PolyCube-Maps

Tarini, Marco; Hormann, Kai; Cignoni, Paolo; Montani, Claudio

doi:10.1145/1015706.1015810

Cited by 200 publications

(139 citation statements)

References 23 publications

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“…The parameterization on polycubes originated for seamless texture mapping with low distortion [18]. Polycubes serve as nice parametric domains because they approximate well the geometry of the model and possess great regularity.…”

Section: Related Workmentioning

confidence: 99%

“…Polycubes serve as nice parametric domains because they approximate well the geometry of the model and possess great regularity. A polycube mapping can be constructed either manually [18], [19], [20] or automatically [21], [22]. Based upon specially designed surface parameterization, Wang et al [19] build manifold bivariate T-spline over a polycube that can handle models with arbitrary topology.…”

Section: Related Workmentioning

confidence: 99%

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Restricted Trivariate Polycube Splines for Volumetric Data Modeling

Wang

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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Abstract-This paper presents a volumetric modeling framework to construct a novel spline scheme called restricted trivariate polycube splines (RTP-splines). The RTP-spline aims to generalize both trivariate T -splines and tensor-product B-splines; it uses solid polycube structure as underlying parametric domains and strictly bounds blending functions within such domains. We construct volumetric RTP-splines in a top-down fashion in four steps: 1) Extending the polycube domain to its bounding volume via space filling; 2) building the B-spline volume over the extended domain with restricted boundaries; 3) inserting duplicate knots by adding anchor points and performing local refinement; and 4) removing exterior cells and anchors. Besides local refinement inherited from general Tsplines, the RTP-splines have a few attractive properties as follows: 1) They naturally model solid objects with complicated topologies/ bifurcations using a one-piece continuous representation without domain trimming/patching/merging. 2) They have guaranteed semistandardness so that the functions and derivatives evaluation is very efficient. 3) Their restricted support regions of blending functions prevent control points from influencing other nearby domain regions that stay opposite to the immediate boundaries. These features are highly desirable for certain applications such as isogeometric analysis. We conduct extensive experiments on converting complicated solid models into RTP-splines, and demonstrate the proposed spline to be a powerful and promising tool for volumetric modeling and other scientific/engineering applications where data sets with multiattributes are prevalent.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Restricted Trivariate Polycube Splines for Volumetric Data Modeling

Wang

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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“…However, an initial polycube of the meccano could be generated by using an octree subdivision, and the surface parameterization could be built using PolyCube-Maps [24,34,36]. The remaining stages of the method are similar to the genus-zero case.…”

Section: Solid With Surface Of Genus Greater Than Zeromentioning

confidence: 99%

“…The key lies on having a volumetric parameterization of the solid following the mecano method described in [27,28]. In this method the surface parameterization must be explicitly given, but we think that this handicap could be overcome by applying a technique similar to PolyCubeMaps [24,34,36]. The rest of the procedure would follow the same steps than the ones described in this paper.…”

Section: Conclusion and Challengesmentioning

confidence: 99%

The meccano method for isogeometric solid modeling and applications

Escobar

Montenegro

Rodríguez

et al. 2012

Engineering with Computers

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We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. We take a genus-zero solid as a basis of our study, but at the end of the work we explain the way to generalize the results to any genus solids. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation. We present some results of the application of isogeometric analysis with T-splines to the resolution of Poisson equation in solids parameterized with this technique.

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“…Polycube maps [THCM04] provide a special kind of mapping for efficient texturing. Here, the base domain of a surface is approximated by a simple configuration of cubes.…”

Section: Alternative Objectives and Approachesmentioning

confidence: 99%