Offsetting operations in solid modelling
Computer Aided Geometric Design
Interactive techniques for implicit modeling
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Sweeping of three-dimensional objects
Computer-Aided Design
Hierarchical segmentations of algebraic curves and some applications
Mathematical methods in computer aided geometric design
Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
More Powerful Solid Modeling Through Ray Representations
IEEE Computer Graphics and Applications
Real functions for representation of rigid solids
Computer Aided Geometric Design
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Modeling generalized cylinders via Fourier morphing
ACM Transactions on Graphics (TOG)
Functionally based virtual computer art
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
IEEE Transactions on Visualization and Computer Graphics
Computational Methods for Geometric Processing. Applications to Industry
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
A Scan Line Algorithm for Rendering Curved Tubular Objects
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Generalized sweep templates for implicit modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Boundary of the volume swept by a free-form solid in screw motion
Computer-Aided Design
Classifying points for sweeping solids
Computer-Aided Design
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This paper studies a function representation of point sets swept by moving solids. The original solid-generator is defined by an inequality f(x, y, z, t) 驴 0 where x, y, z are Cartesian coordinates and t is treated as the time. This definition allows us to include solids which change their shapes in time. Constructive solids can be used as generators also when described by R-functions. The trajectory of the generator can be defined in parametric form as movement of its local coordinate system. In the paper, we did it with superposition of time-dependent affine transformations. To get the function representation F(x, y, z) 驴 0 of the swept solid, we apply the concept of envelope used before basically for boundary represented objects. We have reduced the problem of swept solid description to global extremum search by t variable. The algorithm of procedural swept solid modeling is discussed.The benefit of our model is that it is applied not only for visualization but allows one to use the swept solid as an argument for other operations. For example, the swept solid can be intersected with other ones that are useful for the implementation of such operations as cutting and drilling. Ordinary texture mapping and hypertexturing can also be applied to it. The possibility of using a functionally defined generator with the variable shape allows us to achieve a complexity of the swept solids which was hardly possible before.