Geometric optimization approximation based minimum region fitting method for profiles of parabolas

A minimum area, geometric optimization technology, applied in special data processing applications, instruments, electrical digital data processing, etc., can solve problems such as low efficiency, cumbersome methods, and large errors in fitting methods, achieving high efficiency, simple and clear methods, Effects that are easy to understand and implement

Inactive Publication Date: 2015-06-03
HENAN UNIV OF SCI & TECH
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Problems solved by technology

[0004] The purpose of the present invention is to provide a method for fitting the smallest area of ​​a parabolic profile based on geometric optimization approximation, so as to solve the problems of large errors, cumbersome methods and low efficiency of the existing fitting methods

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  • Geometric optimization approximation based minimum region fitting method for profiles of parabolas
  • Geometric optimization approximation based minimum region fitting method for profiles of parabolas

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Embodiment Construction

[0014] The minimum area fitting method of the parabolic profile based on geometric optimization approximation of the present invention, the steps are as follows:

[0015] Step 1. Select the initial reference focus and initial reference vertex

[0016] Let the measurement point be , using the average value of all measured point coordinates to obtain the initial reference focus of the fitted parabola, use , and choose a point close to the parabola vertex in the measurement point as the initial reference vertex, use express. Its specific determination method is:

[0017] , or (1)

[0018] Step 2. Calculate the initial error

[0019] Let the general equation of a parabola be , then the coefficients of the fitted initial parabola are determined by the following formula:

[0020] (2)

[0021] In the formula:

[0022] (3)

[0023] hypothetical point for the measuring point is the orthogonal point to the par...

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Abstract

The invention relates to in-plane curve fitting methods, in particular to a geometric optimization approximation based minimum region fitting method for profiles of parabolas. The method comprises the steps: firstly, approximate coordinates of an initial focus and a vertex of a measured parabola are roughly estimated according to coordinates of measuring points, and a series of auxiliary points are arranged around the initial focus and the vertex according to certain rules; next, supposed that the auxiliary points around the initial focus and the vertex are focuses and vertexes of the parabolas to be fit, the supposed focuses and vertexes can be used for constructing a series of parabolas; then, range values from the measuring points to the parabolas are calculated, and finally, the minimum region fitting of the measured parabola is realized through comparing, judging and transforming reference points and establishing a new supposed auxiliary parabola. The method has the advantages that the fitting process is simple, the accuracy of fitting is high, and the minimum region fitting and evaluation of profile tolerance errors of the parabolas can be effectively realized.

Description

technical field [0001] The invention relates to a fitting method of a parabola in a plane, in particular to a method for fitting a minimum area of ​​a parabola profile based on geometric optimization approximation. Background technique [0002] Curve profile recognition and measurement methods are key technologies in computer graphics and image processing, especially in the fitting and error evaluation technologies of basic curves such as parabolas, ellipses, and hyperbolas. In the field of mechanical design and processing, parabolic parts are also widely used, such as parabolic blades of radial turbines in aviation and aerospace propulsion systems, parabolic twist drills used in deep hole processing, and parabolic rolling bodies of bearings. Convexity, etc. These mechanical parts with parabolic contours have data fitting problems in the design process, manufacturing, and testing processes. The quality of fitting will directly affect the quality of design and products. The ...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F19/00
Inventor 雷贤卿漫睿东涂鲜萍高作斌
Owner HENAN UNIV OF SCI & TECH
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