JP2017009557A - Boundary point extraction method and measurement method using total station - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a boundary point extraction method which enables highly accurate measurement of place dimension of a measurement object and a measurement method using a total station.SOLUTION: The measurement method using a total station includes the steps of: setting a first base point P1 and a second base point P2 sandwiching a measurement object line 4 on a surface of a measurement object; extracting a boundary point on the measurement object line by a bisection method using the first base point P1 and the second base point P2; projecting the boundary point onto a three-dimensional plane; converting a three-dimensional plane coordinate on the three-dimensional plane into a two-dimensional coordinate; and calculating, by using the two-dimensional coordinate on the boundary point, a straight line equation on the measurement object line by a least square method.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a boundary point extraction method and a measurement method using a total station.

When measuring the planar dimensions of a structure, a method of measuring a target installed in the structure with a total station or the like is generally employed. However, it is difficult to install a target at each measurement point for a large structure.
On the other hand, if the measurement is performed in a non-contact manner, the measurement can be performed simply and safely. As a method for measuring such a structure in a non-contact manner, a method based on an image photographed by a camera (for example, see Patent Document 1) or a method using measurement data obtained by a 3D scanner (for example, Patent Document 2). See).

JP 2013-224861 A Japanese Patent No. 4769028

The method using a photographed image of a camera has a limit on the number of camera pixels, and an error of about several millimeters may occur in the measurement of a large structure. In addition, camera lens distortion may affect the measurement results.
In addition, since the 3D scanner measures with a mirror that rotates mechanically at a constant cycle, the point cloud is measured at a predetermined pitch. For this reason, there is a possibility that the position of the measuring point set on a particularly large structure cannot be measured accurately.
From such a viewpoint, an object of the present invention is to propose a boundary point extraction method and a measurement method using a total station, which can measure the planar dimension of a measurement object with high accuracy.

  In order to solve the above-described problem, the boundary point extraction method of the present invention includes a first step of measuring a distance to two measuring points having different collimation directions of the total station, and a magnitude of the distance to the two measuring points. Are different from each other, the second step of setting the midpoint between the two base points, the third step of measuring the distance to the midpoint, and the midpoint And the distance to each of the base points, and set a new midpoint between the base points, with the base point having the larger difference from the distance to the midpoint and the midpoint as a new base point. A fourth step, and thereafter, the boundary point is obtained by repeating the third step and the fourth step.

According to this boundary point extraction method, it is possible to extract the boundary of the edge of the structure, the step, and the like with high accuracy without using a target or the like. That is, since the boundary point is extracted by repeating the operation of comparing the measurement values and controlling the measurement direction, it is possible to ensure the accuracy higher than the measurement accuracy of a distance measuring instrument such as a total station.
Note that the boundary extraction method is preferably performed by an automatically controlled non-prism total station.

  In addition, the measuring method using the total station of the present invention includes the first base point and the second base point so as to sandwich the measuring object line on the surface of the measuring object, or inside and outside the circle on the surface of the measuring object, respectively. A step of setting a base point of the method, a step of extracting a boundary point on the measurement target line or a circle by a bisection method using the first base point and the second base point, and the boundary point on a three-dimensional plane Projecting on the three-dimensional plane, converting the three-dimensional plane coordinates of the boundary point on the three-dimensional plane into two-dimensional coordinates, and using the two-dimensional coordinates of the boundary point, the straight line of the measurement target line by the least square method And calculating a coordinate value of the center of the equation or the circle.

  According to the measuring method using such a total station, even if the structure is large, the plane dimension can be measured with high accuracy. It becomes possible to measure the boundary of the edge or step of the structure, and the center point of the bolt hole or the like with high accuracy. Therefore, it is possible to carry out highly accurate product inspections and current state surveys regardless of the scale and shape of the measurement object.

  According to the boundary point extraction method and the measurement method using the total station of the present invention, it is possible to measure the planar dimension of the measurement object with high accuracy.

It is a schematic diagram which shows the measuring method of 1st embodiment of this invention. It is a schematic diagram which shows the boundary point extraction method. It is a schematic diagram which shows the measuring method of 2nd embodiment of this invention.

<First embodiment>
In the first embodiment, as shown in FIG. 1, a case will be described in which the planar dimensions of a wall board 2 are measured by a non-prism total station 1 for a plate-like wall board 2 having an uneven surface.
Although this embodiment demonstrates the case where the rectangular convex part 3 is formed in the surface on the wall board 2, the shape of the convex part 3 is not limited.

The edge part of the convex part 3 is displayed as a line in a top view. In order to compare the completed shape with a design drawing or the like, it is necessary to extract the edge (boundary line 4) of the convex portion 3. In the present embodiment, boundary points (points on the boundary line 4) are extracted by the total station 1.
The planar dimension measuring method using the total station 1 of this embodiment includes a base point setting step, a boundary point extraction step, a three-dimensional plane projection step, a two-dimensional coordinate conversion step, and a linear equation calculation step.

The base point setting step is a step of setting a first base point P1 and a second base point P2 that sandwich the step (boundary line 4) of the wall board 2, as shown in FIG.
In the base point setting step, first, the boundary line 4 is roughly collimated, and thereafter, the total station 1 measures the distances L1 and L2 to two measuring points set in different directions on the wall board 2.
When the distances L1 and L2 to the two measuring points are different in size, these two measuring points are set as the first base point P1 and the second base point P2, respectively. On the other hand, when the magnitudes of the two distances are the same, the swing angle of the total station 1 is changed and the distance to the new measurement point is measured again.
In the present embodiment, the base point setting step is performed by automatically controlling the total station 1.

The boundary point extraction step is a step of extracting boundary points by a so-called bisection method using the first base point P1 and the second base point P2.
The boundary point extraction process of this embodiment includes a midpoint setting step, a distance measurement step, a distance comparison step, and a base point setting step.

In the midpoint setting step, a midpoint P3 is set in an intermediate direction between the first base point P1 and the second base point P2. The midpoint P3 is an intermediate direction of both the base point P1, P2, the direction of the angle theta ₁ of half of the angle theta ₂ from the first base point P1 to a second base point P2 (= θ _1/2) Set to (interval decomposition). That is, the midpoint P3 is set on the bisector of the corner O.
In the distance measuring step, the total station 1 measures the distance L3 to the midpoint P3.
In the distance comparison step, the distance L3 to the middle point P3 is compared with the distances L1 and L2 to the base points P1 and P2.
In the base point setting step, the base point (the first base point P1 in the present embodiment) and the midpoint P3 having a larger difference from the distance L3 to the midpoint P3 are set as the new first base point P1 ′ and the second base point, respectively. To the base point P2 ′.

By repeating the midpoint setting step, the distance measuring step, the distance comparing step, and the base point setting step until the interval resolution in the midpoint setting step reaches a minimum value (dividing the swing angle is minimum) (P1 ″ to P3 in FIG. 1). ”), The boundary point U of the step is extracted.
After extracting the boundary point U, the three-dimensional coordinates of the boundary point U are measured.
Note that the boundary point extraction step is performed by automatic control using the total station 1.
In the present embodiment, as shown in FIG. 1, four boundary points U1 to U4 along the upper side of the rectangular projection 3 and four boundary points D1 to D2 along the lower side of the projection 3 are defined. Extract each one. Note that the number of boundary points U and D may be set to three or more from the viewpoint of obtaining a least-squares direct equation.

The three-dimensional plane projection step is a step of projecting the extracted boundary points U1 to U4 and D1 to D4 on the three-dimensional plane.
First, as shown in FIG. 1, three-dimensional coordinates of arbitrary three points B1, B2, and B3 on the same plane of the wall board 2 (in this embodiment, a plane other than the convex portion 3) are measured.
Next, the coordinate values of these three points B1, B2, and B3 are defined as coordinate values on a two-dimensional plane. In the present embodiment, the point B1 is the origin (0, 0), the length of the line segment B1-B2 is L12, and the coordinate value of the point B2 is (L12, 0). That is, a two-dimensional plane coordinate having B1-B2 as the X axis is defined.
Subsequently, the side length between B1-B2 and between B1-B3 is obtained, and the two-dimensional coordinates (X _B3 , Z _B3 ) of the point B3 are obtained geometrically.

Here, the three-dimensional coordinates and two-dimensional coordinates of the points B1, B2, and B3 are defined as follows.
Point B1: Three-dimensional coordinates (x ₁ , y ₁ , z ₁ ), two-dimensional coordinates (0, 0)
Point B2: three-dimensional coordinates (x ₂ , y ₂ , z ₂ ), two-dimensional coordinates (X _B2 , 0)
Point B3: three-dimensional coordinates (x ₃ , y ₃ , z ₃ ), two-dimensional coordinates (X _B3 , Z _B3 )

A reference plane equation is obtained using the three-dimensional coordinates of the points B1, B2, and B3.
First, an operation for making the three-dimensional coordinates of the points B1, B2, and B3 correspond to the matrix of Expression 1 is performed.

Next, a three-dimensional plane equation by the least square method is derived from the matrix of Equation 1.
Since the constant terms (a, b, c) of the plane equation are determined by the calculation of the least square method (Equation 2), the reference plane equation (Equation 3) is obtained.

Next, the coordinate values (x, y, z) of the boundary point coordinates are projected onto a three-dimensional plane. If the coordinate values projected onto the three-dimensional plane are (x _R , y _R , z _R ), they can be converted into coordinates on the reference plane by Equation 4.

The two-dimensional coordinate conversion step is a step of converting the three-dimensional plane coordinates (x _R , y _R , z _R ) of the boundary points on the three-dimensional plane into two-dimensional coordinates (x _P , 0, z _P ).
First, a two-dimensional matrix is created from the measured coordinate values of the points B1, B2, and B3 using Equation 5. At this time, Y = 0 is set for XZ plane conversion.
When the two-dimensional matrix is created, the three-dimensional coordinates are converted into the two-dimensional coordinates by Expression 6.

The linear equation calculation step is a step of calculating a linear equation (Ax + z + B = 0) of the step boundary line 4 by the least square method using the two-dimensional coordinates of the boundary point.
A linear equation is calculated for each of the upper side and the lower side.
Similarly, by performing the base point setting step, the boundary point extraction step, the three-dimensional plane projection step, the two-dimensional coordinate conversion step, and the linear equation calculation step on the left and right sides of the convex portion 3, the shape of the convex portion 3 is set on the plane. It becomes possible to draw on.

When calculating the length of the side of the convex part 3, the coordinates (X _P , Z _P ) of an arbitrary point P0 on the plane of the convex part 3 (enclosed by each side) are given, and each straight line is calculated from that point. What is necessary is just to calculate the length H of the perpendicular to the equation according to Equation 7. That is, if the perpendicular length from the coordinates (X _P , Z _P ) to the upper side and the perpendicular length to the lower side are calculated and added, the side lengths of the left and right sides can be calculated.

According to the measurement method using the total station of the present embodiment, even if the wall board 2 is large, the step (boundary line 4) of the wall board 2 can be extracted with high accuracy, so that the plane dimension is highly accurate. Can be measured.
In other words, since the boundary point is extracted by repeating the operation of comparing the measurement values and controlling the measurement direction, it is possible to ensure the accuracy higher than the measurement accuracy of the total station by measuring in this way. .
Therefore, it becomes possible to carry out highly accurate product inspection and current situation survey regardless of the scale and shape of the wall board 2.
Since the entire coordinate system is calculated with the coordinate system of an arbitrary point set on the surface of the wall board (measurement object), it is converted into a coordinate display that is easy to check by rotating and translating the coordinates. be able to.

<Second Embodiment>
In the second embodiment, as shown in FIG. 3, a case will be described in which the planar dimensions of a plate-like wall board 2 having irregularities on the surface are measured by a non-prism total station 1.
Although this embodiment demonstrates the case where the circular recessed part 5 is formed in the surface of the wall board 2, the recessed part 5 formed in 2 of the wall board is not limited to a circle.
The level difference formed by the recess 5 is displayed as a line in the plan view. If the center and radius of the bottom surface of the circular recess 5 are extracted, the position of the step (boundary line 4) can be grasped. In this embodiment, the center and radius of the bottom surface of the recess 5 are measured.

  The planar dimension measuring method using the total station 1 of this embodiment includes a base point setting step, a boundary point extraction step, a three-dimensional plane projection step, a two-dimensional coordinate conversion step, and a center coordinate calculation step.

The base point setting step is a step of setting the first base point P1 and the second base point P2 that sandwich the step (boundary line 4) of the wall board 2.
In the present embodiment, the first base point P <b> 1 is set substantially at the center of the recess plane 5, and the second base point P <b> 2 is set outside the recess plane 5.
When the first base point P1 and the second base point P2 are set, the distances L1, L2 from the total station 1 to the base points P1, P2 are measured.

The boundary point extraction step is a step of extracting the boundary point C by the bisection method using the first base point P1 and the second base point P2.
In the present embodiment, a plurality of boundary points C1 to Cn are extracted along the edge (boundary line 4) of the recess plane 5.
Note that the details of the boundary point extraction step are the same as those described in the first embodiment, and thus detailed description thereof is omitted.
After the boundary points C1 to Cn are extracted, the three-dimensional coordinates of the boundary points C1 to Cn are measured.

The three-dimensional plane projection step is a step of projecting the extracted boundary points C1 to Cn on a three-dimensional plane.
Note that details of the three-dimensional plane projection step are the same as the contents shown in the first embodiment, and thus detailed description thereof is omitted.
The two-dimensional coordinate conversion step is a step of converting the three-dimensional plane coordinates of the boundary points C1 to Cn on the three-dimensional plane into two-dimensional coordinates.
Note that the details of the two-dimensional coordinate conversion step are the same as those described in the first embodiment, and thus detailed description thereof is omitted.

The center coordinate calculation step is a step of calculating the coordinate value of the center of the bottom surface of the recess 5 by the least square method using the two-dimensional coordinates of the boundary points C1 to Cn.
Here, it is assumed that the two-dimensional coordinates of the boundary points _C1 to _Cn are (X _C1 , Z _C1 ) to (X _Cn , Z _Cn ).
First, the center coordinate value (X ₀ , Z ₀ ) of the circle and the radius R ₀ of the circle are set arbitrarily, and are obtained by the iterative calculation method (Newton method) by iteration.
First, Equation 8 is converted into a linearized approximate equation (Equation 9).

From Equation 9, R = A · ΔX is obtained. That is, ΔX = A ⁻¹ · R is a solution to be obtained. Here, A is a variable matrix.

The calculation result of Expression 10 is substituted into Expression 11, and the calculation is sequentially performed until Δx, Δz, and Δs converge, and the least square solution is calculated. The converged final values (x ₀ , z ₀ , R ₀ ) indicate the center coordinate value and radius of the circle.

According to the measuring method using the total station of the present embodiment, the center point of a circle such as a bolt hole and the radius of the circle can be measured with high accuracy. Therefore, it becomes possible to carry out highly accurate product inspection and current situation survey regardless of the scale and shape of the wall board 2.
Since the entire coordinate system is calculated with the coordinate system of any point set on the surface of the wall board 2 (measurement object), it is converted into a coordinate display that is easy to check by rotating and translating the coordinates. can do.

Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and the above-described constituent elements can be appropriately changed without departing from the spirit of the present invention.
In addition, although the said embodiment demonstrated the case where the step part of a wall board was measured, you may use the measuring method using a total station for the measurement of the edge part of a wall board.
Moreover, in the said embodiment, although the wall board was employ | adopted as a measuring object, the measuring object to measure is not limited and can be applied to all structures.
In the above embodiment, the case where measurement is performed by automatic control has been described. However, the total station does not necessarily need to be automatically controlled.
The distance between the total station and the wall board (assumed object) is not limited and may be set as appropriate.

1 Total station 2 Wall board (object to be measured)
3 Convex 4 Border (Measuring line)
5 Recesses P1, P2 Base point P3 Midpoint L1, L2, L3 Distance U1-U4 Boundary point D1-D4 Boundary point

Claims (3)

A first step of measuring the distance to two stations with different collimation directions of the total station;
A second step of setting a midpoint between the two measurement points as a base point, between the base points;
A third step of measuring the distance to the midpoint;
Compare the distance to the midpoint and the distance to each base point, and use the base point with the larger difference between the distance to the midpoint and the midpoint as a new base point, and add a new intermediate point between the base points. And a fourth step for setting a midpoint,
Thereafter, the boundary point is obtained by repeating the third step and the fourth step. A step of setting a first base point and a second base point across the measurement target line on the surface of the measurement object;
Using the first base point and the second base point to extract boundary points on the measurement target line by a bisection method;
Projecting the boundary point onto a three-dimensional plane;
Converting the three-dimensional plane coordinates of the boundary points on the three-dimensional plane into two-dimensional coordinates;
And a step of calculating a linear equation of the measurement target line by a least square method using the two-dimensional coordinates of the boundary point, and a measurement method using a total station. Setting a first base point and a second base point on the inside of the circle on the surface of the measurement object and on the outside of the circle, respectively;
Using the first base point and the second base point to extract boundary points on the circle by a bisection method;
Projecting the boundary point onto a three-dimensional plane;
Converting the three-dimensional plane coordinates of the boundary points on the three-dimensional plane into two-dimensional coordinates;
And a step of calculating a coordinate value of the center of the circle by a least square method using the two-dimensional coordinates of the boundary point, and a measuring method using a total station.

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