3 research outputs found
On the Complexity of Smooth Spline Surfaces from Quad Meshes
This paper derives strong relations that boundary curves of a smooth complex
of patches have to obey when the patches are computed by local averaging. These
relations restrict the choice of reparameterizations for geometric continuity.
In particular, when one bicubic tensor-product B-spline patch is associated
with each facet of a quadrilateral mesh with n-valent vertices and we do not
want segments of the boundary curves forced to be linear, then the relations
dictate the minimal number and multiplicity of knots: For general data, the
tensor-product spline patches must have at least two internal double knots per
edge to be able to model a G^1-conneced complex of C^1 splines. This lower
bound on the complexity of any construction is proven to be sharp by suitably
interpreting an existing surface construction. That is, we have a tight bound
on the complexity of smoothing quad meshes with bicubic tensor-product B-spline
patches
A Spline-based Volumetric Data Modeling Framework and Its Applications
In this dissertation, we concentrate on the challenging research issue of
developing a spline-based modeling framework, which converts the conventional
data (e.g., surface meshes) to tensor-product trivariate splines. This
methodology can represent both boundary/volumetric geometry and real volumetric
physical attributes in a compact and continuous fashion. The regular
tensor-product structure enables our new developed methods to be embedded into
the industry standard seamlessly. These properties make our techniques highly
preferable in many physically-based applications including mechanical analysis,
shape deformation and editing, virtual surgery training, etc.Comment: Ph.D thesis, Computer Science Department, Stony Brook Universit
GPU Conversion of Quad Meshes to Smooth Surfaces
We convert any quad manifold mesh into an at least C¹ surface consisting of bi-cubic tensor-product splines with localized perturbations of degree bi-5 near non-4-valent vertices. There is one polynomial piece per quad facet, regardless of the valence of the vertices. Particular care is taken to derive simple formulas so that the surfaces are computed efficiently in parallel and match up precisely when computed independently on the GPU