CN111721272A - Engineering surface measurement method based on ellipsoid calculation - Google Patents
Engineering surface measurement method based on ellipsoid calculation Download PDFInfo
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- CN111721272A CN111721272A CN202010567367.7A CN202010567367A CN111721272A CN 111721272 A CN111721272 A CN 111721272A CN 202010567367 A CN202010567367 A CN 202010567367A CN 111721272 A CN111721272 A CN 111721272A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C15/00—Surveying instruments or accessories not provided for in groups G01C1/00 - G01C13/00
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2433—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures for measuring outlines by shadow casting
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/28—Measuring arrangements characterised by the use of optical techniques for measuring areas
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Abstract
The invention discloses an engineering surface measurement method based on ellipsoid calculation, which comprises the following steps: s1, converting the space coordinates of each sampling point on the earth surface to an earth ellipsoid through Gaussian coordinates to obtain the earth coordinates of each sampling point; s2, determining the range of the engineering area to be tested on the earth ellipsoid through the point location relation according to the geodetic coordinates of the sampling points; s3, calculating the meridian curvature radius and the prime circle curvature radius of the engineering area to be measured according to the geodetic coordinates of the sampling points; s4, calculating the area of the engineering area to be measured according to the ellipsoidal meridian curvature radius and the prime circle curvature radius; the method is suitable for calculating the engineering surface area with large area or large topographic relief, and solves the problems that the prior projection method projects the measurement observation value onto a plane and then calculates the surface area, and the projection error is generated when the measurement observation value is projected onto the plane, so that the engineering surface area calculation is influenced.
Description
Technical Field
The invention belongs to the technical field of measurement, and particularly relates to an engineering surface measurement method based on ellipsoid calculation.
Background
At present, in actual engineering measurement operation, for an engineering surface area calculation method, a traditional projection method is generally adopted to project a measurement observation value onto a plane and then calculate the surface area, but any projection condition cannot avoid deformation in the earth ellipsoid projection process, so that various errors caused by the influence of the projection condition on the observation value in the projection process onto the plane cannot be avoided, and further errors are brought to the engineering surface area calculation.
The existing method for calculating the surface area of the irregular terrain is more, and the more common methods at home and abroad comprise the following steps: the method comprises the steps of generally projecting an observation value to a plane, and then calculating the area by using a plane analysis method, wherein in the process, the projection error is generated when the measurement observation value is projected to the plane, so that the calculation of the engineering surface area is influenced. For the actual engineering, the method generates larger projection errors for the ground surface measurement with large span range or the area with large elevation relief.
For example, in practical engineering, a calculation principle based on a helenlun formula is often adopted, and the helenlun formula is a method for solving an area by using three side lengths of a triangle. When the surface area of the irregular terrain is calculated, the irregular terrain is approximately divided into a plurality of small triangles, the area of each triangle is calculated based on the Helen formula and the Excel table and summed, and finally the approximate surface area of the terrain is obtained. However, this method is only suitable for small area surface calculation, and the difference in the control of the side length of the divided triangle may cause different surface area calculation results, so this method is not suitable for large area or large relief engineering surface area calculation.
Disclosure of Invention
Aiming at the defects in the prior art, the engineering surface measurement method based on ellipsoid calculation is suitable for large-area or large-relief engineering surface area calculation, and solves the problems that the existing projection method projects the measurement observation value onto a plane and then carries out surface area calculation, and projection errors are generated when the measurement observation value is projected onto the plane, so that the engineering surface area calculation is influenced.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: an engineering surface measurement method based on ellipsoid calculation comprises the following steps:
s1, performing inverse calculation on the spatial coordinates of the various sampling points on the earth to an ellipsoid of the earth through Gaussian coordinates to obtain the geodetic coordinates of the various sampling points;
s2, determining the range of the engineering area to be tested on the earth ellipsoid through the point location relation according to the geodetic coordinates of the sampling points;
s3, calculating the meridian curvature radius and the prime circle curvature radius of the engineering area to be measured according to the geodetic coordinates of the sampling points;
and S4, calculating the area of the engineering area to be measured according to the ellipsoidal meridian curvature radius and the prime circle curvature radius.
Further, the ellipsoidal meridian radius of curvature and the prime circle radius of curvature of the engineering area to be measured in step S3 satisfy the following formulas:
N＝a(1-e2sin2(B2-B1))
wherein M is the radius of curvature of the meridian, N is the radius of curvature of the prime circle, a is the half-axis of the ellipsoid of the earth, e is the eccentricity of the engineering area to be measured, B2Upper boundary latitude, B, of the project area to be measured1The latitude of the lower boundary of the engineering area to be measured.
Further, the area of the engineering region to be measured in step S4 satisfies the following formula:
wherein P is the area of the engineering region to be measured, L2Is the right boundary longitude, L of the project area to be measured1The left boundary longitude of the project area to be tested.
The invention has the beneficial effects that:
1. the method does not need to adopt the traditional geometric analysis plane to calculate the surface area of the projection plane, and compared with the traditional plane analysis calculation method, the method has the advantages that the projection deformation is avoided or the deformation is minimized in the process of changing the measurement result into the ellipsoid, so that the error generated in the process of projecting the ground observation station to the plane in the traditional method is effectively avoided, and the purpose of no deformation or minimum deformation influence on the projection of the measurement calculation result is achieved.
2. The invention integrates the transformation and deformation calculation of various data on a reference ellipsoid surface and a Gaussian surface; the data calculated on the reference ellipsoid can obtain results on various projection surfaces according to various projection rules, so that the calculated data has reusability and universality.
3. In the actual engineering measurement, the geodetic coordinates of the measurement sampling points can be directly used for calculating the surface area of the engineering area to be measured, and the method is more suitable for the actual engineering measurement.
Drawings
FIG. 1 is a flow chart of an engineering surface measurement method based on ellipsoid calculations.
Fig. 2 is a schematic diagram of the transformation of the spatial coordinates of the sampling points onto the ellipsoid of the earth.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, an engineering surface measurement method based on ellipsoid calculation includes the following steps:
s1, performing inverse calculation on the spatial coordinates of the various sampling points on the earth to an ellipsoid of the earth through Gaussian coordinates to obtain the geodetic coordinates of the various sampling points;
in this embodiment, as shown in fig. 2, four sampling points Q1, N1, M1, and P1 are located on the earth surface, and are transformed to the earth ellipsoid through gaussian coordinates, so as to obtain respective geodetic coordinates a1, B1, C1, and D1 of the four sampling points.
S2, determining the range of the engineering area to be tested on the earth ellipsoid through the point location relation according to the geodetic coordinates of the sampling points;
s3, calculating the meridian curvature radius and the prime circle curvature radius of the engineering area to be measured according to the geodetic coordinates of the sampling points;
the ellipsoidal meridian radius of curvature and the unitary radius of curvature of the engineering area to be measured in the step S3 satisfy the following formulas:
N＝a(1-e2sin2(B2-B1)) (2)
wherein M is the radius of curvature of the meridian, N is the radius of curvature of the prime circle, a is the half-axis of the ellipsoid of the earth, e is the eccentricity of the engineering area to be measured, B2Upper boundary latitude, B, of the project area to be measured1The latitude of the lower boundary of the engineering area to be measured.
And S4, calculating the area of the engineering area to be measured according to the ellipsoidal meridian curvature radius and the prime circle curvature radius.
The area of the engineering region to be measured in the step S4 satisfies the following formula:
after the project area range is determined through steps S2 and S3, equations (1) and (2) are taken into equation (3), and the equations are expanded as follows:
wherein P is the area of the engineering region to be measured, L2Is the right boundary longitude, L of the project area to be measured1The longitude of the left boundary of the engineering area to be measured, d curved surface infinitesimal, B ═ B2-B1，L＝L2-L1And D is the range of the engineering area to be measured.
The invention has the beneficial effects that:
1. the method does not need to adopt the traditional geometric analysis plane to calculate the surface area of the projection plane, and compared with the traditional plane analysis calculation method, the method has the advantages that the projection deformation is avoided or the deformation is minimized in the process of changing the measurement result into the ellipsoid, so that the error generated in the process of projecting the ground observation station to the plane in the traditional method is effectively avoided, and the purpose of no deformation or minimum deformation influence on the projection of the measurement calculation result is achieved.
2. The invention integrates the transformation and deformation calculation of various data on a reference ellipsoid surface and a Gaussian surface; the data calculated on the reference ellipsoid can obtain results on various projection surfaces according to various projection rules, so that the calculated data has reusability and universality.
3. In the actual engineering measurement, the geodetic coordinates of the measurement sampling points can be directly used for calculating the surface area of the engineering area to be measured, and the method is more suitable for the actual engineering measurement.
Claims (3)
1. An engineering surface measurement method based on ellipsoid calculation is characterized by comprising the following steps:
s1, performing inverse calculation on the spatial coordinates of the various sampling points on the earth to an ellipsoid of the earth through Gaussian coordinates to obtain the geodetic coordinates of the various sampling points;
s2, determining the range of the engineering area to be tested on the earth ellipsoid through the point location relation according to the geodetic coordinates of the sampling points;
s3, calculating the meridian curvature radius and the prime circle curvature radius of the engineering area to be measured according to the geodetic coordinates of the sampling points;
and S4, calculating the area of the engineering area to be measured according to the ellipsoidal meridian curvature radius and the prime circle curvature radius.
2. The method for measuring an engineering surface based on ellipsoidal calculation according to claim 2, wherein the radius of curvature of the ellipsoidal meridian and the radius of curvature of the unitary mortise in the engineering area to be measured in step S3 satisfy the following formulas:
N＝a(1-e2sin2(B2-B1))
wherein M is the radius of curvature of the meridian, N is the radius of curvature of the prime circle, a is the half-axis of the ellipsoid of the earth, e is the eccentricity of the engineering area to be measured, B2Upper boundary latitude, B, of the project area to be measured1The latitude of the lower boundary of the engineering area to be measured.
3. The method of claim 2, wherein the area of the engineering region to be measured in step S4 satisfies the following formula:
wherein P is the area of the engineering region to be measured, L2Is the right boundary longitude, L of the project area to be measured1The left boundary longitude of the project area to be tested.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115098830A (en) * | 2022-06-28 | 2022-09-23 | 中国人民解放军战略支援部队信息工程大学 | Method and device for calculating difference between curvature radii of leveling surface and leveling ellipsoid |
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Application publication date: 20200929 |