Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2000-04-18
2004-03-23
Frejd, Russell (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
Reexamination Certificate
active
06711530
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for evaluating a shape error of a free curved surface.
2. Description of the Prior Art
Conventionally, in press working or injection molding processing, a curved surface (i.e. an original curved surface), such as target CAD (Computer Aided Design) data and a curved surface associated therewith (i.e. a distorted curved surface), are typically “visually” compared. Any forming defects in the working or the processing are evaluated based on a difference, noted during the “visual” inspection, between these original and distorted curves. That is, for example in press working, if the distorted curved surface has been “bent” and “twisted” relative to the original curved surface, both curved surfaces are visually judged against one another and the metal mold is experientially adjusted.
The above-described visual experiential evaluation of the curves is simple and convenient, but it has problems to include large individual differences, dependence on the evaluator's experience, and extremely high arbitrariness. Therefore, a means for evaluating the entire bends and twists of the free curved surface by an objective, less arbitrary means for evaluation is desirable.
On the other hand, for this purpose, a formed article (i.e., distorted curved surface) that was actually formed by using, for example, formed sheet metal and the like, is measured by a Coordinate Measuring Machine or a digitizer. In this way, an image of the obtained measured result is displayed together with the original curved surface (i.e., CAD data and others) so that a shape error, such as bent or twisted shape error, can be roughly recognized by visual inspection. With this technique, however, it is difficult to visually recognize three-dimensional differences. Specifically, when a reference shape is not flat but has a complicated curve, a difference in the three-dimensional measurement between the distorted curved surface and the original curved surface can hardly be visually recognized.
Furthermore, if the distorted curved surface has a local “wrinkle”, “bump” or “dent”, the image is largely changed and the entire shape error is hard to evaluate by means of the conventional method.
SUMMARY OF THE INVENTION
The present invention is intended to solve the above-mentioned problems. Thus, a main object of the present invention is to provide a method for evaluating a shape error of a free curved surface, wherein an entire shape of an original curved surface, such as CAD data, is compared with an entire shape of a distorted curved surface, such as provided after forming, to easily and objectively determine a difference (i.e., error). Another object of the present invention is to provide a method capable of evaluating the entire shape of a free curved surface without being affected by a local “wrinkle”, “bump” or “dent” in the free curved surface. Yet another object of the present invention is to provide a method for evaluating a shape error of a free curved surface in which the numerical calculation is facilitated, and the influence of errors in the numeric values and in the measurements are minimized so the method can be applied to both a parametric curved surface and a cloud of points.
According to the present invention, a method for evaluating a shape error of a free curved surface is provided which comprises: (a) step A for dividing an original curved surface S into up to six curved surface units by combinations of signs (+, 0, −) of a principal curvature (K
1
, K
2
) in each point on the curved surface; (b) step B for associating a distorted surface S′ with the original curved surface S and dividing the distorted curved surface S′ into curved surface units having the same boundary by projection along the normal vectors of S; (c) step C for obtaining an average normal vector for each curved surface unit with respect to the original curved surface and the distorted curved surface; (d) step D for obtaining “a bent component” and “a twisted component” of all combinations of pairs of the different curved surface units with respect to the original curved surface and the distorted curved surface; and (e) step E for calculating a difference between “a bent component” and “a twisted component” of the respective components in the original curved surface and “a bent component” and “a twisted component” of the same respective components in the distorted curved surface.
According to the above method of the present invention, if the curved surface remains to be continuous even after distortion, local irregularities (i.e., wrinkles, bumps or dents) can be canceled by taking an average of the normal vectors in each region (i.e., curved surface unit) of the free curved surface, and a global direction of that region (i.e., average normal vector) can be determined. Therefore, geometrical properties (i.e., a bent component, and a twisted component) of the curved surface can be readily and objectively evaluated, without ambiguity, based on the directional relationship relative to another region (i.e., another curved surface unit) of the average normal vector.
Moreover, since the geometrical properties (i.e., a bent component, and a twisted component) can be easily calculated using only the normal vector in each point on the curved surface, the numerical calculation is facilitated, and the influence of numeric errors and measurement errors is reduced. Consequently, the method in accordance with the present invention can be applied to both a parametric curved surface and clouds of points.
Furthermore, according to a preferred embodiment of the present invention, each curved surface unit is divided into two directions orthogonal to each other and the average normal vectors of the two divided regions are calculated in step C, and “a bent component” and “a twisted component” are obtained with respect to combinations of pairs of the average normal vectors in the two divided regions in the respective curved surface units in step D.
With this method in accordance with the present invention, dividing the same curved surface units in the original curved surface S into two directions provides two pairs of the bent component and the twisted component in the corresponding region, as well as the above-mentioned relationship relative to another region. Thus, it is possible to evaluate both the relationship with another region, and a change in shape in the corresponding region, with respect to each curved surface unit by this two-stage evaluation. In this way, the two-stage evaluation performs a more accurate shape error evaluation.
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Gershon Elber, Elaine Cohen, “Second-Order Surface Analysis Using Hybrid Symbolic and Numerical Operators”, Apr. 1993, ACM Transactions on Graphics, pp. 160-178.*
Farin, G.: “Curves and Surfaces for Computer-Aided Geometric Design”, Book, 1988, Chapter 22, pp. 348-355, A Practical Guide, Academic Press, United States.
Gadh, R. and Sonithi, R.: “Geometric Shape Abstractions for Internet-Based Virtual Prototyping”, Article, 1998, pp. 473-486, vol. 30, No. 6, Computer-Aided Design, Great Britain.
Craig Dwin M.
Frejd Russell
Griffin & Szipl PC
Riken
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