Patent
1995-09-11
1998-02-10
Nguyen, Phu K.
G06F 1500
Patent
active
057178470
DESCRIPTION:
BRIEF SUMMARY
FIELD OF THE INVENTION
The invention relates to a method for generating plane technical curves or contours for technical equipment, in which plane, curved, geometric objects must be represented or generated on a partially large scale in very high resolution and/or under real time requirements. The inventive solution enables digital approximations for special plane curves in the area of graphic data processing to be generated rapidly and accurately.
BACKGROUND
The splines considered are used in graphic design systems as efficient and flexible means for describing curved, linear and 2-dimensional geometric objects and for approximately describing mathematically complicated curves. Digital approximations (discretizations) of the splines are required for the graphic representation of the objects described by splines in a square grid as well as for energizing technical equipment, which illuminate objects described by splines in a square grid or convert them in some other form for generating curves, contours or surfaces. Such uses are, for example, laser illuminators (printers, plotters, etc.), microlithography with electron beams or x-ray beams, microsystem technology, binary and integrated optics, manufacture of optical wave guides, 2-D robot controls, printing technology and the visualization of design data.
In many technical areas, graphic design systems are indispensable tools for product development and for generating manufacturing data. In classical fields, such as machinery, automobile, ship and aircraft construction or for the development of microelectronic circuits, there are efficient, complex and, in some cases, highly automated design systems. It is characteristic of these that they use splines, preferably parametric, cubic splines, for modeling curved plane or spatial curves and surfaces.
Splines combine the advantages of flexibility and universality as a design aid with simple computerized manageability and low data requirements for describing even complicated objects. Until a few years ago, polynomial splines were used exclusively. Now, however, rational splines offer greater design leeway while the increase in calculations is only insignificant and find acceptance in newer design systems and also as geometric primitives in computer graphic standards. A further advantage of rational splines consists therein that they represent quadratic curves (arcs of circles, ellipses, parabolas, hyperbolas) exactly.
To visualize the results of the design and to energize technical equipment, which converts the designs into industrial products, coordinate-controlled devices with a maximum, discrete coordinate resolution are generally used. Therefore only points of a square grid can be coded and selected and the object arises of generating digital approximations for curves and contours described by splines. This is a data-intensive process, which requires much computing time.
With the development of the microstructure technology, technical applications arise, for which there are not yet any specialized, graphic design systems and which place greater demands on digitizing. The resolution is increased significantly and the numbers of grid points, which must be generated, and, with that, the computing times required increase greatly. Designs become necessary, for which complete digitizing would lead to unjustifiably large quantities of data and for which, therefore, digitizing must take place parallel to the technical control process and accordingly under real time conditions. The accuracy required for the contours produced is growing.
On the whole, the status of design technology in this and similar fields is characterized in that the problem of digitizing cubic splines is an impediment to their use for modeling, curved geometric objects. Arcs of circles or ellipses are used instead. Rapid and simple methods exist for digitizing them exactly. On the other hand, complicated arcs are approximated by (data-intensive and imprecise) polygonal courses. In some systems, the necessary computing time is shortened owing
REFERENCES:
Hoschek, Circular Splines, Nov. 1992, Computer Aid Design pp. 611-617.
Wu et al., Curve Algorithms, 1989, IEEE Computer Graphics and Applications, No. 3, pp. 56-69.
McIlroy, Getting Raster Ellipses Right, AT&T Bell Lab, pp. 260-275, 1992.
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