JP2000132580A - Arithmetic unit for geometric parameter - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make a geometric parameter obtainable in a high efficiency and high accuracy by providing a designation means which designates a performance function and an arithmetic means which obtains a geometric parameter of an object three-dimensional environment from the coordinate data and the performance function and by means of a nonlinear programming. SOLUTION: The visual data 14 serving as an image obtained by photographing a real space where an operator visually designates an image of an object three-dimensional environment are stored in a storage 4 together with the three-dimensional coordinate group data 42 corresponding to the data 41. When a computer system is started, a program and the measurement data are read out of a main memory 2. A CPU 1 executes a processing program to calculate a geometric parameter from the outer surface coordinate data which are visually and intuitively selected by the operator and a geometric expression that is defined for every shape such as a column or globe that is designated by an operator among those obtained measurement data and by means of an arithmetic method using the nonlinear programming.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a geometric parameter computing device for determining geometric parameters such as the height, inclination, and center position of a three-dimensional environment based on measurement data of a three-dimensional environment such as an existing structure. In particular, it relates to a three-dimensional modeling system in which such a geometric parameter operation device is applied to a three-dimensional CAD device.

[0002]

2. Description of the Related Art The shape and size evaluation of an existing structure such as an existing plant (hereinafter referred to as a three-dimensional environment) is conventionally performed by measuring a target three-dimensional environment and converting it to a three-dimensional CAD model. Has been done by

FIG. 4 is a flowchart of a conventional three-dimensional environment measurement data processing for evaluating the shape and dimensions of an existing three-dimensional environment. In FIG. 4, first, three-dimensional coordinates of a three-dimensional environment are measured (step S1). As a measuring method, there are a laser measuring method, a stereo photograph measuring method, and the like. A group of measurement data obtained by these methods is a group of three-dimensional coordinates on the outer surface of the three-dimensional environment. Therefore, in order to evaluate the shape and dimensions, it is necessary to calculate numerical values (hereinafter, referred to as geometric parameters) such as the center position, height, and inclination of the three-dimensional environment from the measurement data (step S2).

[0004] Specifically, for geometrical formulas defined for each shape such as a cylinder and a sphere, geometric parameters are set to several unknowns and some three selected from measurement data.
It is derived geometrically by fitting the dimensional coordinates as a known number.

FIG. 5 is a diagram showing an example of calculating geometric parameters when the shape is a cylinder. First, (1) the center coordinates O1 and the radius r of the circle are obtained by selecting the edge points P1 to P4 of the end face A of the cylinder and solving the equation of the circle. next,
(2) The center coordinates O2 of the circle are obtained by selecting the edge points P5 to P8 of the other end face B of the cylinder and solving the equation of the circle in the same manner. Then, (3) the height of the cylinder and the inclination of the center line are obtained from the center coordinates O1 and O2.

Conventionally, such sequential calculation of geometric parameters is conventionally performed manually by an operator, and the result is recorded in a calculation memo (step S3), and the operator refers to the calculation memo. While again by hand,
The obtained geometric parameters are input to a geometric parameter processing device (for example, a three-dimensional CAD device) (step S4).
Then, the necessary processing was performed by the processing device (step S5), and the processing result was evaluated (step S6).

[0007]

However, this method has the following problems.

First, the calculation of the geometric parameters requires the coordinates of a portion called a feature point such as an edge or a corner of the target three-dimensional environment. To select such data from the measurement data, In this case, the operator has to rely on the manual operation of the operator. Then, as the target three-dimensional environment becomes larger and more complicated, the manual work of the operator becomes enormous, and the efficiency becomes poor.

Second, as the target three-dimensional environment becomes more complicated, overlaps and shadows occur, making it difficult to extract measurement data of feature points.

Third, in a real three-dimensional environment such as a plant, since complicated shapes are continuously combined (for example, piping), there is not always a feature point.

Fourth, in the sequential calculation of geometric parameters, the accuracy of the measurement result may be reduced because the accuracy is directly affected by the accuracy of the measurement data and the errors are accumulated.

In view of the above problems, an object of the present invention is to provide a geometric parameter calculation device capable of efficiently and accurately obtaining a geometric parameter.

Further, an object of the present invention is to provide a three-dimensional CA in which the above-mentioned geometric parameter calculation device is applied to a three-dimensional CAD device.
D-modeling system.

[0014]

According to a first aspect of the present invention, there is provided a geometric parameter computing apparatus for designating coordinate data of a target three-dimensional environment and an evaluation function corresponding to a geometric shape of the target three-dimensional environment. From the designation means, the coordinate data and the evaluation function, the geometric parameters of the target three-dimensional environment are
And a calculating means for calculating by a calculation using a non-linear programming method.

Further, in order to achieve the above object, the configuration of the three-dimensional CAD modeling system of the present invention comprises a designating means for designating coordinate data of a target three-dimensional environment and an evaluation function corresponding to a geometric shape of the target three-dimensional environment. An arithmetic unit for obtaining a geometric parameter of a target three-dimensional environment from a coordinate data and an evaluation function by an operation using a nonlinear programming method; and a generating unit for generating a three-dimensional CAD model based on the geometric parameter. It is characterized by.

The non-linear programming method includes, for example, a simplex method, a sequential quadratic programming method, and a complex method.

More specifically, the arithmetic unit of the geometric parameter arithmetic unit and the three-dimensional CAD modeling system includes a plurality of evaluation functions corresponding to a plurality of evaluation function values obtained from the coordinate data and a plurality of arbitrarily set parameters. The variance is calculated, and a parameter corresponding to a variance that is a minimum value among a plurality of variances and smaller than a predetermined convergence determination value is obtained as a geometric parameter for the geometric shape of the target three-dimensional environment.

[0018]

Embodiments of the present invention will be described below. However, the technical scope of the present invention is not limited to the present embodiment.

In the embodiment of the present invention, the geometric parameter computing device of the present invention will be described as a three-dimensional environment modeling system applied to a three-dimensional CAD device. Therefore, in the embodiment of the present invention, in the three-dimensional CAD modeling system, the processing up to obtaining the geometric parameters is called a geometric parameter computing device for convenience, and the processing required for the obtained geometric parameters is performed. The process of generating a CAD model is called a three-dimensional CAD model device.

FIG. 1 is a diagram showing a configuration example of a three-dimensional environment modeling system according to an embodiment of the present invention. As shown in FIG. 1, the three-dimensional environment modeling system includes a CPU 1, a main memory 2, a display device 3, a storage device 4, a keyboard 5, a pointing device (mouse).
6 is a computer system such as an EWS (Engineering Work Station) or a PC (Personal Computer). The storage device 4 stores a processing program (described later) characteristic of the present invention for obtaining geometric parameters, a CAD program for three-dimensional CAD modeling, and measurement data.

As the measurement data, the storage device 4 stores visual data 41 which is an image of a real space for an operator to visually specify an image of a target three-dimensional environment, and three-dimensional coordinate group data 42 corresponding thereto. Is stored within. When the computer system is started, the program and the measurement data are read out to the main memory 2 (or sequentially read out from the storage device 4 according to an operator's designation), and the CPU 1 executes them, whereby the geometric parameters are set. Desired.

FIG. 2 is a flowchart of a three-dimensional environment modeling process according to the embodiment of the present invention. In FIG. 2, first, three-dimensional coordinates of a target three-dimensional environment are measured (step S11). Then, among the obtained measurement data, the geometric parameters are determined from the outer surface coordinate data intuitively selected by the operator and the geometrical formula defined for each shape such as a cylinder or a sphere designated by the operator. The processing determined by the calculation method described later is performed by the CPU 1 executing the processing program (step S12).

When the geometric parameters are obtained,
Subsequently, the CPU 1 executes the CAD program, performs geometric parameter processing (step S13), and executes the three-dimensional CA.
Generate a D model. As described above, in step S12, calculation of geometric parameters conventionally performed manually,
Recording (steps S2 and S3 in FIG. 4) is performed automatically,
Further, the input operation of the geometric parameter (step S4 in FIG. 4), which has been performed manually in the related art, becomes unnecessary.

Next, a specific method of calculating the geometric parameters executed in step S12 of FIG. 2 will be described.
In the present embodiment, a nonlinear programming method is used as a method for calculating geometric parameters, and a simple search method, a sequential quadratic programming method, a complex method, or the like, which is a direct search method, is used as a nonlinear programming solver (hereinafter, this solver). Is applied. Hereinafter, a calculation method using the simplex method will be described. The simplex method is a typical algorithm for solving a nonlinear programming problem, and a simplex is defined as a simplex formed by n + 1 points in an n-dimensional space.

The present solver is a characteristic part of the present invention. When outer surface coordinate data of a target three-dimensional environment and its target geometry are specified by an operator, the solver is used to generate CAD primitives based on them. This is a program for calculating geometric parameters required for each CAD primitive, such as required radius, height, and width. Here, the target geometric shape is a flag that specifies an evaluation function prepared for each CAD primitive used in the nonlinear programming solver.

First, an evaluation function f (αi) in which n parameters αi (i = 0... N) of the target geometric shape are unknown is given. Then, for the evaluation function f (αi), n
Based on a simplex point composed of +1 points, a parameter αi satisfying the following equation (1) for obtaining the variance of the evaluation function value is obtained by a convergence operation. In this solver, the evaluation function f (αi) is defined by the least squares method in order to determine how close each measurement data is to the primitive surface in a total sense.

[0027]

(Equation 1) ε is a convergence determination value of one simplex loop operation. That is, in equation (1), a set of parameters αi in which the difference between all the evaluation function values of the N simplex points and the average value of the evaluation function values is smaller than ε is obtained.
Note that N is generally n + 1, where n is the parameter αi of the evaluation function.

Here, the evaluation function f (αi) will be described using a plane as an example. When the plane equation is expressed by four parameters a, b, c, and d, it can be expressed by equation (2).

Ax + by + cz + d = 0 (2) The coordinates of the m measurement points are represented by (x _i , y _i , z _i ) (i = 1.2.. .M)
Then, the evaluation function value at each simplex point j (j = 1... N) is obtained by Expression (3).

[0030]

(Equation 2) Here, a _j , b _j , c _j , and _dj are parameters at the simplex point j and are given by random numbers. In addition,
Not only the plane expression but also the function expression of Expression (2) is not unique, and an optimal evaluation function may be selected within a reasonable range. There is no upper limit on the number of measurement coordinates to be given as long as the number is N or more.

Then, the evaluation function value for each simplex point is obtained by Expression (3), and the variance of the calculated evaluation function value is obtained by Expression (1). Such convergence calculation by the simplex method is repeated until the variance becomes smaller than the convergence determination value ε (or until the convergence calculation count reaches the upper limit number). At this time, in the calculation of the evaluation function value, the calculation of the evaluation function value is performed a plurality of times while changing the setting of the parameter by a random number. Then, among the calculated evaluation function values, the parameter whose variance is minimized is selected as the solution of the geometric parameter to be obtained.

As described above, by using the simplex method which is one of the direct search methods in the nonlinear programming method, it is possible to efficiently and simply input the outer surface coordinate data of the target three-dimensional environment and its target geometric shape. Accurate geometric parameters can be determined.

There is no upper limit to the number of coordinates to be input as long as it satisfies the mathematical minimum.
As the number of input coordinates increases, the calculation accuracy improves.) Therefore, the geometric parameter calculation can be performed with high flexibility because it is not affected by the coordinate measuring method and the restriction on the number of sampled coordinates is relaxed.

Further, the coordinates to be inputted are arbitrary coordinates of the outer surface of the target three-dimensional environment, and need not be feature points such as edges and corners. Therefore, the work of sampling the input coordinates can be reduced.

FIG. 3 is a flowchart of the geometric parameter calculation (operation performed in step S12 in FIG. 2) using the simplex method according to the embodiment of the present invention. In FIG. 3, first, the outer surface coordinate data of the target three-dimensional environment and its target geometric shape are specified by man-machine interface means such as the keyboard 5 and the mouse 6 (step S100).

In this solver, the simplex method loop is divided into a first step S110 and a second step 120. First,
The first stage is a loop for searching for an initial solution of the parameter αi described above. The search for the initial solution is performed a plurality of times (a predetermined number of times). This is because the convergence calculation in the nonlinear programming does not always converge to the minimum solution at one time, and the predetermined number may be set in accordance with the allowable calculation time.

More specifically, when the initial solution search for the parameter αi starts (step S111), first, in the first initial solution search loop, an unknown number (parameter) α using random numbers is used.
i is initialized (step S113). Then, a simplex method operation is performed on the parameter αi (step S114). That is, each simplex point j
Is calculated by substituting the parameter αi initially set in Equation (1) into Equation (1), and calculating the variance of the calculated evaluation function value. When the obtained variance satisfies the formula (1) (when it is smaller than the convergence judgment value ε), the parameter αi in the search loop is provisionally set as the optimal solution of the initial solution of the parameter αi.

Further, in the second and subsequent initial solution search loops, similarly, the calculation of the equation (1) for the unknown number (parameter) αi set as the initial solution by random numbers is repeated. If the equation (1) is satisfied, the parameter αi in the search loop is compared with the above-mentioned optimal solution (step S115). If the variance of the search loop is smaller than the variance of the optimal solution, the optimal solution is updated to the parameter αi of the search loop (step S116).

When the initial solution search loop is performed a predetermined number of times (step S112), the initial solution search loop
It ends (step S117), and the second stage (step S1)
Proceed to 20).

In the second step, a more accurate simplex method operation is executed using the optimal solution of the initial solution of the parameter αi obtained in the first step. That is, first, the optimal solution obtained in the initial solution search loop in the first stage is set as the parameter αi in the second stage. (Step S1
21). Then, a simplex operation is performed on the parameter αi (step S122). Specifically, the calculation of Expression (1) similar to that in step S114 is performed. At this time, in step S122, a value smaller than the convergence determination value ε of Expression (1) used in step S114 is used. As a result, a more accurate convergence operation is performed, and the accuracy of the parameter αi can be determined.

Then, in step S123, when the expression (1) is satisfied (converged), the parameter αi
Is determined as the geometric parameter of the given target geometry, and the geometric parameter and the target geometry are
Input to the dimensional CAD modeling process (step S1
30). Thereby, the above-described step S13 in FIG. 2 is executed, and a three-dimensional CAD model can be generated.

On the other hand, if the equation (1) is not satisfied in step S123, an error is displayed on the display device 3 (step S140).

The calculation target of the geometric parameter calculation device for performing the geometric parameter calculation processing according to the embodiment of the present invention is:
As long as it is defined as an evaluation function, it is not limited to CAD primitives and may be applied to devices other than three-dimensional CAD devices, and its versatility is high.

[0044]

As described above, according to the geometric parameter computing device of the present invention, the nonlinear programming method (for example, one of the direct search methods) can be used.
(Simplex method), it is possible to efficiently and accurately determine geometric parameters from the coordinate data of the target three-dimensional environment and the target geometric shape.

The number of designated coordinates has no upper limit as long as it satisfies the mathematical minimum. Accordingly, the geometric parameter calculation device can be provided with high flexibility because it is not affected by the method of measuring coordinates and the restriction on the number of sampled coordinates is relaxed.

Further, the designated coordinates are sufficient to be the coordinates of the outer surface of the target three-dimensional environment, and need not be the coordinates of feature points such as edges and corners. Therefore, reduction of coordinate sampling work is achieved.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a configuration example of a three-dimensional environment modeling system according to an embodiment of the present invention.

FIG. 2 is a flowchart of a three-dimensional environment modeling process according to the embodiment of the present invention.

FIG. 3 is a flowchart of calculating a geometric parameter according to the embodiment of the present invention.

FIG. 4 is a flowchart of a conventional three-dimensional environment measurement data process for evaluating the shape and dimensions of a three-dimensional environment.

FIG. 5 is a diagram illustrating an example of calculating geometric parameters when the shape is a cylinder;

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 CPU 2 Main memory 3 Display device 4 Storage device 5 Keyboard 6 Mouse

──────────────────────────────────────────────────の Continued on the front page (51) Int.Cl. ⁷ Identification symbol FI Theme coat ゛ (Reference) G06F 15/62 415 (72) Inventor Emi Shioi 1-1-1 Wadazakicho, Hyogo-ku, Hyogo-ku, Kobe-shi, Hyogo Prefecture Mitsubishi Heavy Industries, Ltd. Kobe Shipyard F-term (reference) 2F065 AA04 AA53 BB05 DD06 FF05 JJ03 QQ31 UU05 5B046 AA02 AA03 DA02 FA18 GA01 5B056 AA06 BB64 BB71 DD03 HH03 5B057 CH08 DA06 DB03 DC09

Claims (6)

[Claims] 1. An object 3D environment coordinate data and the object 3
Designating means for designating an evaluation function corresponding to the geometrical shape of the three-dimensional environment; and calculating means for obtaining the geometric parameters of the target three-dimensional environment from the coordinate data and the evaluation function by calculation using a nonlinear programming method. A geometric parameter calculation device, comprising: 2. The geometric parameter operation device according to claim 1, wherein said operation means uses a simplex method in said nonlinear programming. 3. The method according to claim 2, wherein the calculating means calculates a plurality of variances corresponding to a plurality of values of the evaluation function obtained from the coordinate data and a plurality of parameters set arbitrarily. A geometric parameter calculating device for obtaining a parameter corresponding to a variance that is a minimum value among the plurality of variances and smaller than a predetermined convergence determination value as a geometric parameter for the geometric shape of the target three-dimensional environment. . 4. Coordinate data of a target three-dimensional environment and the target 3
Designating means for designating an evaluation function corresponding to the geometric shape of the three-dimensional environment; calculating means for calculating the geometric parameters of the target three-dimensional environment from the coordinate data and the evaluation function by a calculation using a nonlinear programming method; Generating means for generating a three-dimensional CAD model based on the geometric parameter.
D modeling system. 5. The three-dimensional CAD modeling system according to claim 4, wherein said calculating means uses a simplex method in said nonlinear programming. 6. The method according to claim 5, wherein the calculating means calculates a plurality of variances corresponding to a plurality of values of the evaluation function obtained from the coordinate data and a plurality of arbitrarily set parameters. Three-dimensional CAD modeling, wherein a parameter corresponding to a variance that is a minimum value among the plurality of variances and smaller than a predetermined convergence determination value is obtained as a geometric parameter for the geometric shape of the target three-dimensional environment. system.