An Introduction to Polar Forms
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Proceedings of the 2005 ACM symposium on Solid and physical modeling
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Adaptive T-spline surface fitting to z-map models
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Manifold splines with single extraordinary point
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Automatic and interactive mesh to T-spline conversion
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
A C1 globally interpolatory spline of arbitrary topology
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Control point removal algorithm for t-spline surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Technical Section: A divide-and-conquer approach for automatic polycube map construction
Computers and Graphics
Technical Section: Feature-aligned harmonic volumetric mapping using MFS
Computers and Graphics
Hexahedral shell mesh construction via volumetric polycube map
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Modeling 3D facial expressions using geometry videos
Proceedings of the international conference on Multimedia
Manifold-based surfaces with boundaries
Computer Aided Geometric Design
Editable polycube map for GPU-based subdivision surfaces
I3D '11 Symposium on Interactive 3D Graphics and Games
SMI 2011: Full Paper: A topology-preserving optimization algorithm for polycube mapping
Computers and Graphics
Modeling 3D articulated motions with conformal geometry videos (CGVs)
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Parameterization of star-shaped volumes using green's functions
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
SMI 2012: Full Local approximation of scalar functions on 3D shapes and volumetric data
Computers and Graphics
SMI 2012: Mixed-element volume completion from NURBS surfaces
Computers and Graphics
Constructing hexahedral shell meshes via volumetric polycube maps
Computer-Aided Design
PolyCut: monotone graph-cuts for PolyCube base-complex construction
ACM Transactions on Graphics (TOG)
Fitting polynomial volumes to surface meshes with Voronoï squared distance minimization
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Polycube T-spline has been formulated elegantly that can unify T-splines and manifold splines to define a new class of shape representations for surfaces of arbitrary topology by using polycube map as its parametric domain. In essense, The data fitting quality using polycube T-splines hinges upon the construction of underlying polycube maps. Yet, existing methods for polycube map construction exhibit some disadvantages. For example, existing approaches for polycube map construction either require projection of points from a 3D surface to its polycube approximation, which is therefore very difficult to handle the cases when two shapes differ significantly; or compute the map by conformally deforming the surfaces and polycubes to the common canonical domain and then construct the map using function composition, which is challenging to control the location of singularities and makes it hard for the data-fitting and hole-filling processes later on. This paper proposes a novel framework of user-controllable polycube maps, which can overcome disadvantages of the conventional methods and is much more efficient and accurate. The current approach allows users to directly select the corner points of the polycubes on the original 3D surfaces, then construct the polycube maps by using the new computational tool of discrete Euclidean Ricci flow. We develop algorithms for computing such polycube maps, and show that the resulting user-controllable polycube map serves as an ideal parametric domain for constructing spline surfaces and other applications. The location of singularities can be interactively placed where no important geometric features exist. Experimental results demonstrate that the proposed polycube maps introduce lower area distortion and retain small angle distortion as well, and subsequently make the entire hole-filling process much easier to accomplish.