Image analysis – Pattern recognition – Feature extraction
Reexamination Certificate
1999-10-25
2004-01-27
Chang, Jon (Department: 2623)
Image analysis
Pattern recognition
Feature extraction
C382S141000, C702S155000, C345S960000
Reexamination Certificate
active
06683985
ABSTRACT:
This application claims priority on Japanese Patent Application No. 10-9139/1997, filed Apr. 25, 1997, the entire diclosure which is incorporated herein by reference.
BACKGROUND OF THE INVENTION
1. Technical Field
The present invention relates to a method of determining a shape error of a free-form surface.
2. Background Art
With respect to formings formed by press working such as the body of an automobile, discrepancy has been conventionally evaluated by experiences. That is, the free-form surface has been conventionally evaluated mainly by “visual observation”. In recent years, however, designing using a computer (CAD) has been spread and a deformation upon processing can be simulated. Accordingly, means for evaluating a free-form surface, that is, for objectively defining discrepancy in a forming and displaying it is desired.
FIG. 1
shows a forming sample showing discrepancy in a plate forming.
FIG. 2
is a diagram showing an example of a conventional method of evaluating a shape error in a free-form surface. The example relates to a result of numerical simulation using simulation software (ITAS-3D) reported in “Simulation of 3-D sheet bending process” (Takizawa et al., 1991, VD1 BERICHTE NR. 894), “Some advances in FEM simulation of sheet metal forming processes using shell elements” (Kawka et al., 1995, Simulation of Materials Processing, Shen & Dawson (eds.), Balkema, Rotteerdam, pp. 735-740), and the like.
In
FIG. 2
, a white part shows a shape as a reference (for example, the shape of a die) and a mesh part indicates a shape obtained by a forming simulation. The reference shape and the simulation shape are displayed at the same position and only a part positioning on the front side is displayed. Consequently, a shape error between the simulation shape and the reference shape can be roughly determined from the displayed white and mesh parts. The method has, however, the following problems.
(1) It is necessary to determine a reference position and make the reference shape and the simulation shape accurately coincide with each other at the reference position. The result is largely influenced according to the way the reference position is determined.
(2) Since the position of the other part is largely displaced due to a partial bending, it is difficult to find the cause of occurrence of an error.
(3) How much the shapes coincide with each other as a whole cannot be shown by an objective numerical value.
FIG. 3
shows CMM data (about 40,300 points) measured by using a three coordinate measuring machine “Mitsutoyo Super BHN 506”.
FIG. 4
shows the top view of
FIG. 3
(about 8,000 points). As shown in these figures, the shape of a forming item actually formed by using a die can be displayed as images as shown in
FIGS. 3 and 4
by measuring the forming item by the three coordinate measuring machine. From the images, shape errors such as projected and recessed parts and a twisted part can be roughly determined from the views. The method, however, also has the above-mentioned problems (2) and (3) in the numerical simulation and has a problem that (4) when the reference shape is not flat but has a complicated curve, the difference from the result of the three coordinate measurement can be hardly determined.
As mentioned above, methods of experiment, measurement, and display of result for evaluating the shape error have not been systematized yet. There has not been a simple and clear definition as an index of a forming discrepancy and, further, an evaluation method which can be repeatedly performed has not been existed conventionally.
SUMMARY OF THE INVENTION
The present invention is made in order to solve the problems. That is, a principle object of the invention is to provide a method of determining a shape error of a free-form surface which can accurately grasp a different part between two three-dimensional shapes of an actual forming shape and a simulation shape by a computer simulation, a reference shape by CAD, or the like. It is another object of the invention to provide a method of determining a shape error of a free-form surface which can be applied without making the reference positions accurately coincide with each other, find the cause of occurrence of an error such as a partial bending, show how much the shapes coincide with each other as a whole by an objective numerical value, and easily determine the error even if the reference shape is complicated.
The inventors of the present invention have invented “extended Gaussian curvature” as an evaluation model which does not depend on the coordinate system. According to the invention, a local shape error of a free-form surface is classified into three types (mountain, valley, and twist) by comparing an actual curved surface with, for example, a CAD curved surface as a reference. A method of calculating the ratio of the same labels by using the image processing technique has also been invented. The invention is based on the novel ideas.
According to the invention, there is provided a method of determining a shape error of a free-form surface by obtaining a principle curvature of a target curved surface S′ and a principle curvature of a corresponding position of a reference surface S; and displaying each part by classifying it from the difference between the principle curvatures into (a) a case where the two principle curvatures increase, (b) a case where the two principle curvatures decrease, and (c) a case where one of the principle curvatures increases and the other decreases.
That is, according to a preferred method of the invention, &Dgr;&kgr;
1
=&kgr;
1
′−&kgr;
1
, &Dgr;&kgr;
2
=&kgr;
2
′−&kgr;
2
are obtained from the principle curvature (&kgr;
1
′, &kgr;
2
′) of the target curved face S′ and the principle curvature (&kgr;
1
, &kgr;
2
) of the reference curved face S. (1) When &Dgr;&kgr;
1
≧0 and &Dgr;&kgr;
2
≧0, (a) it is determined that the two curvatures increase. (2) When &Dgr;&kgr;
1
≦0 and &Dgr;&kgr;
2
≦0, (b) it is determined that two curvatures decrease. (3) When &Dgr;&kgr;
1
·&Dgr;&kgr;
2
<0, (c) it is determined that one of the curvatures increases and the other decreases. Preferably, (a), (b), and (c) are determined as mountain, valley, and twist, respectively, and are displayed in different symbols or colors on an image. Further, it is preferable that the ratio of the same labels is calculated from the labels (a), (b), and (c) and is used as a coincidence ratio.
The Gaussian curvature K is a product &kgr;
1
&kgr;
2
of the principle curvatures &kgr;
1
and &kgr;
2
of three-dimensional surfaces. (1) When K>0, it is known that the shape is elliptic. (2) When K=0, it is known that the shape is parabolic. (3) When K<0, it is known that the shape is hyperbolic.
The invention relates to an extended Gaussian curvature. That is, according to the method of the invention, the principle curvature of a target curved surface S′ including an error and the principle curvature of a corresponding position of a reference curved surface S are obtained and each part is classified into (a), (b), and (c) from the difference between the principle curvatures, namely, the parts can be displayed while being classified into the case where two principle curvatures increase, the case where two principle curvatures decrease, and the case where one of the principle curvatures increases and the other decreases. Thus, the different part between two three-dimensional shapes can be accurately grasped.
According to the method, the shape error can be determined by obtaining the principle curvatures of corresponding positions. Consequently, the invention can be applied without making the reference positions of two three-dimensional shapes accurately coincide with each other and the cause of occurrence of an error such as a partial bending can be found.
Further, by calculating the ratio of the same labels from the labels (a), (b), and (c) and using it as a coincidence ratio, how much the shapes coincide with each other as a whole can be gras
Kase Kiwamu
Kondo Tetsuya
Makinouchi Akitake
Mori Naomichi
Chang Jon
Griffin & Szipl
Riken
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