JP2796728B2 - Graphic processing method and apparatus - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a graphic processing method and apparatus, and more particularly to a graphic processing method and apparatus suitable for creating data of an analysis program based on a finite element method and supporting analysis result processing. .

[Conventional technology]

As an example of a method of defining a free-form surface by sweeping a curve, there is a method of moving a curve equation along a control curve as described in Japanese Patent Application Laid-Open No. 62-131384. To analyze a structure including a beam element using a finite element method structural analysis program, for example, ADINA, it is necessary to specify a node that defines a local coordinate system of the beam. However, a node rarely exists at a position convenient for designating a local coordinate system, and the user usually inputs coordinate values of points other than the nodes constituting the finite element. Further, the user also inputs a vector for determining the direction of the load.

In structural analysis and fluid analysis, the finite element method is described in, for example, JP-A-62-97070 and is widely used. The physical quantities (for example, temperature, pressure, stress, etc.) obtained from the analysis result using the finite element method are calculated as values on each node where the system to be analyzed is mesh-divided into various elements. For this reason, the finer the mesh division, the more detailed the physical quantity distribution of the system can be obtained. In this case, when the system is small and simple, there is no particular problem. However, as the system becomes larger and more complex, the number of mesh divisions becomes enormous, and the computer memory and calculation time required for finite element analysis also become enormous. . Therefore, in the calculation of a large-scale system, the mesh division is coarsened to reduce the number of divisions, thereby reducing the load on the computer. As a result, in order to obtain the state distribution of the system, it is necessary to predict the physical quantity between the nodes using the physical quantity of each node obtained by the finite element analysis. As a physical quantity prediction method, there is a method of performing a straight line or curve approximation using the physical quantity of each node and interpolating the physical quantity between the nodes.

[Problems to be Solved by the Invention] In the prior art described in the above-mentioned JP-A-62-131384,
It is assumed that a sequence of points such as a control curve of a curved surface has been input in some way, and how to give the sequence of points is not considered. Therefore, in an existing graphic processing apparatus, for example, a graphic processing apparatus that defines a three-dimensional shape by inputting a point in a three-dimensional space, a user reads a point sequence of a control curve from a three-sided view of the shape and reads it. It was necessary to input the coordinate value of the point sequence. For this reason, preparation before using the graphic processing apparatus takes time and labor, and errors are likely to occur. A similar problem has occurred in the case of a graphic processing device that defines a three-dimensional shape from a two-dimensional drawing.

Also, in the above-mentioned method of interpolating the physical quantity between nodes by performing a straight line or curve approximation using the physical quantities of the nodes obtained by the finite element method, it is necessary to predict the physical quantity in the plane of the element enclosed between the nodes. Is impossible. Meanwhile, structural analysis,
As the target system becomes larger and more complex as in fluid analysis, more detailed analysis is required. Although computers are increasing in size at an accelerating scale, the analysts are forced to compromise between the number of mesh divisions and the capacity of the computers used, resulting in highly accurate prediction of physical quantities in the finite element model. There is a need for a possible interpolation method.
As described above, in the above-described related art, no consideration is given to the interpolation of the physical quantity of the surface surrounded by the nodes, and there is a problem in the accuracy of predicting the state quantity distribution of the surface.

A first object of the present invention is to semi-automatically convert the above-described point sequence using points and vectors determined by the positional relationship between points, lines and surfaces of a shape defined in the process of defining a three-dimensional shape. The purpose of the present invention is to reduce the labor of preparing and inputting data and to improve the operability.

The second object of the present invention is to use a positional relationship between defined mesh points to define a local coordinate system of a beam element,
By generating a load vector, it is possible to reduce the trouble of preparing and inputting data and to improve the operability.

A third object of the present invention is to obtain a physical quantity distribution of a surface of an element obtained by dividing a finite element with high accuracy by interpolation.

[Means for solving the problem]

The above object includes an input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. An input unit NA for inputting designation of existing points, planes, and lines to a graphic processing device that supports data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space; The tangent vector of the curve, the direction vector of the straight line,
An operation unit EA for obtaining a surface normal vector, an input unit NB for inputting a starting point of the vector and its size, and a start point and a size connected to the input unit NB and the operation unit EA and designated by the input unit NB. And a calculation unit EB for obtaining a vector parallel to the vector obtained by the calculation unit EA and an end point thereof.

The first object includes an input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. An input unit NA for inputting designation of existing vertices, planes, and lines to a graphic processing apparatus that supports data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space;
A calculation unit EA that obtains the tangent vector of a curve, the direction vector of a straight line, and the normal vector of a surface based on the coordinate values of vertices, surfaces, and lines and / or equations connected to the NA, and the starting point of the vector and its size Input section NB for inputting the
An arithmetic unit EB connected to the NB and the arithmetic unit EA and having a start point and a size specified by the input unit NB and having a vector parallel to the vector obtained by the arithmetic unit EA and an end point thereof
And an input unit NC for inputting data relating to the sweep, a sweep connected from the input unit NC and the data input from the input unit NC connected to the arithmetic unit EB, the vector obtained by the arithmetic units EA and EB, and the start point thereof. For calculating control curve
EC, a display unit connected to the operation unit EC and displaying the operation result, and a storage unit connected to the operation units EA, EB, EC and the display unit and exchanging data with them. Is achieved by

The first object also includes an input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. Prepared, 3
A graphics processing device that supports the creation of data for analysis programs such as structural analysis from the shape of an object defined in a three-dimensional space,
An input unit NA for inputting designation of an existing point / plane / line, and a tangent vector, a direction vector of the line based on the coordinate values and / or equations of the input point / plane / line connected to the input unit NA.
An operation unit EA for obtaining a surface normal vector, an input unit NB for inputting a starting point of the vector and its size, and a start point and a size connected to the input unit NB and the operation unit EA and designated by the input unit NB. And an operation unit EB for obtaining a vector parallel to the vector obtained by the operation unit EA and its end point, an input unit NC for inputting data related to sweep, and an input unit connected to the input unit NC and the operation unit EB. An operation unit EC that obtains a sweep control curve from the data input from the NC, the vectors obtained by the operation units EA and EB, and its starting point, and an input unit that inputs the designation of points, planes, and lines to be swept. ND
An operation unit ED connected to the input unit ND and the operation unit EC to execute a sweep operation; a display unit connected to the operation unit ED to display the operation result; and the operation units EA, EB, EC, And a storage unit connected to the ED and the display unit for exchanging data therewith.

The second problem includes an input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. An input unit NE for inputting a command of an existing node to a graphic processing device that supports data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space, and is connected to the input unit NE. An operation unit EA for obtaining a tangent vector of a curve defined by an input node, a direction vector of a straight line, and a normal vector of a surface, an input unit NF for inputting designation of a beam element, the input unit NF, and the operation unit An operation unit EF that is connected to the EA and obtains a position vector of a point existing on the beam element specified by the input unit NF or an extension thereof, and a vector connected to the operation unit EF and obtained by the operation units EA and EF And find the end point coordinate value Calculation unit EG, a display unit connected to the calculation unit EG and displaying the calculation result as a point defining the local coordinate system of the beam element, and a display unit connected to the calculation units EA, EF, EG and the display unit. And a storage unit for exchanging data between the storage units.

Further, the second problem is that an input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, a display unit connected to the storage unit and the operation unit, With
An input unit NE for inputting designation of an existing node into a graphic processing device for supporting the creation of data of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space;
A calculation unit EA for obtaining a tangent vector, a direction vector of a curve, and a normal vector of a surface defined by a node connected to and input to the NE, an input unit NG for inputting a magnitude of the vector, and the input unit NG And an operation unit EH connected to the operation unit EA and having a size specified by the input unit NG and obtaining a load vector parallel to the vector obtained by the operation unit EA.
And a display unit connected to the operation unit EH and displaying a calculation result, and a storage unit connected to the operation units EA, EH and the display unit and exchanging data therewith. Is done.

The third subject includes an input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. A graphic processing device for displaying the output of an analysis program such as a structural analysis from the shape of an object defined in a three-dimensional space is provided with a point sequence in a space comprising node coordinate values and a physical quantity of the node as an analysis result. An operation unit EI that creates data of the above, an operation unit EJ that is provided connected to the operation unit EI, and selects sample points required for interpolation from data of a point sequence created by the operation unit EI, and an operation unit EJ. An operation unit EK that is provided connected and obtains an equation of an interpolation surface defined by a sample point; a display unit that is connected to the operation unit EK and displays an operation result; and the operation units EI, EJ, EK, and Connected to the display unit and exchanges data with them And a storage unit.

Further, the first problem is to input an existing point, plane, and line designation into a graphic processing method that supports creation of data of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space. A procedure for calculating a tangent vector of a curve, a direction vector of a straight line, and a normal vector of a surface based on the input coordinate values of points, surfaces, and lines and / or equations;
A procedure for inputting a starting point and a magnitude of a vector, an arithmetic procedure having a starting point and a magnitude designated by the procedure and a vector parallel to the vector determined by the arithmetic procedure and an end point thereof, and data relating to sweep. , A calculation procedure for obtaining a sweep control curve from the data input by the procedure, the vector obtained by the calculation procedure, and the starting point thereof, and specifying a point, plane, and line to be swept. This can also be achieved by providing a procedure for inputting, a procedure for performing a sweep calculation, and a procedure for displaying a calculation result.

In addition, the second problem is to input a designation of an existing node into a graphic processing method for supporting data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space. A calculation procedure for obtaining a tangent vector of a curve defined by the set nodes, a direction vector of a straight line, and a normal vector of a surface; and a procedure for inputting designation of a beam element.
An operation procedure for obtaining a position vector of a point existing on a specified beam element or an extension thereof, an operation procedure for obtaining a coordinate vector of an end point of the vector obtained by the operation procedure, and an operation result Displaying the beam element as a point that defines the local coordinate system of the beam element.

Further, the third problem is to provide a graphic processing method for displaying an output of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space, by using a coordinate value of a node and a physical quantity of the node as an analysis result. An operation procedure for creating data of a point sequence in the space consisting of: an operation procedure for selecting a sample point required for interpolation from the data of the point sequence created by the operation procedure; and an equation of an interpolation plane defined by the sample point And a procedure for displaying the calculation result.

[Action]

A specified point from existing points, lines, and faces in space,
A line or surface is defined based on either the line or the surface, and a tangent vector, a direction vector, a normal vector of the defined line or the surface, or a vector obtained by linearly transforming these vectors is obtained. The starting point and the size of the obtained vector are designated, and the coordinates of a new point on the three-dimensional space are obtained.

〔Example〕

Hereinafter, embodiments of the present invention will be described with respect to shape definition, K-point definition, load vector definition, and analysis result interpolation. What is common to these is that a normal vector, a tangent vector, and a direction vector of a surface or a line defined by a sequence of points known in space are generated by computation, and A new point is generated by generating a new plane or straight line using the positional relationship of the obtained vectors, for example, an orthogonal relationship, or by giving a starting point or a size to the obtained vector. . In addition, by performing the same operation using the equation of a plane or a line known in space, a new vector, plane,
That is, lines and points are generated.

FIG. 1A shows the configuration of the first embodiment of the present invention. The present embodiment generates a control curve for defining a shape by sweeping, and an input unit NA101 for inputting designation of vertices, lines, and surfaces that have been defined in the process of defining the shape, and A specified vertex, which is provided in connection with the unit NA101,
An operation unit EA102 for calculating a tangent vector and a normal vector of a line based on coordinate values and equations of a line and a surface, and a normal vector of a surface, and an input unit NB103 for inputting designation of a starting point and a size of the vector. And the input unit 103 and the arithmetic unit EA10
A calculation unit EB104, which is connected to the input unit NB103 and has a starting point of a vector input from the input unit NB103, has a magnitude, and calculates a coordinate value of a vector parallel to the vector determined by the calculation unit 102 and an end point of the vector; , An input unit NC105 to which information on sweep is input, and an input unit NC105 connected to the input unit NC105 and the arithmetic unit EB104.
An operation unit EC106 for obtaining a sweep control curve from the vector, the point obtained by the step 04, and the information on the sweep inputted from the input unit NC105, and a display unit 108 provided connected to the operation unit EC106 for displaying the operation result. And the arithmetic unit E
A102, EB104, EC106 and is provided connected to the display unit 108,
A storage unit 109 for exchanging necessary data with them is provided.

FIG. 1B shows the flow of processing in this embodiment. Each procedure in FIG. 1B is denoted by a reference numeral corresponding to the block in charge of the procedure in FIG. 1A.

Next, FIG. 1C shows a main configuration of a second embodiment in which the first embodiment is partially modified. This embodiment is an apparatus for defining a solid model, a surface model, and a wireframe model. In addition to the configuration shown in FIG. 1A, an input unit ND107 for inputting designation of a surface, a line, and a point to be swept.
And an operation unit ED110 that is connected to the input unit 107 and the operation unit 106 and performs a sweep of a plane, a line, and a point specified by the input unit 107.
08 is connected not to the operation unit 106 but to the operation unit 110, and instead of the storage unit 109, the operation units 102, 104, 106, 110, the display unit 10
The storage unit 119 is connected to the storage unit 8 and exchanges necessary data with them.

FIG. 1D shows the flow of processing in this embodiment. Each procedure in FIG. 1D is provided with a procedure corresponding to the block in charge of the procedure in FIG. 1C.

An example in which each of the solid model, the surface model, and the wire frame model is defined by the above device will be described below.

(A) Definition of solid model Section 6 of shape 5 of the solid model shown in FIG. 2A
Is a region surrounded by an ellipse E having a major axis a and a minor axis b shown in FIG. 2B. Shape 5 is a partial shape 7 having a length l _{1 and} a center of curvature P _R
Is divided partial shape 8 having a radius of curvature r, and the three partial shape 9 of length l _2. A procedure for defining the shape 5 by sweeping the cross section 6 will be described.

(I) Definition of Region 6 The position of the ellipse E is defined in the three-dimensional space. Here, the position is defined based on the shape attribute of the ellipse, the coordinates of the center P _{1 of} the ellipse E, the end point P ₂ of the major axis of the ellipse E, and the end point P ₃ of the minor axis of the ellipse E. A region 6 surrounded by the ellipse E is defined by the ellipse E and the internal point Py.

(Ii) Definition of Partial Shape 9 A method of defining the partial shape 9 by sweeping the area 6 will be described with reference to FIG. 3A. The direction of the sweep is defined as the normal direction of the area 6. Normal vector is a point
It is obtained by the following equation using the coordinate values of P ₁ , P ₂ , and P ₃ .

Suppose that the ellipse E is reflected on the ellipse E 'by the sweep. An arbitrary point Px on the ellipse E is captured by a sweep to a point Px ′ represented by the following equation.

The above procedure is shown in FIG. 3B.

(Iii) Definition of Partial Shape 8 A method of defining the partial shape 8 will be described with reference to FIG. 4A.
Here, take on an extension of a straight line connecting the curvature center P _R a 'and the point P _2' the point P _1, the radius of curvature r. Coordinate value of the point P _R is obtained by the following expression.

Radius And the clockwise rotation by θrad in the plane defined by the normal vector. The sweep at this time is performed in the following procedure. First of all, the origin of the point P _R, vector Direction 方向 axis, vector η axis, vector Is the ζ axis. At this time, in the 1-η-ζ space, the point P ₁ ′
Is (−r, 0,0). Point "coordinate values (xi] 'P _1' and xi]-eta points in the plane P _R around the point was θrad rotated clockwise of _{P 1, η", ζ "} ) is given by the following equation.

Further, a point Py ′ existing in a plane surrounded by the ellipse E ′
(Ξy ′, ηy ′, ζy ′) is reflected on Py ″ by rotation.
The coordinate value (ξyP, ηy ″, ζy ″) of the point Py ″ is obtained by the following equation.

The coordinate values of these points are calculated as xy from the ξ-η- 、 coordinate system.
By converting to the −z coordinate system, the partial shape 8 is defined. The above procedure is shown in FIG. 4B.

(Iv) Definition of the partial shape 7 The definition of the partial shape 7 is performed by performing the same operation as in the case of the partial shape 9.

Although the method of defining the solid model by sweeping the area 6 has been described above, it is also possible to sweep an area having a curved surface or a hole.

(B) Definition of Surface Model The procedure for defining the curved surface shape S shown in FIG.

The plane A defined by the radius r of the circle c and the radius r 'of the circle c' is parallel to the plane A 'defined by the circle c'. The distance between the plane A and the plane A 'is d plane A Vector connecting the normal to the center P ₁ of circle c and the center P ₁ ′ of circle c ′ First, a circle c is defined in a three-dimensional space. As shown in Figure 5B, the center point P ₁ of the circle c origin, the plane A x-y plane,
The circle c is represented by the following equation, where the normal direction of the plane A is the z-axis.

Next, as shown in Figure 5B, move along the center P ₁ of the circle c in the direction vector forming a normal vector and the angle θ of the plane A. Circle c obtained by sweeping up away the circle c distance D "is the equation of the center of the circle P _1"
(X ₁ ″, y ₁ ″, z ₁ ″) and the radius is r ″, which is expressed by the following equation.

Now, if a direction vector forming an angle θ with the normal vector is taken on the yz plane, the center P ₁ ″ (x ₁ ″, y ₁ ″,
z ₁ ″) and the radius r ″ are represented by the following equations.

Where dF is the distance between the intersection of the extension line of the straight line connecting the points P ₁ and P ₁ ′ and the extension line of the straight line connecting the points of the circles c and c ′ having the smallest value in the y-axis direction to the circle c ′ It is.

With the above procedure, sweeping is performed while reducing the radius of the circle. FIG. 5c illustrates the above procedure.

(C) Definition of wireframe model The procedure for sweeping points to define the three-dimensional curve l shown in FIG. 6A will be described. The curve 1 shown in the figure has a linear shape as shown in FIG. 6B, and has a height Δh and a radius ΔR every one rotation.
Change. First, the rotation center point P is set in the xyz space.
₀ (x ₀ , y ₀ , z ₀ ), a sweep start point P (x, y, z), and a point Ph (xh, yh, zh) defining a height direction are defined. next,
The point P ₀ as shown in 6c Figure, P, based on the coordinate values of Ph, the point P ₀
Is the origin, vector ▲ ▼ is the ξ axis, a straight line P ₀ P from point Ph
A coordinate axis is defined in which the vertical direction is set to the ζ axis, the ξ axis, and the η axis is the vector direction orthogonal to the ζ axis.

Assuming that the length of the line segment ▼ is R, the equation of the curve l is expressed by the following equation using the parameter θ.

The above procedure is summarized in FIG. 6D. By mapping the above equations into the original xyz space, a wireframe model is defined.

According to the first and second embodiments, the three-dimensional data is obtained based on the data of the positional relationship (inclination, distance, etc.) between the surface, line, and point at the start of the sweep and the surface, line, and point after the end of the sweep. The shape can be defined, the operability is improved, and even a beginner can easily operate.

Next, a point (hereinafter referred to as a K point) that defines the local coordinate system of the beam element is generated. FIGS. 7A and 7B show a third embodiment of the present invention.
This will be described with reference to FIGS. 8A and 8B. The present embodiment is an apparatus for generating the K points, an input unit NE201 for inputting designation of a node constituting a mesh-divided shape, and a node connected to the input unit 201 and designated by the input unit 201. An operation unit EA102 for obtaining a vector such as a normal vector of a surface defined by a group or a tangent vector of a line using node coordinates, an input unit NF203 for inputting designation of a beam element, the input unit 203 and the operation unit An operation unit EF204 for obtaining a position vector of an arbitrary point S on a beam element B specified by the input unit 203 or a straight line extending from the beam element provided by the input unit 203; and an operation unit EF204 provided to be connected to the operation unit 204. Vector ▲ ▼ = + with the vector obtained by the arithmetic unit 102 and the arithmetic unit 204
(Point O is the origin of the global coordinate system, Point K is the K point)
An operation unit EG205 for obtaining coordinate values of points, a display unit 108 connected to the operation unit 205 for displaying an operation result, and each unit provided for connection to the operation units 102, 204, 205 and the display unit 108, A storage unit 209 for exchanging data.

FIG. 7B shows the flow of the processing of this embodiment, and the steps shown in FIG. 7B are denoted by the same reference numerals as those of the blocks shown in FIG. 7A that actually perform the processing. Hereinafter, an example of a method of calculating a vector will be described.

First, a method using two nodes will be described. this is,
As shown in FIG. 8A, a method utilizing a vector ▲ ▼ connecting the two existing nodes P _1, P ₂ as a vector, ▲ ▼ and nodal P _1, P ₂ so that not parallel beam elements You need to choose.

Next, a method using three nodes will be described. This is
As shown in FIGS. 9A and 9B, this method uses the normal vector of the plane A defined by the existing three nodes P ₁ , P ₂ , and P ₃ .

Next, a method using a curved surface equation will be described. This is a method in which a normal vector of a curved surface at a point P on the curved surface is set as a vector, and the calculation procedure is as follows. First, an equation of a curved surface is obtained using a point near the point P.
The equation f (x, y, z) of the normal vector of the curved surface is represented by the following equation.

f (x, y, z) = ▽ (10) ▽: Hamilton operator By substituting the coordinate value of the point P into the above equation (10),
The normal vector of the curved surface at the point P is obtained.

Further, there is a method in which a vector obtained by combining a vector obtained by any of the above methods and a vector defined outside is used as a vector.

Next, a fourth embodiment of the present invention for defining a load vector will be described. This embodiment shown in FIG.10A has an input unit NE20 for inputting designation of a node constituting a mesh-divided shape.
1 and an operation unit EA102 which is connected to the input unit 201 and obtains a vector such as a normal vector of a surface or a tangent vector of a line defined by the node group specified by the input unit 201 using the node coordinates. , An input unit NG303 for inputting designation of a vector size n, and a load vector provided in connection with the input unit 303 and the arithmetic unit 102 and having a size specified by the input unit 303. A calculation unit EH304 that obtains the calculation result, a display unit 108 that is provided connected to the calculation unit 304 and displays the calculation result, and a storage unit 309 that exchanges necessary data between the calculation units 102 and 304 and the display unit 108, Have. FIG. 10B shows the flow of the procedure of the process according to the present embodiment, and each procedure is denoted by the same reference numeral as that of the block shown in FIG. 10A for implementing the procedure.

 Next, an example of calculation performed by the calculation unit will be described below.

It is assumed that a load of a unit size is applied to the node N of the finite element model shown in FIG. 10C in the same direction as the longitudinal direction of the beam B. At this time, the node N _i which constitutes the beam B, and using the coordinate values of N _j, load vectors are obtained by the following equation.

The above procedure is summarized in FIG. 10D.

According to the third and fourth embodiments, the coordinate value and the load vector of the point (point K) defining the local coordinate system of the beam element can be defined without considering the entire coordinate system, Operability is improved.

Next, a fifth embodiment of the present invention for interpolating the analysis result will be described. The embodiment of the present invention shown in FIG.10E is connected to an arithmetic unit ET401 for creating data of a point sequence in a space composed of coordinate values of nodes constituting a shape and coordinate values of physical quantities as an analysis result, and is connected to the arithmetic unit 401. An arithmetic unit EJ402 for selecting sample points necessary for interpolation from the data of the point sequence newly created by the arithmetic unit 401, and an interpolation unit connected to the arithmetic unit 402 and defined by the sample points. An operation unit EK403 for performing an operation for obtaining an equation of a surface; a display unit 108 provided connected to the operation unit 403 to display an operation result; and the operation unit 40
1, 402, 403 and a display unit 108, and a storage unit 409 for exchanging necessary data with them.

FIG. 10F shows the flow of the processing of this embodiment, and the respective steps are denoted by the same reference numerals as those of the blocks described in FIG. 10E for implementing the procedure. An example of a calculation performed by the calculation unit will be described below.

FIG. 11 shows a two-dimensional plate model divided into shell elements, and the temperature T of a node when an arbitrary amount of heat is applied to the node of the plate model is a function of position and time. Node i
Is represented by (x _i , y _i ), the temperature of the node i at the time t is represented by T (x _i , y _i , t).

The temperature of each node at a certain time t = t _k known.
At this time, the temperature T = T (x, y,
t _k ) is obtained by interpolation with a plane or a curved surface.

First, interpolation using a plane will be described. In the vicinity of the point P, as shown in FIG. 12A, three points P ₁ , P ₂ , and P ₃ are selected as sample points, and coordinate values of the points P ₁ , P ₂ , and P _{3 on} the xy plane and Nodal temperatures were determined as coordinate values. Point P ₁ ′ (x ₁ , y ₁ ,
The normal vector of the plane A defined by T ₁ ), P ₂ ′ (x ₂ , y ₂ , T ₂ ), and P ₃ ′ (x ₃ , y ₃ , T ₃ ) is obtained. This normal vector is obtained by the following equation. a, b, and c are coefficients.

Here, i = (1,0,0) j = (0,1,0) k = (0,0,1) Next, this normal vector and points P ₁ ′, P ₂ ′, and P ₃ ′ An equation is established using the fact that a vector connecting any one point and the point P '(x, y, T) is orthogonal. Vector Is as follows.

・ = 0 (13) a (x−x ₁ ) + b (y−y ₁ ) + c (T−T ₁ ) = 0 (14) By substituting, the temperature T at the point P is obtained. By substituting the temperature T into the equation (14), an equation of an isotherm in the xy plane can be obtained. The above procedure is shown in FIG. 12B.

In the above-described calculation example, the coordinates of the nodes of the two-dimensional flat plate are set on the xy plane. However, it is of course possible to set the coordinate values in a three-dimensional space. In that case, the problem reduces to solving a plane equation in four-dimensional space.

In the above example, only one type (temperature T) is considered as the physical quantity to be interpolated. However, it is also possible to simultaneously interpolate several other related physical quantities, and the calculation procedure in that case is shown in FIG. It was shown to. In this case, the calculation method is exactly the same except for the number of sample points (P _{1 to} P _n ) used for interpolation.

Next, interpolation using a quadratic surface will be described. The quadratic surface is defined by the following equation.

^{_{a 1 x 2 + a 2 y}} 2 + a 3 T 2 + a 4 xy + a 5 yT + a 6 xT + a 7 x + a 8 y + a 9 T + a 10 = 0 ...... (15) where, a ₁ ~a ₁₀ are coefficients. Therefore, in order to define a quadric surface in a three-dimensional space, first, ten sample points are required. Therefore, as shown in FIG. 14A, the nodes P _{1 to} P ₁ near the point P of the two-dimensional plate model
Choose ₁₀ as the sampling point.

Next, the equation of the quadric surface A defined by the points P ₁ ′ to P ₁₀ ′ having the coordinate values of the xy plane of P _{1 to} P ₁₀ and the node temperatures as the coordinate values is obtained. The temperature T of the point P is determined by substituting the x, y coordinate values of the point P into the equation of the obtained curved surface.

By substituting the temperature T into the quadratic surface equation, a quadratic curve equation of an isotherm in the xy plane is obtained. By drawing the isotherm as a quadratic curve, drawing an isotherm C that draws a closed loop in an element as shown in FIG. 15, for example, in a region surrounded by P ₁ , P ₂ , and P ₃ Is also possible.

The above is an example of interpolation using a quadratic surface, which is shown in FIG. 14B. In the case of interpolation using a quadratic surface, the dimension can be expanded in the same manner as in the case of interpolation using a plane. The quadratic surface when the sum of the order of the coordinate system with the mesh surface and the order of the physical quantity is set to the nth order is expressed by the following equation.

x _i , x _j : variables a _ij , b _i , c: coefficients Here, if a _ij = a _ji , the equation (16) becomes the following equation.

From equation (17), the total number N of coefficients of the quadratic surface equation is It is. Therefore, the number of sample points required to determine the quadratic surface is Becomes The interpolation procedure in this case is shown in FIG. The calculation procedure is the same as in the case described above, except for the number of sample points.

According to the fifth embodiment, a physical quantity in a plane surrounded by nodes can be predicted with high accuracy by interpolation.

〔The invention's effect〕

According to the present invention, a new point in a three-dimensional space is defined based on existing point, line, and plane data, so that it is easy to specify a new point in structural analysis and the like. This has the effect of simplifying preparations and facilitating interpolation of analysis results.

[Brief description of the drawings]

FIG. 1A is a block diagram showing a schematic configuration of a first embodiment of the present invention, FIG. 1B is a flowchart showing a processing procedure of the embodiment shown in FIG. 1A, and FIG. 1C is a second embodiment of the present invention. FIG. 1D is a block diagram showing a schematic configuration of the example, FIG. 1D is a procedure diagram showing a processing procedure of the embodiment shown in FIG. 1C, FIG. 2A is a perspective view illustrating a method of defining a solid model by sweeping, and FIG. IIB in Figure 2A
FIG. 3A is a perspective view for explaining a method of defining a solid model by sweeping, and FIG.
FIG. 4A is a procedure diagram showing a procedure for obtaining a part of a ring by sweeping, and FIG. 4B is a procedure diagram showing a procedure described in FIG. 4A. 5A and 5B are perspective views for explaining a method of defining a surface model by sweeping, and FIG.
6A and 6C are perspective views showing a method of defining a wireframe model by sweeping, FIG. 6B is a front view of FIG. 6A, and FIG. 7A is a block diagram showing a schematic configuration of a third embodiment of the present invention, and FIG. 7B is a flowchart showing a processing procedure of the embodiment shown in FIG. 7A. FIG. 7C is a perspective view illustrating a method of generating the K point, FIG. 8A is a perspective view illustrating another method of generating the K point, and FIG. 8B is a perspective view illustrating the procedure of the method illustrated in FIG. 8A. 9A is a perspective view for explaining still another method of generating the K point, FIG. 9B is a procedure diagram showing the procedure of the method shown in FIG. 9A, and FIG. 10A is a fourth embodiment of the present invention. 10B is a block diagram showing a schematic configuration of the embodiment, FIG. 10B is a procedure diagram showing a processing procedure of the embodiment shown in FIG. 10A, and FIG. FIG. 10D is a flowchart showing the procedure of the calculation method shown in FIG. 10C, FIG. 10E is a block diagram showing a schematic configuration of the fifth embodiment of the present invention, FIG. FIG. 10F is a procedure diagram showing a processing procedure of the embodiment shown in FIG. 10E, FIG. 11 is a perspective view illustrating an interpolation problem to be addressed by the present invention, and FIG. 12A is a perspective view illustrating interpolation using a three-dimensional plane. FIG. 12B is a procedure diagram showing a procedure of interpolation using a three-dimensional plane, FIG. 13 is a procedure diagram showing a procedure of interpolation using an n-dimensional plane, FIG. 14A is a perspective view illustrating interpolation using a three-dimensional quadratic surface, Fig. 14B shows 3D 2
FIG. 15 is a perspective view showing an example of a closed-loop isotherm obtained by quadratic surface interpolation, and FIG. 16 is a flowchart showing interpolation by an n-dimensional quadratic surface. . 101: Input unit NA, 102: Operation unit EA, 103: Input unit NB, 104: Operation unit EB, 105: Input unit NC, 106: Operation unit EC, 107: Input unit ND, 108 Display unit 109, 119 Storage unit 110 Operation unit ED, 201 Input unit NE, 203 Input unit NF, 204 Operation unit EF, 205 Operation unit EG, 209 Storage Section, 303, input section NG, 304, operation section EH, 309, storage section, 401, operation section EI, 402, operation section EJ, 403, operation section EK, 409, storage section.

──────────────────────────────────────────────────続 き Continuing from the front page (72) Inventor Takashi Yamaguchi 502 Kandachicho, Tsuchiura-shi, Ibaraki Pref. Machinery Research Laboratory, Hitachi, Ltd. Others "Electromagnetic field calculation by Voronoi-Delaune discretization method (IV) Post processing and application to iterative solution" (58) Fields investigated (Int.Cl. ⁶ , DB name) G06T 17/20 JICST file (JOIS)

Claims (5)

(57) [Claims] An input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. An input unit NA for inputting designation of an existing point, plane, or line, in a graphic processing apparatus that supports data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space,
A calculation unit EA that calculates the tangent vector of a curve, the direction vector of a straight line, and the normal vector of a surface based on the coordinate values and / or equations of points, surfaces, and lines input to An input unit NB for inputting the input unit NB and a vector connected to the input unit NB and the operation unit EA, having a start point and a size specified by the input unit NB, and a vector parallel to the vector obtained by the operation unit EA and an end point thereof. And a calculation unit EB to be obtained. An input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. An input unit NA for inputting designation of existing vertices, planes, and lines in a graphic processing apparatus for supporting data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space,
A calculation unit EA that obtains the tangent vector of a curve, the direction vector of a straight line, and the normal vector of a surface based on the coordinate values of vertices, surfaces, and lines and / or equations connected to the NA, and the starting point of the vector and its size Input section NB for inputting the
An arithmetic unit EB connected to the NB and the arithmetic unit EA and having a start point and a size specified by the input unit NB and having a vector parallel to the vector obtained by the arithmetic unit EA and an end point thereof
And an input unit NC for inputting data relating to the sweep, a sweep connected to the input unit NC and the data input from the input unit NC connected to the operation unit EB, the vector obtained by the operation units EA and EB, and the start point thereof. For calculating control curve
EC, a display unit connected to the operation unit EC to display the operation result, and a storage unit connected to the operation units EA, EB, EC and the display unit and exchanging data with them. A graphic processing device. An input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. An input unit NA for inputting designation of an existing point, plane, or line, in a graphic processing apparatus that supports data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space,
A calculation unit EA that calculates the tangent vector of a curve, the direction vector of a straight line, and the normal vector of a surface based on the coordinate values and / or equations of points, surfaces, and lines input to An input unit NB for inputting the input unit NB and a vector connected to the input unit NB and the operation unit EA, having a start point and a size specified by the input unit NB, and a vector parallel to the vector obtained by the operation unit EA and an end point thereof. A calculation unit EB to be obtained, an input unit NC for inputting data related to sweep, and the input unit NC
An arithmetic unit EC that is connected to the NC and the arithmetic unit EB to obtain a sweep control curve from the data input from the input unit NC and the vector obtained by the arithmetic units EA and EB and its starting point,
An input unit ND for inputting designation of a point / plane / line to be swept; an operation unit ED connected to the input unit ND and the operation unit EC to execute a sweep operation; and an operation unit ED connected to the operation unit ED. A display unit for displaying a calculation result, and the calculation units EA, EB, EC, E
And a storage unit connected to the display unit and the display unit for exchanging data with the display unit. 4. An input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. In a graphic processing device that supports data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space, an input unit NE for inputting designation of an existing node, and an input unit NE connected to the input unit NE for input. A connection unit of a curve defined by the nodal point, a direction vector of a straight line, an operation unit EA for obtaining a surface normal vector, an input unit NF for inputting designation of a beam element, and the input unit NF and the operation unit EA An operation unit EF that is connected to obtain a position vector of a point existing on the beam element specified by the input unit NF or on an extension thereof, and a sum of vectors connected to the operation unit EF and obtained by the operation units EA and EF. Find a vector and calculate the coordinates of its end point. Calculation unit EG, a display unit connected to the calculation unit EG and displaying the calculation result as a point defining the local coordinate system of the beam element, and a display unit connected to the calculation units EA, EF, EG and the display unit. And a storage unit for exchanging data between the two. 5. An input unit, an operation unit connected to the input unit, a storage unit connected to the operation unit, and a display unit connected to the storage unit and the operation unit. In a graphic processing device that supports data creation of an analysis program such as a structural analysis from a shape of an object defined in a three-dimensional space, an input unit NE for inputting designation of an existing node, and an input unit NE connected to the input unit NE for input. A calculation unit EA for obtaining a tangent vector of a curve defined by the nodal point, a direction vector of a straight line, and a normal vector of a surface, and an input unit NG for inputting a magnitude of the vector,
An operation unit EH connected to the input unit NG and the operation unit EA and having a size specified by the input unit NG and obtaining a load vector parallel to the vector obtained by the operation unit EA; and connected to the operation unit EH. A graphic processing device comprising: a display unit for displaying the calculated operation result; and a storage unit connected to the operation units EA, EH and the display unit for exchanging data with them.