JP2000149067A - Method and device for generating curved surfaces - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate curved surface data having little distortion, which passing through plural measuring points on a real curved surface or nearby these measuring points from three-dimensional(3D) measuring data expressing the positions of these measuring points. SOLUTION: When a temporary curved surface plate divided into patches corresponding to respective measuring points pm is set by a temporary curved surface plate setting means 32, based on a 3D measuring data expressing the positions of plural measuring points pm on the real curved surface, an elastic member is attached with the temporary curved surface plate from the plural measuring points pm by an elastic member attaching means 42, the position of a point for attaching the elastic member to the curved surface plate is defined by using the distance between the measuring points pm by an attaching point defining means 46. When the position of the point is used for attaching the elastic member to the curved surface plate defined by the attaching point defining means 46, a curved surface data calculating means 50 calculates curved surface data which expresses the curved surface of the temporary curved surface plate for minimizing a distortion energy sum U=(ΣU1+ΣU2) of a distortion energy U1 of the temporary curved surface plate and a distortion energy U2 of the elastic member attached to that plate.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curved surface generating method for generating curved surface data representing a curved surface passing through measurement points from three-dimensional measurement data representing the positions of a plurality of measured points on an actual curved surface, and executing the method. The present invention relates to a device for performing

[0002]

2. Description of the Related Art From three-dimensional measurement data obtained by measuring the positions of a plurality of measurement points on an actual curved surface and indicating the coordinate positions in a three-dimensional space representing the positions of the measurement points, the plurality of measurement points are measured. It is desired to create surface data representing a smooth surface passing through the measurement points. This is because the curved surface data corresponds to the actual curved surface, and is used as basic data for product evaluation using the CAD / CAM system, product design, and design and processing of a manufacturing die.

As a method for generating the above-mentioned curved surface data, for example, as described in Japanese Patent Publication No. 8-27184, a first free curve which smoothly passes through a sequence of measurement points for each measurement section from three-dimensional measurement data. Is calculated, and the first free curve is equally divided into n (n is an arbitrary integer), and the first free curve is calculated again so as to smoothly pass through each equal point of the first free curve. , I of the first free curve (i is 0 to n)
Calculating a second free curve that smoothly passes through the second division point in a direction intersecting with the first free curve, and tangent to a space surrounded by the obtained first free curve and the obtained second free curve; A free-form surface generation method has been proposed which calculates free-form surface data that is common to both. According to this,
Even if the pitch of the measurement point sequence and the number of measurement points vary,
There is an advantage that the unit free-form surface is not greatly distorted or non-uniform.

[0004]

In the above-described conventional curved surface generation method, a free curve that smoothly connects the measurement points is calculated according to a predetermined formula even if the positions of the measurement points are different. Since the error included in the measurement point cannot be sufficiently removed, there is a problem that the generated curved surface is distorted.

The present invention has been made in view of the above circumstances, and an object thereof is to substantially pass through three-dimensional measurement data representing the positions of a plurality of measurement points on an actual curved surface. It is an object of the present invention to provide a curved surface generating method and apparatus capable of generating curved surface data representing a curved surface having almost no distortion.

[0006]

A first object of the present invention to achieve the above object is to provide a method for measuring the positions of a plurality of measurement points on a real curved surface from three-dimensional measurement data. A curved surface generation method for generating curved surface data representing a curved surface passing in the vicinity thereof, comprising: (a) a patch corresponding to each measurement point whose position is represented by the three-dimensional measurement data based on the three-dimensional measurement data; A temporary curved surface plate setting step of setting a temporary curved surface plate divided into; (b) an elastic member attaching step of temporarily attaching an elastic member to the temporary curved surface plate from a plurality of measurement points on the actual curved surface; c) an attachment point position defining step of defining the position of the attachment point of the elastic member with respect to the temporary curved surface plate using the distance between the measurement points; and (d) the elastic member defined in the attachment point position definition step. Of the mounting point with respect to the temporary curved surface plate And a curved surface data calculating step of calculating curved surface data representing a curved surface of the temporary curved surface plate in which the sum of the strain energy of the temporary curved surface plate and the strain energy of the elastic member attached thereto is minimized. It is in.

[0007]

A second aspect of the present invention, which is an apparatus for implementing the method of the first aspect of the present invention, is to form a plate material into a curved surface by plastic working. A surface generating apparatus for generating surface data representing a curved surface passing through the measurement points or the vicinity thereof from three-dimensional measurement data representing positions of a plurality of measurement points on an actual curved surface, wherein (a)
A temporary curved surface plate for setting a temporary curved surface plate having the same properties as the plate material, which is divided into patches based on the three-dimensional measurement data and corresponding to each measurement point whose position is represented by the three-dimensional measurement data Setting means, (b) elastic member attaching means for temporarily attaching an elastic member between the plurality of measurement points on the actual curved surface and the temporary curved plate, and (c) attaching points of the elastic member to the temporary curved plate. A mounting point position defining means for defining the position using the distance between the measurement points, (d) using the position of the mounting point with respect to the temporary curved plate of the elastic member defined in the mounting point position defining means, Surface data calculating means for calculating surface data representing a curved surface of the temporary curved plate in which the sum of the strain energy of the temporary curved plate and the strain energy of the elastic member attached thereto is minimized. .

[0008]

[Effects of the first invention and the second invention]
In the provisional curved surface plate setting step (means), based on the three-dimensional measurement data representing the positions of the plurality of measurement points on the actual curved surface,
When a temporary curved surface plate divided into patches is set in correspondence with each measurement point whose position is represented by the dimension measurement data, an elastic member attaching step (means) is used to determine the temporary curved surface from a plurality of measurement points on the actual curved surface. The elastic member is temporarily attached to the curved plate, and the position of the attachment point of the elastic member with respect to the temporary curved plate is defined by the attachment point position defining step (means) using the distance between the measurement points, and In the curved surface data calculating step (means), using the position of the attachment point of the elastic member with respect to the temporary curved surface plate defined in the attaching point position defining step (means), the distortion energy of the temporary curved surface plate and the elasticity attached thereto Curved surface data representing the curved surface of the temporary curved plate that minimizes the sum of the strain energy and the strain energy of the member is calculated. For this reason, since the physical properties of the temporary curved surface plate are reflected on the curved surface, curved surface data with almost no distortion can be obtained.

[0009]

In another preferred embodiment, (e) an error calculating step (means) for obtaining an error between each patch of the curved surface represented by the curved surface data and each of the measurement points; An error evaluation step (means) for determining whether or not the error calculated in the error calculation step exceeds a preset allowable value;
(g) a sub-dividing step (means) for sub-dividing, among the temporary curved surface plates divided into the patches, those patches determined by the error evaluating step to have the error exceeding a preset allowable value;
And (h) in the patch subdivided in the subdivision step, the distortion energy of the temporary curved plate and the distortion energy of the elastic member attached thereto while maintaining the smoothness of the shape between adjacent patches having different sizes. And a subdivision patch curved surface data calculation step (means) for calculating surface data representing a curved surface of the temporary curved surface plate in which the sum of the distortion energy is minimum. In this way, in the subdivided patches, the surface data representing the surface with the minimum distortion energy sum is calculated while maintaining the smoothness of the shape between the adjacent patches having different sizes, so that the measurement is performed. There is an advantage that curved surface data more suitable for a point can be obtained.

Preferably, (i) a change rate calculating step (means) for calculating a change rate of the surface shape in each direction of each patch of the temporary curved surface plate, and (j) the change rate calculating step. If the difference in the change rate of the surface shape in each direction obtained in the step (means) exceeds a preset value,
A temporary curved plate changing step (means) for changing the temporary curved plate to an anisotropic material. With this configuration, in each patch of the temporary curved surface plate, if the difference in the obtained rate of change of the surface shape in each direction exceeds a preset value, the temporary curved surface plate is converted to an anisotropic material. Since it is changed, there is an advantage that curved surface data more suitable for the measurement point can be obtained.

[0011]

Preferred embodiments of the present invention will be described below in detail with reference to the accompanying drawings.

FIG. 1 shows the configuration of a curved surface generating apparatus 10 that executes a curved surface generating method according to one embodiment of the present invention. FIG.
, A curved surface generating device 10 includes an operation control device main body 12 composed of a so-called computer, and an operation device 14 having operation keys operated by an operator and supplying an operation signal to the operation control device main body 12. An image display device 16 for displaying the execution contents or execution result of the above-mentioned surface generation method in accordance with the output from the arithmetic and control unit 12
An input data storage device 18 for storing input data such as three-dimensional measurement data representing the positions of a plurality of measurement points on an actual curved surface; the number of curved surface patches; a curved surface equation coefficient data sequence of each curved surface patch; An output data storage device 20 for storing output data obtained by calculation of data or the like.

The curved surface generating apparatus 10 is provided with an input interface 22. A plurality of measuring points on an actual curved surface measured by a three-dimensional measuring machine 24 equipped with a touch signal probe, a scanning probe, a laser probe, and the like. Is input directly through the input interface 22 or indirectly through a predetermined storage medium, and is stored in the input data storage device 18. . The above three-dimensional measuring machine 24
Is a clay model composed of clay in a predetermined shape,
The position of a plurality of measurement points at predetermined intervals at a predetermined interval is measured by a contact probe or a non-contact probe on an actual curved surface represented by a prototype model in which a sheet material is bent by sheet metal processing, and the measurement points are measured. It outputs three-dimensional measurement data respectively indicating coordinate positions in a three-dimensional space representing the positions of.

Here, prior to the description of the control function of the arithmetic and control unit 12, a preliminary description will be given below. First,
A general curved surface is represented by f (x, y, z) = 0. For example, x ² + y ² + z ² −1 = 0 represents a spherical surface having a center of (0,0,0) and a radius of 1. Such a curved surface is represented by a spherical surface, a cylindrical surface, and a paraboloid of revolution, and is called a function curved surface. But,
Since the shape of an industrial product represented by the shape of the outside of a car is complicated and it is difficult to express it with a single function, the complicated surface shape is divided into small quadrangular regions (triangles are also possible) called patches. 3rd order to the surface shape of each square area,
Each curved surface shape is expressed by a plurality of curved surface expressions by applying a quartic, quintic, etc. equation. Such a curved surface is referred to as a free-form surface to be distinguished from the functional surface.

There are various methods of expressing a curved surface expression representing each free-form surface of each of the patches, and an example will be described below with reference to FIG. 2 showing one patch.
In the following description, European double-byte characters in the expression indicate vectors.

The free-form surface of the patch of FIG.
It is represented by two parameters (variables). The x component in the case of the cubic expression of u and v is shown in Expression 1. In Equation 1, F ₀ (u) = 1−F ₁ (u) _, F ₁ (u) = u ² (−
2u + 3) _, G ₀ (u) = u (1-u) ² _, G ₁ (u) = u ² (1-v),
There is a property shown in Expression 2. Therefore, it can be generalized as shown in Equations 3, 4, 5, and 6.

[0017]

X (u, v) = x ₀₀ F ₀ (u) F ₀ (v) + x ₁₀ F ₁ (u) F ₀ (v) + x ₀₁ F ₀ (u) F ₁ (v) + x ₁₁ F ₁ (u) F ₁ (v) + Tux ₀₀ G ₀ (u) F ₀ (v) + Tux ₁₀ G ₁ (u) F ₀ (v) + Tux ₀₁ G ₀ (u) F ₁ (v ) + Tux ₁₁ G ₁ (u) F ₁ (v) + Tvx ₀₀ F ₀ (u) G ₀ (v) + Tvx ₁₀ F ₁ (u) G ₀ (v) + Tvx ₀₁ F ₀ (u) G ₁ (v) + Tvx ₁₁ F ₁ (u) G ₁ (v) + Mx ₀₀ G ₀ (u) G ₁ (v) + Mx ₁₀ G ₁ (u) G ₀ (v) + Mx ₀₁ G ₀ (u) G ₁ (v) + Mx ₁₁ G ₁ (u) G ₁ (v) ・ ・ ・ (1)

[0018]

## EQU2 ## F ₀ (0) = 1 _, F ₁ (0) = 0 _, G ₀ (0) = 0 _, G ₁ (0) = 0 _, F ₀ (1) = 0 _, F ₁ (1) = _{1, G 0 (1) =} 0, G 1 (1) = 0, dF 0 / du | u = 0 = 0, dF 1 / du | u = 0 = 0, dG 0 / du | u = 0 = 1 _{, dG 1 / du | u =} 0 = 0, dF 0 / du | u = 1 = 0, dF 1 / du | u = 1 = 0, dG 0 / du | u = 1 = 0, dG 1 / du | _{u = 1} = 1 _, ... (2)

[0019]

X (0,0) = x _00, x (1,0) = x _10, x (0,1) = x _01, x (1,1) = x ₁₁ That is, x (i, j ) = X _ij (where i and j are 0 or 1) (3)

[0020]

[Number 4] _{∂x / ∂u | u = 0,} v = 0 = Tux 00, ∂x / ∂u | u = 1, v = 0 = Tux 10, ∂x / ∂u | u = 0, v = ₁ = Tux ₀₁ , ∂x / ∂u | _{u = 1} , _{v = 1} = Tux ₁₁ , ie, ∂x / ∂u | _{u = i, v = j} = Tux _ij (4)

[0021]

[Number 5] _{∂x / ∂v | u = 0,} v = 0 = Tvx 00, ∂x / ∂v | u = 1, v = 0 = Tvx 10, ∂x / ∂v | u = 0, v = _{1 = Tvx 01, ∂x / ∂v} | u = 1, v = 1 = Tvx 11, _{i.e., ∂x / ∂v | u = i} , v = j = Tvx ij ··· (5)

[0022]

[6] _{∂x / ∂u ∂v | u = i} , v = j = Mx ij ··· (6)

Each of the above equations indicates a value used in the expression of the curved surface equation, and their meanings can be summarized as follows. That is, the x, coordinate values of the four corners of the patch 34 is represented by _{x 00, x 10, x 01} , x 11, the value of ∂x / ∂u its four corners _{Tux 00, Tux 10, Tux 01} , Tux 1 It is represented by ₁ and its four corners ∂
The value of x / ∂v is represented by Tvx ₀₀ , Tvx ₁₀ , Tvx ₀₁ , Tvx ₁₁ , and the values of ∂x / ∂u ∂v at the four corners are represented by Mx ₀₀ , Mx ₁₀ , Mx ₀₁ , Mx ₁₁ . y and z can be expressed using the above four values at the four corners in the same manner as x. That is, for y, the coordinate values of the four corners of the patch 34 are y _00, y
_10, y _01, y ₁₁ and the 隅 y / ∂u values at the four corners are Tu
y ₀₀ , Tuy ₁₀ , Tuy ₀₁ , Tuy ₁₁ ∂y / ∂v at the four corners
Are represented by Tvy ₀₀ , Tvy ₁₀ , Tvy ₀₁ , and Tvy ₁₁ , and the values of ∂y / ∂u ∂v at the four corners are represented by My ₀₀ , My ₁₀ , My ₀₁ , My ₁₁ , and z
, The coordinate values of the four corners of the patch 34 are z _00, z _10, z _01, z
Is represented by _11, the value of ∂z / ∂u its four corners Tuz _00, Tuz _10, T
uz ₀₁ , Tuz ₁₁ and the ∂z / ∂v values at the four corners are Tv
z ₀₀ , Tvz ₁₀ , Tvz ₀₁ , Tvz ₁₁ ∂z / ∂u
The value of ∂v is represented by Mz ₀₀ , Mz ₁₀ , Mz ₀₁ , and Mz ₁₁ .

Next, the vector expression of the surface equation will be described below.
Will be described. First, P₀₀= (X₀₀, Y₀₀, Z₀₀) Is x,
y and z coordinates are x₀₀, Y₀₀, Z₀₀Represent a point that is
Then, it is expressed as Equation 7 (where i and j are 0 or less).
Or 1). Similarly, Tu₀₀= (Tux₀₀, Tuy₀₀, Tuz₀₀ ) Is
x, y, z coordinates are x₀₀, Y₀₀, Z₀₀∂x / ∂ when
the value of u, Tv₀₀= (Tvx₀₀, Tvy₀₀, Tvz₀₀ ) Is x, y, z
Coordinates x₀₀, Y₀₀, Z ₀₀∂x / ∂v value when, M
₀₀= (Mx₀₀, My₀₀, Mz₀₀) Indicates that the x, y, and z coordinates are x ₀₀,
y₀₀, Z₀₀Is the value of ∂x / ∂u ∂v
Are represented as Expression 8, Expression 9, and Expression 10, respectively.
You. Then, a surface equation S representing the free-form surface of the patch is expressed by Equation 1
Assuming that 1, the curved surface equation S is expressed by Equation 12.

[0025]

P _ij = (x _ij , y _ij , z _ij ) (7)

[0026]

[Expression 8] Tu _ij = (Tux _ij , Tuy _ij , Tuz _ij ) (8)

[0027]

Tv _ij = (Tvx _ij , Tvy _ij , Tvz _ij ) (9)

[0028]

M _ij = (Mx _ij , My _ij , Mz _ij ) (10)

[0029]

S (u, v) = [x (u, v), y (u, v), z (u, v)] (11)

[0030]

S (u, v) = Σ [P _ij F _i (u) F _j (v) + Tu _ij G _i (u) F _j (v) + Tv _ij F _i (u) G _j (u ) + M _ij G _i (u) G _j (u)] ・ ・ ・ (12)

FIG. 2 shows, for example, P ₀₀ = (0,0,0) and P ₁₀ =
(64.2, -5,0), P ₀₁ = (0, -5,40), P ₁₁ = (64.2, -5,4
0), Tu ₀₀ = (64.2, -1.6,0), Tu ₁₀ = (64.2,0.37,0)
, Tu _{0 1} = (64.2, -0.9,0), Tu ₁₁ = (64.2,0.8,0),
Tv ₀₀ = (0, -3.7,40), Tv ₁₀ = (0, -3.1,40), Tv ₀₁
= (0, -6.3,40), Tv ₁₁ = (0, -5.8,40), M ₀₀ = (0,0.
_{7,0), M 10 = (0,0.47,0} ), M 01 = (0,0.59,0), M 11 =
(0,0.38,0) and the variables u and v are 0,
.., 0.9, 1.0 when it is changed as shown by the curved surface equation S (u, v).

FIG. 3 is a functional block diagram showing a main part of the arithmetic function of the arithmetic and control unit 12. As shown in FIG. In FIG.
The three-dimensional measurement data reading means 30 measures the measurement data in advance and generates the input data storage device 1 before generating the curved surface data.
The three-dimensional measurement data stored in 8 is read. FIG.
, When the real curved surface is a curved surface of a fender portion of a vehicle represented by the clay model, it indicates the position of the measurement point p _m which is set at a predetermined interval in the top of the curved surface,
In this case, the three-dimensional measurement data is obtained by expressing the spatial position of each of the measurement points p _m by coordinate values, for example, xyz rectangular coordinate values p _mi (x _i , y _i , z _i ).

The provisional curved plate setting unit 32, based on the three-dimensional measurement data, by using the respective measurement points p _m that position is represented from its three-dimensional measurement data, as shown in FIG. 5, parallelogram , Rectangular or square surface patch (small surface) 3
By creating a spline network (mesh) composed of splines (mesh lines) 36 serving as boundaries of 4, a temporary curved surface plate 38 divided into patches is set corresponding to each measurement point. That is, the spline 36 is formed at predetermined intervals along the arrangement direction of the measurement point p _m. Incidentally, the temporary curved plate 38 is a resilient flat plate having physical properties such as appropriate elasticity and rigidity in order to produce a smooth curve from the plurality of measuring points, substantially above each measuring point p _m It is a virtual member used for calculation generated to be in contact or close proximity. The curved surface of the temporary curved surface plate 38 is represented by each curved surface expression S (u, v) as shown in Expression 12 representing the surface shape of each curved surface patch 34 constituting the curved surface plate.

In the temporary curved plate setting means 32, a spline 36 for the temporary curved plate 38 is formed as described below. First, as shown in FIG. 6, three-dimensional measuring a set of maximum coordinate values of the measurement point p _m of the data from the position represented and the minimum coordinate values of the rectangle in which the temporary curved plate 38 enters just a box (rectangular frame) 40 Is required. Then, as shown in FIG. 7, a group of measurement points p _m i.e. curve a when the temporary curved plate 38 was cut across a horizontal plane, b, c are determined. In this case, the column is small part in terms of measurement points p _m is determined by using the interpolation calculation and extrapolation calculations. Subsequently, as shown in FIG. 8, the curve b to Li of a cutaway of the set of measuring points p _m i.e. Provisional curved plate 38 to cross the vertical plane are determined. Then, as shown in FIG. 9, the curves e and f are obtained by connecting the line ends of the curves a to l. The curves a to f and the curves a to r obtained in this way correspond to the splines 36, whereby the temporary curved surface plate 38 is divided into small pieces to form a plurality of curved surface patches 34. . Thus, the values x _ij , y _ij , z _ij , and Tu of the four corner points of the surface patch 34 are obtained.
x _ij , Tuy _ij , Tuz _ij , Tvx _ij , Tvy _ij , Tvz _ij , M
Since x _ij , My _ij , and Mz _ij are unknown values, the grid points (intersections) of the spline 36 are temporarily determined.

Returning to FIG. 3, the elastic member attaching means 42
Attaching a plurality of elastic members for example a coil spring 44 elastically deformable between a plurality of the measurement points p _m the provisional curved plate 38 on the real curved surface, respectively. The coil spring 44 is also a virtual member used for calculation and has a predetermined elastic coefficient. 10, both end portions are conceptually shows a mounting state of the coil spring 44 fixed between the plurality of measurement points p _m and the temporary curved plate 38 on the real surface. In FIG. 10, x mark indicates the attachment point p _s on the interim curved plate 38 i.e. surface patch 34 of the coil spring 44, ● mark indicates the mounting position of the coil spring 44 a measurement point p _m.

The attachment point defining means 46 defines i.e. respectively determined by using the distance between the position of the measurement point p _m of the attachment points for the temporary curved plate 38 of the coil spring 44. That is, as briefly illustrated in Figure 11, along the vertical direction in a linear distance a1, a2, a3, · ·, and a predetermined interval between measurement points p _m located along the horizontal direction at a predetermined height linear distance b between the measurement points p _m located Te
1, b2, b3, b4, ... are calculated and the position p of each mounting point p _s
parameters u _k and _s (u _k , v _k )
v _k is determined in proportion to the curve length using the straight line distance between the point sequences. For example, when obtaining the parameters u1 and v1 for specifying a position of a predetermined attachment point p _s is
From Equations 13 and 14, the linear distances a1, a2, a
, And b1, b2, b3, b4,..., The parameters u1 and v1 for indicating the position of the mounting point p _s of the coil spring 44 with respect to the temporary curved plate 38 are calculated to determine the predetermined mounting point. to determine the p _s position p _s (u1, v1).

[0037]

[Expression 13] u1 = a1 / (a1 + a2 + a3 +...) (13)

[0038]

[Expression 14] v1 = b1 / (b1 + b2 + b3 + b4 +...) (14)

The curved surface data calculating means 50 calculates the position p _s (u _k , v _k ) of the mounting point p _s of the coil spring 44 with respect to the temporary curved surface plate 38 defined by the mounting point defining means 46.
Is used to calculate the distortion energy of one of the surface patches 34.
The surface data representing the curved surface of the temporary curved plate 38 where the sum of the distortion energy U = (ΣU ₁ + ΣU ₂ ) of U ₁ and the strain energy U ₂ of the coil spring 44 attached thereto is expressed by the following equation (1).
It is calculated from the curved surface equation S (u, v) as shown in FIG. That is, the coil spring 44 and the provisionally curved plate 38 to which the coil spring 44 is attached are balanced in a state where the sum of the distortion energies (ΣU ₁ + ΣU ₂ ) is minimized.
Under the condition that U ₁ + ΣU ₂ ) is minimized, the surface data S (u, v) representing the surface of the temporary curved plate 38 is obtained.
Coordinate values P _ij at the point of the four corners of the surface patch 34, the differential value by u Tu _ij, v differential value by Tv _ij, since the differential value T _ij by u and v are the unknown, strain energy sum (ΣU ₁ + ΣU ₂₎ By partially differentiating each of the unknowns from the minimum condition, linear equations are derived by the number of unknowns, and the surface is determined by solving the linear simultaneous equations.

Here, assuming that the measurement point is Q _k , the distortion energy U ₂ of the coil spring 44 is expressed by Expression 15, and the distortion energy U ₁ of one curved patch 34 is expressed by Expression 1.
6. Formula 15 is a product-sum formula of k = 1 to K, and α is a spring constant. ΣU ₂ is the strain energy of all coil springs 44 and ΣU ₁ is the strain energy of all patches.

[0041]

U ₂ = αΣ ｛Q _k −S (u _k , v _k )｝ ² (15)

[0042]

U ₁ = (D / 2) ∬ ｛(k ₁ + k ₂ ) ² −2 (1 −ν) k ₁ k ₂ ｝ H dudv (16) where (k ₁ + k ₂ ) ² = (1 / H ⁴ ) ｛S _u ² (nS _vv ) + S _v ² (nS _uu )
_{-2 (S u S v) (} nS uv)} 2 k 1 k 2 = (1 / H 2) {(nS uu) (nS vv) - (nS uv)} 2 H = | S u × S v | _{n = (S u × S v} ) / H S u = ∂S / ∂u, S v = ∂S / ∂v, S uv = ∂S / ∂
u ∂v

The distortion energy U _{1 for} one of the curved surface patches 34
The condition when the sum U = (ΣU ₁ + ΣU ₂ ) of the strain energy U and the strain energy U ₂ of the coil spring 44 attached thereto is minimized is shown in Expression 17.

[0044]

[Number 17] _{∂U / P ij x = 0,} ∂U / P ij y = 0, ∂U / P ij z = 0 ∂U / Tu ij x = 0, ∂U / Tu ij y = 0, ∂U / Tu _ij z = 0 ∂U / Tv _ij x = 0, ∂U / Tv _ij y = 0, ∂U / Tv _ij z = 0 ∂U / M _ij x = 0, ∂U / M _ij y = 0, ∂U / M _ij z = 0

By the way, usually, if two equations are solved,
P _ij , Tu _ij , Tv _ij , and M _ij are obtained.
One equation cannot be easily solved because it is nonlinear. Conventionally, simplified equation 18 has been used assuming that Su ² and Sv ² are very small. The above assumption is correct, since the deformation is very small in buildings and ordinary machines.
However, in the case of curved surface smoothing, this assumption often does not hold, and there is a case where the accuracy of the curved surface data cannot be obtained due to the calculated distortion of the curved surface.

[0046]

U ₁ = (D / 2) ∬ (Suu ² + Suv ² + Svv ² ) dudv (18)

In this embodiment, the shapes of the patches are limited to a square, a rectangle (rectangle), and a parallelogram, and the mounting position p _s (u _k , v _k ) of the coil spring 44 is shown in equations 13 and 14. By determining the variables u and v approximately in proportion to the length of the curve, Su ² and S
The strain energy without the assumption that v ² is very small
U ₁ is simplified as shown in Equation 19. In general,
Although the parameter and the line length do not have a proportional relationship, changing the shape of the function may make it possible to make the parameter and the line length proportional. For example, x = (1-t ² ) / (1+
t ² ), y = 2t / (1 + t ² ) is a circle having the origin at the center and a radius of 1 and becomes a 1/4 circle in the first quadrant at 0 ≦ t ≦ 1. In this case, the line length when t = 0 to 1/3 is 0.634, and t = 1 /
The line length at 3 to 2/3 is 0.533, and the line length at t = 2/3 to 1 is 0.395, and the variation of the variable t is not proportional to the line length. However, if x = cos (π / 2) t and y = sin (π / 2) t, the same 1/4 circle is obtained for 0 ≦ t ≦ 1, but t = 0 to
Line length at 1/3 and t = 1/3 to 2/3 and t =
The line length at the time of 2/3 to 1 is both 0.524, and the variation of the variable t is proportional to the line length. In the above example, the form of the function is changed to a proportional relation, but in the present embodiment, the relation between the curve length and the parameter is obtained in advance. This relationship is incorporated in Equation 15.
That is, in the present embodiment, although the form of the function is not changed, the proportional relationship is approximately satisfied by using the conditional expression of the relationship between the curve length and the parameter. By using this relationship, the following Expression 19 is derived.

[0048]

U ₁ = (D / 2) [(1 / A ³ B ³ sin ³ θ) ∬ ｛B ⁴ Suu ² + 2A ² B ² SuuSvv + A ⁴ Svv ² +4 (AB cos θ) ² Suv ² −4AB ³ cos θ SuuSvv −4A ³ B cosθSuuSuv｝ dudv −2 (1 −ν) (1 / AB sinθ) ∬ (SuuSvv−Suv ² ) dudv] (19)

In FIG. 3, the error calculating means 52 includes a surface represented by the surface data obtained by the surface data calculating means 50, that is, each surface patch 34 and each measurement point p _m.
Is calculated, and the surface patch 3
The maximum value of the distance d determined for each measurement point p _m in 4 determined as maximum error e _max. For example, as shown in FIG. 12, to determine the normal line perpendicular to the plane of the surface patch 34 that passes through each measurement point p _m, the measurement point p on the normal
The distance d between _m and the surface patch 34 is calculated as the error e. Error evaluation means 54, the curved surface data calculation unit 50 maximum error e the maximum distance d determined for each measurement point p _m in surface patches 34 of the curved surface calculated by
It is determined whether or not _max exceeds a predetermined criterion value, that is, a permissible value.
4 is evaluated. The maximum error e of all the surface patches 34
_{If the max} is within the allowable value, the surface data calculated by the surface data calculating means 50 is output. Conversely, if the _max is out of the allowable value, the surface patch 34 outside the allowable value is divided into the subdivision means 56.
To subdivide.

The subdivision means 56 outputs the error e by the error evaluation means 54 of the temporary curved surface plate 38 divided into patches.
Is further subdivided (in this embodiment, divided into four) by the surface patch 34 determined to exceed the preset allowable value. 34d of the surface patch 34 in FIG. 13 indicates a surface patch that is further divided into four. FIG. 14 shows a curved surface patch 34dd obtained by further dividing the curved surface patch 34d into four.

The subdivision patch surface data calculation means 58
The surface patch 34 subdivided by the subdivision means 56
In d, the sum of the strain energy U ₂ of strain energy U ₁ and the coil spring 44 of the provisional curved plate 38 i.e. the surface patch 34d while maintaining the smoothness of the shape between the different neighboring surface patches sizes minimum Surface data representing the surface is calculated from the surface equation S (u, v) in the same manner as described above.
That is, between the finely divided curved surface patch 34d and the adjacent undivided curved surface patch 34, the grid points (four corner points), which are the intersections of the splines 36, on their boundary lines do not coincide with each other. Causes a broken line and loses the continuity of the curved surface. For this reason,
As shown in FIG. 15, a surface patch 34 undivided A, the divided surface patch 34d and B ₁ and B _2, when they surface patch A and the surface patch B ₁ and B ₂ are adjacent to each other, curved The patch A is divided into A ₁ and A ₂ without changing the shape of the patch A, and the surface patches A ₁ and B ₁ , A ₂
Tangent vector across the boundary between the B ₂ is the conditional expression is derived at a mutually equal. For example curved formula ^A1 S (u, v) surface patches A ₁ and a curved type is that ^B1 S (u,
In between the surface patches B ₁ is a v), the tangent vectors ∂ surface patch A ₁ side ^A1 S / ∂u and tangent vector ∂ surface patch B ₁ side ^B1 S / ∂u and conditions that are equal is set You. In the case where the curved surface expression divides the surface patch A is ^A S (u, v) is, u = 0.5 u 'curved formula ^A S (u, v) substituted for the to surface patch A ₁ curved formula ^A1 S (u, v), and u =
0.5 + 0.5 u '' curved formula ^A S (u, v) substituted for the curved surface patch A ₂ curved formula ^A2 S (u, v) become. The same applies to the continuity of the differential values of the second or higher order.

The change rate calculating means 60 calculates the u of the curved surface shape of the subdivided curved surface patch 34 of the temporary curved surface plate 38.
Calculate the rate of change for each direction and v direction. If the difference in the rate of change of the curved surface shape for each direction calculated by the change rate calculating means 60 exceeds the preset value, the provisional curved surface changing means 62 sets the subdivision patch curved surface data calculating means 58. Prior to the calculation of the curved surface data by the
Is changed to an anisotropic material having anisotropy corresponding to the ratio of the change rate in each of the u direction and the v direction. The anisotropic material is a material having different mechanical properties such as hardness, strength, and elastic modulus depending on the direction. For example, a plate material lined with a corrugated sheet corresponds thereto. The properties of this anisotropic material are determined for each curved patch 34. More specifically, the temporary curved plate 38 and the average value d _av of the distance d between the measuring point p _m is determined, the average value d _av and squares of the individual distances d _ij and the difference (d _av -d _ij) ^Two
Are arranged in the u direction and the v direction, respectively, and calculated to obtain their average value, that is, the root mean square error value.
The ratio of the average value in the u direction and the value in the v direction shown in FIG. 16 is calculated. The ratio is multiplied by the material characteristic value of the isotropic material to make a correction to determine the anisotropic material characteristic value. And
The provisional curved plate changing means 62 changes the values of A and B in Expression 19 using the values. For example, if the ratio between the u direction and the v direction is 1: 2, instead of A, 2 · 1 / (1 + 2) =
2/3 / (1 + 2) = 4/3 is substituted for 2/3 and B.
Thereby, the undulation of the curved surface data on which the undulation as shown in FIG. 17 is formed is eliminated as shown in FIG.

By the way, if the division of the surface patch and the calculation of the surface data are repeated to form a small patch, the surface may undulate. In the case where the left portion of FIG. 19 has a shape in which the l direction is substantially straight but the h direction changes greatly, there is a high possibility that undulation as shown in the right portion of FIG. 19 will occur.

FIG. 20 is a flowchart for explaining a main part of the control operation of the arithmetic and control unit 12, and shows a curved surface generation arithmetic control routine. In FIG. 20, SA corresponding to the three-dimensional measurement data reading means 30 is used.
In 1, for example, stored in the input data storage unit 18, the three-dimensional measurement data representing the position of the measurement point p _m of the real curved surface is read. Then, the in provisional curved setting means 32 corresponding to the SA2, by using the location of the measurement point p _m represented by the three-dimensional measurement data, parallelogram, rectangle, or the boundary of the square of the surface patch 34 A temporary curved surface plate 38 on which a spline network is formed is set.

[0055] Then, the elastic member mounting means 42 and the SA3 corresponding to the attachment point defining means 46, a plurality of measurement points on the coil spring 44 is the actual curved p _m and provisional curved plate 3
8 and each mounting point p _{s of the} coil spring 44 with respect to the provisionally curved plate 38.
Position p _s (u1, v1) is defined is calculated respectively from equations 13 and Equation 14 by using the distance between the measuring points p _m.

[0056] In SA4, strain energy sum of the strain energy U ₂ of one component of the strain energy U ₁ a coil spring 44 attached to its surface patch 34 U = (ΣU ₁ +
From the condition of minimizing ΣU ₂ ), the partial derivatives of the coordinate values P _ij , the differential value Tu _ij by u, the differential value Tv _ij by v, and the differential value T _ij by u and v at the four corner points of the surface patch 34 are respectively obtained. By doing so, a linear equation that is simultaneous with the unknown number is derived. Next, in SA5 corresponding to the curved surface data calculating means 50, the linear simultaneous equations are solved to calculate curved surface data representing the curved surface.

Next, SA6 corresponding to the error calculating means 52
, The curved surface calculated by SA5 and the measurement point p
_The error e, which is the distance from _m , is calculated, and the maximum error e _max in each curved surface patch 34 is calculated. In SA7 corresponding to the error evaluator 54, the maximum error e
It is determined whether or not _max is within a preset allowable range. If the determination in SA7 is affirmative, SA14
The surface data is output and stored in the output data storage device 20, for example.

However, if the determination at SA7 is negative, then at SA8 corresponding to the subdivision means 56,
Of the temporary curved surface plate 38 divided into patches, the curved surface patch 34 whose error e has been determined to exceed the preset allowable value by SA7 is subdivided into four. Next, in SA9 corresponding to the change rate calculating means 60, the change rates of the curved surface shape in the u direction and the v direction are calculated for the divided surface patch 34d and compared with each other. Next, in SA10, the divided curved surface patch 34d
It is determined whether or not the difference between the change rate in the u direction and the change rate in the v direction of the curved surface shape is larger than a predetermined reference value. If the determination of SA10 is denied, SA12
Is directly executed, but if affirmative, the anisotropy determined based on the ratio of the magnitude of the shape change in each of the u direction and the v direction is provided in SA11 corresponding to the temporary curved surface plate changing means 62. The temporary curved plate 38 is changed to the anisotropic material.

Next, in SA12, a conditional expression for minimizing the distortion energy sum U is calculated again. In SA13, a conditional expression for smoothly connecting the divided patch 34d and the undivided patch 34 is satisfied. Meanwhile, a simultaneous equation that minimizes the distortion energy sum U as described above is created. Next, SA5 and subsequent steps are repeatedly executed. In the present embodiment, SA13 and SA5 correspond to the subdivided patch surface data calculation unit 58.

[0060] As described above, according to this embodiment, by the temporary curved plate setting unit 32 (SA2), based on the three-dimensional measurement data representing the positions of a plurality of measurement points p _m on the real curved surface, the 3 When temporary curved plate 38 that is divided into patches corresponding to each measurement point p _m that position is represented from dimension measurement data is set by the elastic member mounting means 42 (SA3), a plurality of measurements on the real curved surface with the coil spring (elastic member) 44 between the point p _m and the temporary curved plate 38 is attached, by attachment point defining means 46 (SA3), the position of the attachment point for the temporary curved plate 38 of the coil spring 44 It defined using the interval between the measurement points p _m, and,
The coil spring 44 defined in the attachment point defining means 46 by the curved surface data calculating means 50 (SA5).
Using the position of the attachment point for the temporary curved plate 38, the strain energy sum of the strain energy U ₂ of strain energy U ₁ a coil spring 44 attached thereto of the temporary curved plate _{38 U = (ΣU 1 + ΣU} 2) The curved surface data representing the curved surface of the temporary curved plate 38 that minimizes the following is calculated. Therefore, physical properties of the provisional curved plate 38 because it is reflected in the curved surface, the curved surface data representative of each measurement point p _m or less distortion curved through its vicinity is obtained.

[0061] Further, according to this embodiment, the error calculation unit 52 for obtaining the error e between the patch 34 of the curved surface represented by the surface data and the measurement point p _m (SA6), the error calculating means An error evaluator 54 for determining whether or not the error e calculated by 52 has exceeded a preset allowable value.
(SA7) and the subdivision means 56 (SA8) for subdividing the patches 34 of the provisional curved plate 38 divided into patches, for which the error e has been determined by the error evaluation means 54 to exceed an allowable value set in advance. ), And in the patches 34 subdivided by the subdivision means 56, surface data representing a surface in which the sum of the distortion energies is minimized while maintaining the smoothness of the shape between adjacent patches having different sizes is calculated. Subdivided patch surface data calculation means 50 (SA5, SA
13), in the subdivided patch 34, surface data representing a surface with the minimum distortion energy sum U while maintaining the smoothness of the shape between adjacent patches having different sizes is obtained. Since it is calculated, the measurement point p _m
There is an advantage that curved surface data more suitable for

Further, according to the present embodiment, in each patch 34 of the temporary curved surface plate 38, the change rate calculating means 60 (SA9) for calculating the change rate of the surface shape in each direction, and the change rate calculating means 60 If the difference in the shape change rate in each direction obtained by the above exceeds a preset value, the provisional curved plate 38 is anisotropic material having anisotropy corresponding to the ratio of the change rate in each direction. Temporary plate changing means 62 (SA1
Since 1) and is provided, there is an advantage that more conforming surface data are obtained for the measurement point p _m.

While the embodiment of the present invention has been described with reference to the drawings, the present invention can be applied to other embodiments.

[0064] For example, the elastic member mounting means 42 in the illustrated embodiments, although the coil spring 44 has been mounted between the measuring point p _m and the temporary curved plate 38, the plate spring, other elastic, such as synthetic rubber A deformable member may be used.

In the subdivision patch surface data calculation step 58 of the above-described embodiment, in the subsurface patch 34d subdivided by the subdivision means 56, the smoothness of the shape between adjacent subsurface patches having different sizes is obtained. While maintaining the condition of keeping the temporary surface plate 38, that is, the surface patch 34d.
In order to calculate the surface data representing the curved surface in which the sum of the strain energy U ₁ of the coil spring 44 and the strain energy U ₂ of the coil spring 44 is minimized, that is, to solve the strain energy method with constraints, the Lagrange's undetermined constant method is used. May be used.

The above is merely an example of the present invention, and the present invention can be variously modified without departing from the gist of the present invention.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a configuration of a curved surface generation device that executes a curved surface generation method according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating a curved surface represented by a curved surface expression representing a patch shape used in generating the curved surface of FIG. 1;

FIG. 3 is a functional block diagram illustrating a main part of an arithmetic function of the arithmetic and control unit in FIG. 1;

FIG. 4 is a diagram illustrating a plurality of measurement points of three-dimensional measurement data measured from an actual curved surface, which is used for generating a curved surface by the arithmetic and control unit of FIG. 1;

5 is a diagram showing a temporary curved surface plate divided into patches set based on the three-dimensional measurement data of FIG. 4 in a temporary curved surface plate setting step.

[6] A diagram showing in detail the process step of dividing the patch of Figure 5, the temporary curved plate from a group of maximum coordinate value and minimum coordinate values of the measurement point p _m represented position than the three-dimensional measurement data It is a figure which shows the process of calculating the rectangular box just entered.

[7] a diagram showing in detail the process step of dividing the patch of FIG. 5, and calculates the curve a, b, c when cutting a set of measurement points p _m i.e. Provisional curved plate across a horizontal plane It is a figure showing a process.

[8] A diagram showing in detail the process step of dividing the patch of FIG. 5, the step of calculating a curve b or Li of a cutaway of the set of measuring points p _m i.e. Provisional curved plate across a vertical plane FIG.

FIG. 9 is a diagram specifically illustrating a processing step of dividing into patches in FIG. 5, and illustrating a step of calculating curves e and f by connecting the line ends of the curves a to l.

The [10] the elastic member attaching step is a diagram conceptually showing a coil spring having both ends secured between the plurality of measurement points p _m and the temporary curved plate on the real surface.

11 is a diagram illustrating the linear distance between the measuring points p _m located along the predetermined direction.

FIG. 12 is a diagram illustrating a distance d between a measurement point p _m and a temporary curved plate.

FIG. 13 is a view showing a state in which a patch of a portion where a distance d between the measurement point p _m and the temporary curved surface plate exceeds a predetermined allowable value is subdivided by subdivision means.

FIG. 14 is a diagram illustrating a state in which the patch is further subdivided when the error d exceeds a preset allowable value in a patch subdivided by the subdivision unit.

FIG. 15 is a diagram illustrating the subdivision method of FIG.

[16] 2 of the difference between the average value d _av and the individual distance d _ij of the distance d between the provisional curved plate and the measurement point p _m square value (d _av -d _ij)
FIG. 9 is a diagram illustrating directions when calculating an average value of ² for each direction.

FIG. 17 shows a sum of strain energies in a patch of a temporary curved surface plate.
FIG. 11 is a diagram illustrating a curved surface of a temporary curved plate when the material is an isotropic material when a difference in a change rate in each direction of U exceeds a preset value.

FIG. 18 shows the sum of strain energies in a patch of a temporary curved plate.
FIG. 9 is a diagram showing a curved surface of a temporary curved plate when the change in the rate of change in each direction of U exceeds a preset value and the material is changed to an anisotropic material.

FIG. 19 is a diagram showing the shape of a provisionally curved plate on which the l-direction is substantially straight but the h-direction changes greatly, on which the undulation is assumed;
FIG. 9 is a diagram showing the undulations generated by forming a small patch by repeating the division of the curved surface patch of the temporary curved surface plate and the calculation of the curved surface data.

20 is a flowchart illustrating a main part of an arithmetic control operation of the arithmetic control device in FIG. 1;

[Explanation of symbols]

10: Curved surface generating device 32: Temporary curved plate setting means (temporary curved plate setting step) 34: Curved surface patch 36: Spline 38: Temporary curved plate 42: Elastic member attaching means (elastic member attaching step) 44: Coil spring (elastic member) 46: attachment point definition means (attachment point position definition step) 50: curved surface data calculation means (curved surface data calculation step) 52: error calculation means (error calculation step) 54: error evaluation means (error evaluation step) 56: subdivision Means (subdivision step) 58: Subdivision patch surface data calculation unit (subdivision patch surface data calculation step) 60: Change rate calculation unit (change ratio calculation step) 62: Temporary surface plate change unit (temporary surface plate change step) d: error p _m: measuring point

Claims (4)

[Claims] 1. A method that represents the positions of a plurality of measurement points on an actual curved surface.
A surface generation method for generating surface data representing a curved surface passing through the measurement point or its vicinity from the dimension measurement data, wherein each measurement point whose position is represented by the three-dimensional measurement data based on the three-dimensional measurement data A provisional curved surface plate setting step of setting a provisional curved surface plate divided into patches corresponding to the elastic member attaching step of temporarily attaching an elastic member to the provisional curved surface plate from a plurality of measurement points on the actual curved surface; An attachment point position defining step of defining a position of an attachment point of the elastic member with respect to the temporary curved surface plate using a distance between the measurement points; and a temporary curved surface plate of the elastic member defined in the attachment point position defining step. The surface data representing the curved surface of the temporary curved plate where the sum of the strain energy of the temporary curved surface plate and the strain energy of the elastic member attached thereto is minimized is calculated using the position of the attachment point with respect to And generating a surface data. 2. An error calculating step for obtaining an error between each patch of the curved surface represented by the curved surface data and each of the measurement points, and the error calculated in the error calculating step is set to a predetermined allowable value. An error evaluation step of determining whether or not the error has been exceeded; and a subdivision of a patch of the temporary curved surface plate divided into the patches, in which the error is determined to have exceeded a preset allowable value by the error evaluation step. In the dividing step, in the patch subdivided in the subdividing step, the distortion energy of the temporary curved plate and the distortion energy of the elastic member attached thereto while maintaining the smoothness of the shape between adjacent patches having different sizes A subdivided patch surface data calculation step of calculating surface data representing the surface of the temporary curved surface plate that minimizes the distortion energy sum of the surface. 3. A change rate calculating step of calculating a change rate of a surface shape in each direction of each patch of the temporary curved surface plate, and a change rate of a surface shape in each direction obtained in the change rate calculating step. If the difference exceeds the preset value,
3. A curved surface generating method according to claim 1, further comprising a step of changing the temporary curved surface plate to an anisotropic material. 4. A curved surface for generating a curved surface data representing a curved surface passing through the measurement point or its vicinity from three-dimensional measurement data representing positions of a plurality of measurement points on an actual curved surface in order to plastically work the plate material into a curved surface. A temporary curved surface plate having the same properties as the plate material, which is divided into patches based on the three-dimensional measurement data and corresponding to each measurement point whose position is represented by the three-dimensional measurement data. Provisional curved plate setting means for setting; an elastic member attaching means for temporarily attaching an elastic member to the temporary curved plate from a plurality of measurement points on the actual curved surface; and an attachment point of the elastic member to the temporary curved plate. Mounting point position defining means for defining the position of the elastic member using the distance between the measurement points, and using the position of the mounting point of the elastic member with respect to the temporary curved surface plate defined by the mounting point position defining means, Face plate distortion energy Surface generation apparatus characterized by a surface data calculation means strain energy sum of the formic and strain energy of the attached elastic member thereto to calculate the surface data representing a curved surface of the temporary curved plate made minimum, include.