2,801 research outputs found
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
In this paper, we propose a general framework for constructing IGA-suitable
planar B-spline parameterizations from given complex CAD boundaries consisting
of a set of B-spline curves. Instead of forming the computational domain by a
simple boundary, planar domains with high genus and more complex boundary
curves are considered. Firstly, some pre-processing operations including
B\'ezier extraction and subdivision are performed on each boundary curve in
order to generate a high-quality planar parameterization; then a robust planar
domain partition framework is proposed to construct high-quality patch-meshing
results with few singularities from the discrete boundary formed by connecting
the end points of the resulting boundary segments. After the topology
information generation of quadrilateral decomposition, the optimal placement of
interior B\'ezier curves corresponding to the interior edges of the
quadrangulation is constructed by a global optimization method to achieve a
patch-partition with high quality. Finally, after the imposition of
C1=G1-continuity constraints on the interface of neighboring B\'ezier patches
with respect to each quad in the quadrangulation, the high-quality B\'ezier
patch parameterization is obtained by a C1-constrained local optimization
method to achieve uniform and orthogonal iso-parametric structures while
keeping the continuity conditions between patches. The efficiency and
robustness of the proposed method are demonstrated by several examples which
are compared to results obtained by the skeleton-based parameterization
approach
The Argyris isogeometric space on unstructured multi-patch planar domains
Multi-patch spline parametrizations are used in geometric design and
isogeometric analysis to represent complex domains. We deal with a particular
class of planar multi-patch spline parametrizations called
analysis-suitable (AS-) multi-patch parametrizations (Collin,
Sangalli, Takacs; CAGD, 2016). This class of parametrizations has to satisfy
specific geometric continuity constraints, and is of importance since it allows
to construct, on the multi-patch domain, isogeometric spaces with optimal
approximation properties. It was demonstrated in (Kapl, Sangalli, Takacs; CAD,
2018) that AS- multi-patch parametrizations are suitable for modeling
complex planar multi-patch domains.
In this work, we construct a basis, and an associated dual basis, for a
specific isogeometric spline space over a given AS-
multi-patch parametrization. We call the space the Argyris
isogeometric space, since it is across interfaces and at all
vertices and generalizes the idea of Argyris finite elements to tensor-product
splines. The considered space is a subspace of the entire
isogeometric space , which maintains the reproduction
properties of traces and normal derivatives along the interfaces. Moreover, it
reproduces all derivatives up to second order at the vertices. In contrast to
, the dimension of does not depend on the domain
parametrization, and admits a basis and dual basis which possess
a simple explicit representation and local support.
We conclude the paper with some numerical experiments, which exhibit the
optimal approximation order of the Argyris isogeometric space and
demonstrate the applicability of our approach for isogeometric analysis
Ambient Isotopic Meshing of Implicit Algebraic Surface with Singularities
A complete method is proposed to compute a certified, or ambient isotopic,
meshing for an implicit algebraic surface with singularities. By certified, we
mean a meshing with correct topology and any given geometric precision. We
propose a symbolic-numeric method to compute a certified meshing for the
surface inside a box containing singularities and use a modified
Plantinga-Vegter marching cube method to compute a certified meshing for the
surface inside a box without singularities. Nontrivial examples are given to
show the effectiveness of the algorithm. To our knowledge, this is the first
method to compute a certified meshing for surfaces with singularities.Comment: 34 pages, 17 Postscript figure
Triangular BĂŠzier sub-surfaces on a triangular BĂŠzier surface
This paper considers the problem of computing the BĂŠzier representation for a triangular sub-patch on a triangular BĂŠzier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular BĂŠzier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular BĂŠzier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch
Coonsovo povezivanje klase C1 trokutnih dijelova
A Gordon-Coons-type surface construction starts from three differentiable triangular surface patches, which are defined on the same triangular parameter domain. If one boundary curve of each fits a curvilinear triangle, then the defined surface interpolates to these curves. The connection between the resulting surface and the constituents is C1 continuous along the common boundary curves with the exception of the corner points. This surface definition is an extension of the Gordon--Coons definition of a triangular surface patch constructed from three boundary curves.Gordon-Coonsova konstrukcija plohe kreÄe od tri diferencijabilna trokutna ploĹĄna dijela koji su definirani na istom trokutnom parametarskom podruÄju. Ako po jedna rubna krivulja svakog od njih odgovara krivuljnom trokutu, tada definirana ploha interpolira te krivulje. Veza izmeÄu dobivene plohe i sastavnih dijelova je klase C1 duĹž zajedniÄkih rubnih krivulja, s izuzetkom vrhova. Ova definicija plohe je proĹĄirenje Gordon-Coonsove definicije trokutnog ploĹĄnog dijela konstruiranog iz tri graniÄne toÄke
Multisided generalisations of Gregory patches
We propose two generalisations of Gregory patches to faces of any valency by using generalised barycentric coordinates in combination with two kinds of multisided BĂŠzier patches. Our first construction builds on S-patches to generalise triangular Gregory patches. The local construction of Chiyokura and Kimura providing G1 continuity between adjoining BĂŠzier patches is generalised so that the novel Gregory S-patches of any valency can be smoothly joined to one another. Our second construction makes a minor adjustment to the generalised BĂŠzier patch structure to allow for cross-boundary derivatives to be defined independently per side. We show that the corresponding blending functions have the inherent ability to blend ribbon data much like the rational blending functions of Gregory patches. Both constructions take as input a polygonal mesh with vertex normals and provide G1 surfaces interpolating the input vertices and normals. Due to the full locality of the methods, they are well suited for geometric modelling as well as computer graphics applications relying on hardware tessellation
Conversion of B-rep CAD models into globally G<sup>1</sup> triangular splines
Existing techniques that convert B-rep (boundary representation) patches into Clough-Tocher splines guarantee watertight, that is C0, conversion results across B-rep edges. In contrast, our approach ensures global tangent-plane, that is G1, continuity of the converted B-rep CAD models. We achieve this by careful boundary curve and normal vector management, and by converting the input models into Shirman-SĂŠquin macro-elements near their (trimmed) B-rep edges. We propose several different variants and compare them with respect to their locality, visual quality, and difference with the input B-rep CAD model. Although the same global G1 continuity can also be achieved by conversion techniques based on subdivision surfaces, our approach uses triangular splines and thus enjoys full compatibility with CAD
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