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Geometric objects are basically described using curves and surfaces. The variety of applications that deal with geometric shape description demand different processing tasks to be performed on them. This paper describes new techniques... more
Geometric objects are basically described using curves and surfaces. The variety of applications that deal with geometric shape description demand different processing tasks to be performed on them. This paper describes new techniques developed for processing geometric objects based on the subdivision principle.
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Blends are surfaces that arise in manufacturing and do not usually appear on blue-prints. Methods are presented for modelling them in CAD/CAM systems. Modelling of two types of blends for parametric surfaces is considered; rolling sphere... more
Blends are surfaces that arise in manufacturing and do not usually appear on blue-prints. Methods are presented for modelling them in CAD/CAM systems. Modelling of two types of blends for parametric surfaces is considered; rolling sphere blends and general cross-section blends. The blend surface design task is split into two subtasks: identification of the normal cross section as well as the path followed by it. The path is identified as the intersection of the offsets of the given two surfaces. The offsetting technique establishes a natural parametric correspondence between the two blend boundary curves. The design of the shape of the cross section curve is left to the user. This provides the flexibility demanded by the application at hand.<<ETX>>
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The blending method based on partial differential equations (PDE) is an effective tool to generate a smooth, transition surface between base surfaces. The parameters in the partial differential equations have profound effect on the... more
The blending method based on partial differential equations (PDE) is an effective tool to generate a smooth, transition surface between base surfaces. The parameters in the partial differential equations have profound effect on the geometry of the blending surfaces. But in the existing research, only one vector-valued parameter is considered in the partial differential equations. To improve on the flexibility and versatility of the PDEs, we are proposing a fourth order partial differential equation with three vector-valued parameters to generate blending surfaces. This method actually includes the one-parameter fourth order partial differential equation as a special case, and is able to generate blends suitable for more geometric diversity. To demonstrate the proposed method, blends between two co-axial circular cylinders, between two intersecting planes, and between an elliptic cylinder and a horizontal plane are generated. The closed form solutions of the threeparameter fourth ord...
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A model based on the curve-modulation technique is proposed for designing a parametric blend between two parametrically defined surfaces. The modulants are the cross section and the spine curves. The end position and tangency conditions... more
A model based on the curve-modulation technique is proposed for designing a parametric blend between two parametrically defined surfaces. The modulants are the cross section and the spine curves. The end position and tangency conditions of the cross section are discussed. Its intermediate shape can be left to the designer's choice, and generally depends on the application at hand. Various