CN112037329B - Irregular curved surface construction method - Google Patents
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Abstract
The irregular curved surface construction method comprises the following steps: s1, selecting an existing surface with a control function on an irregular curved surface to be constructed as a reference surface, and extracting space geometric data of the reference surface as a reference surface data set R; s2, editing control points of the irregular curved surface, wherein the control points are used as an initial source data set D; s3, processing an initial source data set D of the curved surface control point by using the reference surface data set R to generate a relative source data set S for interpolation fitting calculation relative to the reference surface; according to the scheme, the reference surface of the existing surface which plays a role in determining the form of the constructed curved surface is selected, the curved surface control points are manually edited based on the reference surface, the influence of fluctuation change of the reference surface is eliminated, the shape of the curved surface can be effectively controlled by using fewer control points, and then an appropriate fitting algorithm and a corresponding transformation function are adopted to better generate an irregular curved surface.
Description
Technical Field
The invention relates to the field of geological three-dimensional modeling, in particular to a construction method of an irregular curved surface morphologically controlled by the existing curved surface in the three-dimensional modeling process, which is also suitable for construction of similar irregular curved surfaces in other natural science fields.
Background
In both the construction and geological mineral industries, geological surveys of the field are required. The expression of geological conditions by geological investigation is not separated from an irregular curved surface, and in the traditional geological investigation, mining and engineering investigation design and construction processes, two-dimensional drawing pieces (sectional drawings, plane drawings, contour drawings and the like) are often adopted to indirectly express the three-dimensional spatial distribution of a real geologic body, so that the method has great defects. With the development of computer technology, BIM three-dimensional building information models are increasingly widely applied to various industries, and the BIM three-dimensional building information models have the advantages of unique visualization, harmony, simulability, optimizability and the like, can directly generate two-dimensional drawings, and serve the full life cycle process of projects. In the geological field, BIM is mainly embodied as a geological three-dimensional model, so that geological conditions can be expressed more accurately and directly, most geological surfaces of the geological model such as a terrain surface, a bedrock surface, a weathered surface, a ground water level surface, a relative water-proof surface, a sedimentary rock/soil surface and the like are expressed by irregular curved surfaces, and a great deal of correlation exists among the surfaces, such as the ground water level surface, the weathered surface and the bedrock surface are limited by the terrain surface, and strong correlation exists among the sedimentary rock/soil layer surfaces. The modeling of the irregular curved surface with correlation is difficult, only a small number of existing accurate control points are often obtained through means of drilling, hole detection, geophysical prospecting, geological mapping and the like, the number of the existing accurate control points is limited, a reasonable geological surface is difficult to directly construct, engineering technicians are required to add a large number of manual control points and an appropriate interpolation fitting algorithm is adopted to assist in constructing the reasonable geological surface, more manual control points are required to be added if the influence of fluctuation change of the controlled curved surface is not removed in the curved surface construction process, uncontrollable interpolation fitting calculation results are easy to generate, and the repeated work is large.
In many natural scientific research fields, mathematical modeling is often required to be performed on a research object, and a three-dimensional geometric model is mostly adopted to intuitively display, and also many correlation problems between curved surfaces exist, such as atmospheric isothermal surfaces are greatly limited by terrain surfaces.
In the three-dimensional modeling process, the construction of the irregular curved surface is an important and indispensable working content, so that not only is the efficiency low and the expected effect difficult to achieve, but also the quality of the constructed curved surface is often poor, repeated adjustment and modification are needed, and the workload is high. Thus, it would be significant to improve the efficiency and quality of modeling if some special methods could be employed as appropriate.
Disclosure of Invention
Therefore, the method for constructing the irregular curved surface is provided to solve the problem that the method for constructing the irregular curved surface which is morphologically controlled by a certain existing curved surface in the existing three-dimensional geometric modeling is not efficient enough. The principle is that an existing surface playing a role in controlling is selected as a reference surface, editing manual control points are added, after control point data are extracted and influence of the reference surface is eliminated, control data of a curved surface are generated by interpolation fitting, influence of the superimposed reference surface is restored to form curved surface control data, and finally a required irregular curved surface is generated.
In order to achieve the above object, the present inventors provide a method for constructing an irregular curved surface, comprising the steps of:
s1, selecting an existing surface with a control function on an irregular curved surface to be constructed as a reference surface, and extracting space geometric data of the reference surface as a reference surface data set R;
s2, editing control points of the irregular curved surface, wherein the control points are used as an initial source data set D;
s3, processing an initial source data set D of the curved surface control point by using the reference surface data set R and using a transformation function f1 to generate a relative source data set S relative to the reference surface;
s4, performing interpolation fitting calculation by taking the relative source data set S as an input source to generate a control point data set T of the irregular curved surface;
s5, based on the datum plane data set R, an inversion function F2 is used for restoring the irregular curved surface control point data set T into a curved surface data set F with correct space coordinates;
s6, constructing and generating an irregular curved surface by using the curved surface data set F.
Specifically, in step S3, the function used for processing the initial source data set D of the curved surface control point is F1, and in step S5, the function used for restoring the irregular curved surface control point data set T to the curved surface data set F with correct space coordinates is F2; f2 is the inverse function of f1.
Specifically, f1 is a characteristic correlation function of the irregular curved surface to be constructed and the reference surface, and represents the relation between the irregular curved surface and the reference surface.
Specifically, the interpolation fitting calculation in step S4 may be performed by a kriging method, a DSI discrete smooth interpolation method, a multiple regression method, an inverse distance weighting method, a radial basis function method, a multiple regression method, and a minimum curvature method, and the selection mainly depends on the self-characteristics of the irregular curved surface.
By the method, the existing curved surface which plays a role in controlling the irregular curved surface to be constructed is selected as the reference surface, the fluctuation influence of the reference surface is eliminated before interpolation fitting calculation, control points for editing the irregular curved surface are added, the shape of the curved surface can be effectively controlled by using fewer control points, namely fluctuation change factors of the reference surface are eliminated, curved surface control data are efficiently edited and generated, and finally the required irregular curved surface is restored and generated.
Drawings
FIG. 1 is a flowchart of a method for constructing an irregular curved surface according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the present invention;
fig. 3 is a practical effect diagram of the present invention.
Detailed Description
In order to describe the technical content, constructional features, achieved objects and effects of the technical solution in detail, the following description is made in connection with the specific embodiments in conjunction with the accompanying drawings.
Referring to fig. 1 and fig. 2, a method for constructing an irregular curved surface includes the following steps:
s1, selecting a reference plane and extracting space geometric data of the reference plane to obtain a reference plane data set R: according to the characteristics of the irregular curved surface to be constructed, the correlation between the irregular curved surface and the existing curved surface is analyzed, the existing curved surface which controls or influences the shape of the irregular curved surface is selected as a reference surface (such as a terrain surface), the space geometric data of the reference surface is extracted and used as a reference for processing data before and after interpolation fitting, and the space geometric data is used as a reference surface data set R. As in the case of the operation of selecting the reference plane in fig. 2, the left side is a topographic contour map and the right side is a three-dimensional body.
S2, adding an editing control point by taking the reference surface as a reference surface as an initial source data set D: under the visual interaction environment of the three-dimensional drawing platform of the computer, a specially developed tool (a group of operation tools in three-dimensional drawing platform software is generally adopted), a reference surface is taken as a reference, under the condition of following the self rule of an irregular curved surface, control points of the irregular curved surface are edited, manual control points are added and edited, the manually added control points are merged with the existing accurate control points (high-precision data points which are generally higher in reliability and are acquired in a certain way, such as measurement points and topography characteristic points) of the curved surface, and the points are combined into a group of discrete data point sets to be used as an initial source data set D of curve surface shape control of an interpolation fitting algorithm. As shown in fig. 2, column (2) indicates the state of the edited curved control point, the curved control point on the left side, and the curved control point and the terrain on the right side. The construction of the irregular curved surface is generally far from the existing few accurate control points, a large number of manual control points are needed to be manually added or edited, although the control points are artificially added to a certain extent, the control points are added on the premise of not violating the self characteristics of the irregular curved surface, and the built irregular curved surface has certain difference possibly due to different operators, but accords with the self rules of the irregular curved surface, the situation widely exists when exploring natural objects, the accuracy of human knowledge on the natural objects is limited, and the control points belong to an error range and are acceptable.
S3, processing the initial source data set D of the curved surface control point by using the reference surface data set R to generate a relative source data set S relative to the reference surface for interpolation fitting calculation: based on the reference plane, a suitable transformation function is used according to the relation between the curved surface to be constructed and the reference plane, and the function used here is f1. The f1 is a characteristic correlation function between the irregular curved surface and the reference surface, and converts the correlation characteristic between the two curved surfaces into a functional relation, so as to facilitate the construction of the irregular curved surface, wherein the functional relation can be simple transformation, such as transformation of elevation into relative thickness or depth, and can also be more complex transformation, such as the relation between mineral grade and burial depth, and three-dimensional space. f1 function uses reference surface data set R to process initial source data set D of curved surface control point, and generates relative source data set S for interpolation fitting calculation with respect to reference surface.
S4, taking the relative source data set S as an input source, performing interpolation fitting calculation, and generating a control point data set T of the irregular curved surface: the interpolation fitting calculation method comprises a Kriging method, a DSI discrete smooth interpolation method, a multiple regression method, an inverse distance weighting method, a radial basis function method, a multiple regression method or a minimum curvature method, and the like, and the specific adopted method is preferably selected according to the characteristics of the irregular curved surface. As shown in fig. 2, column (3) shows a graph after interpolation fitting after control point data processing, the left side is a contour line of a curved surface generated by interpolation fitting, and the right side is a curved surface generated by interpolation fitting.
S5, based on the datum plane data set R, restoring the irregular curved surface control point data set T into a curved surface data set F with correct space coordinates: in step S3, the function used for processing the initial source data set D of the surface control point is F1, and in step S5, the function used for restoring the irregular surface control point data set T to the surface data set F with correct spatial coordinates is F2, where F2 is an inverse function of F1.
S6, generating an irregular curved surface by using the curved surface data set F: generally, the generated irregular curved surface needs to be checked, preferably, multiple methods are adopted to check in multiple aspects under the visual interaction environment of the computer three-dimensional drawing platform, if the requirements (such as rationality) cannot be met, the manual control points can be edited (added, deleted and changed) again, and if necessary, the accuracy of the existing accurate control points of the curved surface needs to be checked and rechecked, and the steps S2-S6 are repeated until the requirements are met. In fig. 2, (4) is an irregular curved surface generated after inversion and reduction, the left side is a curved surface to be constructed after inversion and the right side is a positional relationship between the curved surface to be constructed and the terrain.
Referring to fig. 3, the method (named as "reference surface generation method") is used to eliminate the influence of the control surface, then uses less manually added control points to generate surface control data, and then restores the surface control data to real surface control data to generate the final irregular surface (2). Compared with the method for directly editing and generating the irregular curved surface (1), the method has the advantages that the number of required manual control points is obviously reduced, the editing efficiency can be effectively improved, after the influence of a reference surface is eliminated, the control point data difference of the curved surface is relatively reduced, the fluctuation range of the curved surface is further reduced, the influence of characteristic changes of the curved surface which are not the curved surface is eliminated, the possibility of errors is reduced when interpolation fitting operation is applied, the quality of interpolation fitting is improved, and finally the fluctuation of the superimposed control curved surface is reduced, so that the final irregular curved surface is generated. (3) The comparison of the curved surfaces constructed by two different methods is shown, the curved surface constructed by the common interpolation method is smooth, the curved surface constructed by the reference surface generation method has large fluctuation change, and the characteristics of an obvious reference curved surface are shown. (4) For comparing the section position schematic diagram, and (5) comparing the effects of sections at different positions, the reference surface generation method can be seen to keep more reference surface characteristics.
It should be noted that, although the foregoing embodiments have been described herein, the scope of the present invention is not limited thereby. Therefore, based on the innovative concepts of the present invention, alterations and modifications to the embodiments described herein, or equivalent structures or equivalent flow transformations made by the present description and drawings, apply the above technical solution, directly or indirectly, to other relevant technical fields, all of which are included in the scope of the invention.
Claims (2)
1. The method for constructing the irregular curved surface is characterized by comprising the following steps of:
s1, selecting an existing surface with a control function on an irregular curved surface to be constructed as a reference surface, and extracting space geometric data of the reference surface as a reference surface data set R;
s2, editing control points of the irregular curved surface, wherein the control points are used as an initial source data set D;
s3, processing an initial source data set D of the curved surface control point by using the reference surface data set R and using a transformation function f1 to generate a relative source data set S relative to the reference surface;
s4, performing interpolation fitting calculation by taking the relative source data set S as an input source to generate a control point data set T of the irregular curved surface;
s5, based on the datum plane data set R, an inversion function F2 is used for restoring the irregular curved surface control point data set T into a curved surface data set F with correct space coordinates;
s6, constructing and generating an irregular curved surface by using the curved surface data set F;
in the step S3, the transformation function used for processing the initial source data set D of the curved surface control point is F1, and in the step S5, the transformation function used for restoring the irregular curved surface control point data set T into the curved surface data set F with correct space coordinates is F2; f2 is the inverse of f 1;
the transformation function f1 is a characteristic correlation function of an irregular curved surface to be constructed relative to a reference surface.
2. The method of claim 1, wherein the interpolation fitting calculation in step S4 is optional, and includes kriging, DSI discrete smooth interpolation, multiple regression, inverse distance weighting, radial basis function, and minimum curvature.
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