Spatial Data Interpolation and Surface Fitting Method Based on Surface Theory
A technology of surface fitting and spatial data, applied in the field of surface modeling, which can solve the problems of large boundary value dependence and hinder the development of HASM technology.
Inactive Publication Date: 2016-06-29
INST POLICY & MANAGEMENT CHINESE ACADEMY SCI
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It can be seen that the existing HASM method relies heavily on the boundary value, which hinders the development of HASM technology
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[0100] The present invention is described in detail below in conjunction with accompanying drawing:
[0101] For the convenience of description, the spatial data interpolation and surface fitting method based on surface theory provided by the present invention is referred to as the SIST method for short. In the present invention, unless otherwise specified, the so-called HASM method is collectively referred to as a series of methods of different variants of HASM such as HASM4 and HASM5. Among them, HASM4 only considers two equations of surface theory, and HASM5 considers three equations of surface theory.
[0102] Such as figure 1 As shown, the present invention provides a spatial data interpolation and surface fitting method based on surface theory, comprising the following steps:
[0103] S1, setting the initial value matrix F0 of the surface to be fitted and obtaining sampling data; establishing a constraint function;
[0104] The initial value matrix F0 includes the fol...
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The invention provides a spatial data interpolation and curved surface fitting method based on the curved surface theory. The method includes: dispersing a to-be-fitted space into a grid point form, calculating first and second category basic quantity coefficient sum gamma ijk i=1, 2; j=1, 2; k=1, 2 of all grid points, building a target function on the basis of a constraint function and according to three basic equations of the curved surface theory, and for the internal grid points of the to-be-fitted space, minimizing the finite difference quadratic sum of the three equations; using an optimization solution device to solve an optimization control problem to obtain the fitted digital curved surface; judging whether the digital curved face satisfy the precision requirement or not, if not, and iterating the process until the curved surface satisfying the precision requirement is obtained. By the method, the problem of dependence on fitting area boundary value of traditional curved surface fitting methods based on the curved surface theory is solved, and high-precision simulated curved surfaces can be obtained accurately and reliably.
Description
technical field [0001] The invention relates to a surface modeling method in the fields of geosciences, computer-aided design and manufacturing, in particular to a spatial data interpolation and surface fitting method based on surface theory. Background technique [0002] HASM (High Accuracy Surface Modeling) is a new surface modeling method based on differential geometric surface theory proposed by Chinese scholars in the early 21st century. The basic idea of surface theory is: except for its spatial position, the shape of a curved surface is determined by the first type of basic formula and the second type of basic formula. Accurate values of the coefficients of the two types of basic formulas of the surface are obtained through iterative calculation, so that the shape of a surface can be simulated. [0003] At present, the HASM method is mainly used in the research of simulating surfaces from discrete points. The main steps of the existing HASH method are: (1) It is...
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IPC IPC(8): G06F17/50
Inventor 宋敦江刘扬
Owner INST POLICY & MANAGEMENT CHINESE ACADEMY SCI