Dimension-driven parameterized design of free form objects

The paper develops a theoretical basis for dimension-driven parameterized design of free form objects. In traditional parametric computer-aided design (CAD) systems, research is focused on the representation of dimension parameters and constraint satisfaction algorithms. Dimension-driven free form object parameterized design is to obtain a new free form object similar in shape to the old one but with different sets of dimension parameter instantiation. In other words, a new member of the master free form object's family will be designed. However, research on dimension-driven parameterized design of free form objects is an unattempted area. Also, there is no commercial CAD system that can deal with dimension-driven free form objects successfully. In this research, we exploit a new concept of similar shape applicable to 3D rational curves and surfaces. Dimension-driven variation of similar free form objects is then explained and illustrated with an example.

[1]  G. C. Onwubolu.  Modelling sculptured solids in computer-aided design , 1991 .

[2]  David F. Rogers,et al.  Mathematical elements for computer graphics , 1976 .

[3]  G. E. Martin.  Transformation Geometry: An Introduction to Symmetry , 1982 .

[4]  Joe Rooney,et al.  Principles of Computer-Aided Design , 1988 .

[5]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[6]  Hirokaki Chiyokura.  Solid Modeling with Designbase: Theory and Implementation , 1988 .

[7]  Sankarappan Gopalsamy,et al.  Conceptual Representations for Planar Sections of Parametric Surfaces , 1993, ICCG.

[8]  Eliezer Kantorowitz,et al.  Managing the shape of planar splines by their control polygons , 1993, Comput. Aided Des..

[9]  Tim N. T. Goodman,et al.  Shape preserving properties of the generalised ball basis , 1991, Comput. Aided Geom. Des..

[10]  Joris S. M. Vergeest,et al.  Surface fitting for interactive shape design , 1989 .

[11]  R. G. Newell,et al.  A DIMENSION BASED PARAMETRIC DESIGN SYSTEM , 1984 .

[12]  B. Su,et al.  Computational geometry: curve and surface modeling , 1989 .

[13]  Kai-ming. Yu,et al.  Dimensioning and tolerancing in geometric modelling , 1990 .

[14]  Dereck S. Meek,et al.  Shape determination of planar uniform cubic B-spline segments , 1990, Comput. Aided Des..

[15]  L. Piegl.  Modifying the shape of rational B-splines. part2: surfaces , 1989 .

[16]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[17]  Bahram Ravani,et al.  Computer Aided Geometric Design of Line Constructs , 1991 .

[18]  James E. Fowler.  Variant Design for Mechanical Artifacts - A State of the Art Survey , 1993 .