) smoothing (2414 fat triangles)
(a4) smoothing (1160 fat triangles)
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These figures show the multiresolution
fat surface reconstruction (a1) is the input triangualtion. The following three, (a2), (a3),
and (a4), are the C 1 smooth fat surface over the decimated fat triangulations.
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