Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
A unified approach to geometric modelling
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
GEOMED - a geometric editor.
Applications of b-spline approximation to geometric problems of computer-aided design.
Applications of b-spline approximation to geometric problems of computer-aided design.
Smoothing of polyhedral models
SCG '86 Proceedings of the second annual symposium on Computational geometry
Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
The displacement method for implicit blending surfaces in solid models
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Utilizing parametric hyperpatch methods for modeling and display of free-form solids
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Closed smooth piecewise bicubic surfaces
ACM Transactions on Graphics (TOG)
Smoothing polyhedra using implicit algebraic splines
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Modelling techniques for handling non-geometric information
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Smooth spline surfaces over irregular meshes
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Blending, smoothing and interpolation of irregular meshes using N-sided Varady patches
Proceedings of the fifth ACM symposium on Solid modeling and applications
Constraints in constructive solid geometry
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
Blend surfaces for set theoretic volume modelling systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
XVL: a compact and qualified 3D representation with lattice mesh and surface for the Internet
VRML '00 Proceedings of the fifth symposium on Virtual reality modeling language (Web3D-VRML)
Using lattice for web-based medical applications
Proceedings of the sixth international conference on 3D Web technology
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Computer Modeling of Surfaces with Arbitrary Shapes
IEEE Computer Graphics and Applications
Parametric Surface Interpolation
IEEE Computer Graphics and Applications
Shape Models and Object Recognition
Shape, Contour and Grouping in Computer Vision
Scattered Data Techniques for Surfaces
Dagstuhl '97, Scientific Visualization
Lofting curve networks using subdivision surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Technical Section: Parameterised, constraint-based wrapping of freeform shapes
Computers and Graphics
Nonlinear interpolation between slices
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Approximating Catmull-Clark subdivision surfaces with bicubic patches
ACM Transactions on Graphics (TOG)
PNG1 triangles for tangent plane continuous surfaces on the GPU
GI '08 Proceedings of graphics interface 2008
Approximating subdivision surfaces with Gregory patches for hardware tessellation
ACM SIGGRAPH Asia 2009 papers
A geometric criterion for smooth interpolation of curve networks
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Bicubic G1 interpolation of irregular quad meshes using a 4-split
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
LSM: A layer subdivision method for deformable object matching
Information Sciences: an International Journal
A geometric constraint on curve networks suitable for smooth interpolation
Computer-Aided Design
G1 continuity triangular patches interpolation based on PN triangles
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Design techniques for the definition of solid objects with free-form geometry
Computer Aided Geometric Design
Local surface interpolation with Bézier patches
Computer Aided Geometric Design
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We propose a unified method of generating a wide range of three dimensional objects from polyhedra to solids with free-form surfaces. Modeling systems for polyhedra and systems for free-form surfaces have been developed independently in the past because of the difference in their underlying theory and practices. However, this is not desirable for a designer. So in this paper, we have shown a method in which a wide range of shapes are generated in one system by using local modifications. Local modifications are procedures used to change the shape of solids locally. The construction and the modification of three dimensional shapes by these procedures are natural and easy for a designer in many cases. The implementation of these procedures in a computer is easy and their execution does not require much time. Our method to construct a solid with free-form surfaces consists of following three phases. 1) A solid which serves as a basis of free-form shape design is generated by local modifications. Edges of this solid are straight lines but its faces are not necessarily flat planes. 2) From this model, a curve model which adequately represents the characteristics of a free-form shape is generated. 3) Surface equations interpolating over the curve model are generated. We have made a geometric modeling system MODIF. Using this system, a complicated solid with free-form surfaces can be designed easily. MODIF can generate color shaded pictures and cutter path data for making a real object model by NC machining tool.