KR20080032855A - Three dimensions of algorithm for pipe alignment in shape reconstruction and registration - Google Patents

Abstract

A method for restoring and registering a 3D(Dimensional) shape for pipe arrangement is provided to arrange pipes by using an arrangement algorithm capacity matching connection surfaces of the pipes without damaging the surface of the pipes. A NURBS(Non-Uniform Rational B-Spline) curved surface is obtained by applying a NURBS curved surface approximation method to measuring point group data of a pipe(S100). A section of the pipe and coordinates of the center of the section are converted to agree with the center of one reference place and a perpendicular vector of a standard coordinate system(S300). Curved surface coordinates of the measured pipe are rotated to agree with the curved surface coordinates of the pipe designed based on the center and the perpendicular vector of the agreed section(S400). A point group of the curved surface of the pipe is matched with the point group of the designed curved surface of the pipe by using an ICP(Interactive Closet Point) algorithm(S500).

Description

Three dimensions of algorithm for pipe alignment in shape reconstruction and registration}

1 is a perspective view showing the form of an embodiment of a control mechanism of a conventional pipe alignment device.

2 is a front view showing a mounting state of the protective equipment of the conventional pipe alignment device.

3 is a view showing an embodiment of a pipe alignment operation using a conventional pipe alignment device.

4 is a flowchart illustrating a three-dimensional shape restoration and registration method for pipe alignment according to the present invention.

5 is a diagram showing a NURBS curved approximation method of measurement point group data on a pipe of the present invention.

6 is a view showing a method for obtaining coordinates of a coordinate axis, a pipe cut plane, and a center used in the present invention.

7 is a view showing a method of transforming coordinates so that the pipe cut plane of the present invention coincides with the XZ plane.

8 is a view showing a rotation conversion of the box surrounding the pipe of the present invention.

9A illustrates a method of matching a point group of pipe surfaces of the present invention to a point group of designed pipe surfaces.

9B is a graph showing the results obtained through minimizing the error criterion of FIG. 9A.

The present invention relates to a three-dimensional shape restoration and registration method for pipe alignment, and more particularly, to an algorithm for measuring and restoring a shape by measuring a curved surface of a pipe.

When welding each pipe, the welded pipes are welded in a state where the welded parts are not matched, and thus the welded connection parts of the pipes are damaged due to the repeated expansion and contraction caused by the rapid temperature change of the fluid flowing in the pipes.

Therefore, when making pipes, it is important to ensure that the pipes connected together are aligned correctly.

In order to solve the above problems, the following pipe arrangement has been proposed.

1 is a perspective view showing an embodiment of an adjustment mechanism of a conventional pipe alignment device, Figure 2 is a front view showing the mounting state of the protective equipment of the conventional pipe alignment device.

Conventional pipe aligning device is formed in a semi-circular shape and both ends are added to the position of the second pipe (2) in which the end of the bolt 25 abuts the protective device 60 formed by protruding the fixed end 70 is fixed by the bolt It is a structure to use the adjusting device 10 and the protective device 60 installed at the same time. The embodiment configured as described above is installed and used as follows.

In order to manufacture the pipe, several pipes having the same diameter are prepared. After inserting the adjusting tool 10 into one end of the first pipe 1, the adjusting tool 10 is fixed by using the bolt fixing end 50 so as not to move.

After the adjusting tool 10 is inserted into and fixed to the first pipe 1, the second pipe 2 to be welded and connected is approached to the first pipe 1 side, and then the first pipe 1 and the second pipe 2 are approached. The ends of the pipe 2 abut against each other. At this time, the end of the adjustment arm (5) protruding from the side of the adjustment opening (10) is to be located above the second pipe (1).

At this time, although the first pipe 1 and the second pipe 2 are in contact with each other, when the welding operation is performed in a state where the central axis does not coincide, the strength of the completed pipe joint becomes low.

First, since the nut 20 is fixed to the end of the adjustment arm 5, the bolts 25 are inserted into the respective nuts 20, and the respective bolts 25 are rotated to end the bolts 25. Abut on the surface of the second pipe (2).

In this state, as described above, if the central axes of the first pipe 1 and the second pipe 2 are shifted, each bolt 25 fitted to the nut 20 is adjusted to adjust the first pipe. (1) and the central axis of the second pipe (2) to match.

That is, since the diameters of the first pipe and the second pipe are the same, when the central axes coincide, the surfaces of the first pipe and the second pipe must also coincide. If the surfaces of the first pipe and the second pipe do not coincide, the following adjustments are made.

3 is a view showing an embodiment of a pipe alignment operation using a conventional pipe alignment device. If the surface of the second pipe protrudes out of the surface of the first pipe, tighten the bolt on the side from which the second pipe protrudes, and loosen the opposite bolt to move the second pipe. This operation is repeated until the surface of the second pipe coincides with the surface of the first pipe.

When the pipe alignment operation is performed using the adjusting tool as described above, since the end portion of the bolt 25 is in contact with the surface of the second pipe 2, damage may occur to the surface of the second pipe 2.

In order to prevent damage occurring on the surface of the second pipe 2, a protective device 60 having a shape as shown in FIG. 2 is installed and used.

The protective device 60 is formed in a semicircular shape, and both ends are provided with fixed ends 70 fixed by bolts so that the pair of protection devices 60 are coupled to the end side surfaces of the second pipes. Insert the bolt (75) into 70 to fix it.

Accordingly, after the adjusting tool 10 is installed in the first pipe 1, the protective tool 60 is provided at a portion where the bolt 25 attached to the adjusting tool 10 and the second pipe 2 contact each other. Since the end portion of the bolt 25 is in contact with the surface of the protective device 60 during the pipe alignment operation, the occurrence of damage to the surface of the second pipe 2 is prevented.

However, the conventional pipe aligning device as described above has many inconveniences because the pipes can be aligned only by the worker's manual work.

An object of the present invention is to provide a pipe alignment method through an alignment algorithm that can match the mating surface of the pipe without damaging the surface of the pipe, to solve the above problems.

The present invention provides a first step of obtaining a NURBS surface by applying the NURBS surface approximation method to the measurement point group data on the pipe; A second step of obtaining coordinates of the cut plane and the center of the pipe as coordinates of a predetermined reference coordinate system; A third step of converting coordinates of the measured center of the cut plane of the pipe and the coordinates of the normal vector to match the center of the reference plane and the normal vector of the reference coordinate system; A fourth step of rotating the measured surface coordinates of the pipe to coincide with the surface coordinates of the pipe designed based on the center and the normal vector of the cut plane matched in the third step; And a fifth step of matching the point group of the pipe curved surface to the point group of the designed pipe curved surface by using an iterative closet point (ICP) algorithm. do.

Hereinafter, the present invention will be described in detail with reference to the drawings.

4 is a flowchart illustrating a three-dimensional shape restoration and registration method for pipe alignment according to the present invention. Referring to Figure 4, it can be seen schematically about the three-dimensional shape restoration and registration method for pipe alignment of the present invention.

First, a NURBS curved surface approximation method is applied to measurement point group data on a pipe (S100). Here, the NURBS curved approximation method is applied to the scanned direction and the skinning direction.

Thereafter, the coordinates of the cut surface of the pipe and its center are obtained as coordinates of a predetermined reference coordinate system (S200). In order to obtain the coordinates of the cut plane and the center of the pipe, an edge curve placed on the cut plane of the modeled pipe is extracted from the NURBS curved surface, and then a least square method is applied to obtain a plane including the edge curve. The edge curve is rotated such that the plane including the edge curve becomes one plane of the reference coordinate system (for example, the XZ plane of FIG. 6), and then the projection edge is converted to the XZ plane. . Thereafter, the least square method is applied to approximate the edge curve projected on the XZ plane to a circle, and then the edge curve approximated to the circle is converted to the original coordinate system by reverse rotation conversion.

Subsequently, coordinates are transformed so that the coordinates of the center of the cut plane of the pipe and the normal vector are coincident with the center of the reference plane of the reference coordinate system (for example, the XZ plane of FIG. 6) and the normal vector (S300). . Cut plane matching of a pipe is to transform the coordinates of the plane and the normal vector containing the edge curve of the pipe to match the center and normal vector of the XZ plane, respectively. At this time, the shape of the coordinate axis is as shown in FIG.

Thereafter, the measured coordinates of the curved surfaces of the pipe are rotated to match the curved coordinates of the pipe designed based on the center and normal vector of the matched cutting plane (S400).

Finally, the point group of the pipe is matched and registered (S500).

The above process will be described in detail with reference to FIGS. 5 to 9B.

5 is a diagram showing a NURBS curved approximation method of measurement point group data on a pipe of the present invention. Referring to FIG. 5, reference numeral 100 denotes a shape in which measurement point group data on a pipe forms a curved surface, and reference numerals 110 and 120 represent a scanned direction and a scanning direction of the curved surface. When the NURBS curved surface approximation method of the scanned direction and the scanning direction is applied to (100), a NURBS curved surface as shown in (130) can be obtained, where (140) represents the unfolded shape of (130).

The NURBS surface approximation method of the measurement point group data on the pipe as described above is described as follows.

If the point group data on the pipe is D _{k, l} (0≤k≤m, 0≤l≤n), and the degrees of freedom are p and q, D _{k, l} for 0≤k≤m and 0≤l≤n. We can find the B-spline surface S (u, v) of degrees of freedom p, q with = S (s _k , t _l ). Where s _k And t _l are the selected parameter values.

D _{k, l} = S (s _k , t _l ) is represented by Equation 1.

Where P _{i , j} (0 ≦ _i ≦ m, 0 ≦ _j ≦ n) is an unknown control point.

Equation 1 may be rewritten as Equation 2.

6 is a view showing a method for obtaining coordinates of a coordinate axis, a pipe cut plane, and a center used in the present invention. Referring to Figure 6, the method for obtaining the coordinates of the pipe cut surface and the center of the present invention is as follows.

First, the edge curve 200 that lies on the cut surface of the pipe modeled with the NURBS curved surface obtained in FIG. 5 is extracted.

The least squares method is then applied to obtain a plane 210 containing the edge curve. That is, the plane 210 including the edge curve is obtained by obtaining x and α satisfying ∇Ｊ = 0 through Equation 3 representing the distance and Equation 4 representing the objective function.

Here, x represents a point on the plane and α represents the directional cosine of the normal to the plane.

Thereafter, the plane 210 including the edge curve is rotated so as to coincide with the XZ plane. First, the normal vector of the plane 210 including the edge curve and the normal vector of the XZ plane are obtained, and the angles between them are obtained. When the normal vector of the plane 210 including the edge curve is converted to the normal vector of the XZ plane, while viewing the origin of the coordinate axis, α, β, and r are respectively clockwise relative to the X, Y, and Z axes. If it rotates by an angle, Equations 5 to 7 can be used.

After that, the transformed edge curve is projected onto the XZ plane. At this time, since the projection transformation was projected on the XZ plane, the value of y may be 0.

Then, the least square method is applied to approximate the edge curve projected on the XZ plane to the circle 120. That is, the plane 210 including the edge curve is obtained by obtaining x, A, and r satisfying k = 0 through Equation 8 representing a distance and Equation 9 representing an objective function.

Here, x represents the center of the circle, A represents the number of directions of the normal to the plane of the circle, and r represents the radius of the circle. However, A is represented by the normalized value divided by the absolute value.

Thereafter, the edge curve 220 approximated by the circle is converted to the original coordinate system by reverse rotation conversion. In the reverse rotation conversion method, the above Equations 5 to 7 may be used inversely.

7 is a view showing a method of transforming coordinates so that the pipe cut plane of the present invention coincides with the XZ plane.

Referring to FIG. 7, in order to match the cut planes of the pipes, coordinates of the plane 300 including the edge curves of the pipes need to be converted to match the XZ plane 310. At this time, the coordinates are transformed so that the center and normal vectors of the plane 300 including the edge curve of the pipe coincide with the center and normal vectors of the XZ plane, respectively. Equation 10 is used to convert the center of the plane 300 including the edge curve of the pipe, and Equations 5 to 7 are used to convert the normal vector of the plane 300 including the pipe edge curve. Use

8 is a view showing a rotation conversion of the bounding box surrounding the pipe of the present invention.

Referring to FIG. 8, in order to rotate the pipe, a first bounding box 400a of a measurement surface surrounding the measurement surface 400 and the design surface 410, and a second bounding box of the design surface 410a), the bounding boxes match.

At this time, the curved surface coordinates of the pipe are rotated to the curved surface coordinates of the pipe designed using Equation 5 to Equation 7 based on the center and the normal vector of the cut plane matched in FIG. 7.

9A illustrates a method of matching a point group of pipe surfaces of the present invention to a point group of designed pipe surfaces. In order to match the shape of the pipe goes through the detailed process as follows. It uses the ICP (Iterative Closet Point) algorithm.

First, select a point group of pipe surfaces. Reference numeral 500 in FIG. 9A illustrates data points before matching the pipe point group.

The point group of the selected pipe surface is then matched with the point group of the pipe design surface. 9A of FIG. 9A shows a model point group after matching the pipe point group. When the matching of the pipe point group is completed, a registration result as shown in 510 is obtained. That is, in FIG. 9A, points corresponding to each other are formed as one pair, and different weights are given to different pairs. For weighting methods, the article "Godin, G., Rioux, M., and Baribeau, R. Three-dimensional Registration Using Range and Intensity Information," Proc. SPIE: Videometrics III , Vol. 2350, 1994. "

The noisy data is then removed from the pair of weighted points. For a method of removing noisy data, see "Dorai, C., Weng, J., and Jain, A. Registration and Intergration of Multiple Object Views for 3D Model Constrution," Trans. PAMI , Vol. 20, No. 1, 1998. "

9B is a graph showing the results obtained through minimizing the error criterion of FIG. 9A.

As shown in FIG. 9B, an error criterion is defined in the data from which the noise is removed and the error is minimized. 9b minimizes the error by repeating the whole process until the error is within the desired range.

Although the technical idea of the three-dimensional shape restoration and resistance method for pipe alignment as described above has been described with the accompanying drawings, it is intended to illustrate the best embodiments of the present invention by way of example. no. In addition, it will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit of the present invention.

The three-dimensional shape restoration and registration method for pipe alignment according to the present invention provides an algorithm for restoring and restoring a shape by measuring a curved surface of a pipe, whereby the operator was able to align the pipe only by manual labor, which is inconvenient. Improved pipe sorting method.

Claims (4)

Obtaining a NURBS surface by applying a NURBS surface approximation method to the measurement point group data on the pipe; A second step of obtaining coordinates of a cut surface of the pipe and its center as coordinates of a predetermined reference coordinate system; A third step of converting coordinates of the measured center of the cut plane of the pipe and the coordinates of the normal vector to match the center of the reference plane and the normal vector of the reference coordinate system; A fourth step of rotating the measured surface coordinates of the pipe to coincide with the surface coordinates of the pipe designed based on the center and the normal vector of the cut plane matched in the third step; And A fifth step of matching a point group of the pipe curved surface to a point group of a designed pipe curved surface using an iterative closet point (ICP) algorithm; 3D shape restoration and registration method for pipe alignment comprising a. The method of claim 1, The second step, Extracting an edge curve that lies on a cut plane of a modeled pipe in the NURBS surface; Applying a least square method to obtain a plane containing the edge curve; Rotating the edge curve such that the plane containing the edge curve becomes the reference plane; Projecting the rotated edge curve onto the reference plane; Applying a least square method to approximate an edge curve projected on the reference plane to a circle; And Converting the edge curve approximated by the circle to reverse rotation to the original coordinate system; 3D shape restoration and registration method for pipe alignment comprising a. The method of claim 1, The fourth step, Calculating a first bounding box surrounding the measured surface of the pipe and a second bounding box surrounding the curved surface of the designed pipe; And Rotating the first bounding box such that the first bounding box and the second bounding box coincide with each other based on the center and the normal vector of the cut planes matched in the third step; 3D shape restoration and registration method for pipe alignment comprising a. The method of claim 1, The fifth step, Selecting a point group of the pipe curved surface; Matching the point group of the selected pipe surface with the point group of the pipe design surface; Weighting a pair of corresponding points before and after the matching; Removing noisy data from the pair of weighted points; Defining an error criterion and minimizing the error in the noise-free data; And Repeating the above steps until the error is within a desired range; 3D shape restoration and registration method for pipe alignment comprising a.

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