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A Method of Equiangular Approximation of 3D Circle and Ellipse

An isometric, three-dimensional technology, applied in program control, instrumentation, electrical program control, etc., can solve problems such as cumbersome calculations, and achieve the effect of expanding the processing range

Active Publication Date: 2020-10-09
HUAQIAO UNIVERSITY
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0002] At present, the algorithms for approximating straight line segments of curves include equal distance method, equal chord length method, equal error method, etc. If the above approximation algorithm is extended to three-dimensional space, the calculation is more cumbersome

Method used

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  • A Method of Equiangular Approximation of 3D Circle and Ellipse
  • A Method of Equiangular Approximation of 3D Circle and Ellipse
  • A Method of Equiangular Approximation of 3D Circle and Ellipse

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Embodiment 1

[0047] Such as figure 1 Shown, on the one hand, the equiangular approximation method of a kind of three-dimensional circle of the present invention is a kind of equiangular approximation method that carries out data point densification to three-dimensional circle according to parametric equation (with angle as parameter), specifically comprises the following steps:

[0048] Step 101, obtaining the primitive information of the three-dimensional circle from the DXF file

[0049] Specifically, the center point coordinate O'(x C ,y C ,z C ), radius R, starting angle θ S , End angle θ E (closed circle θ S = 0°, θ E =360°), and the normal of its plane

[0050] Step 102, using the vector method to derive the parameter equation of the three-dimensional circle

[0051] Such as Figures 2 to 3 As shown, according to the primitive information of the three-dimensional circle, R is the radius of the three-dimensional circle, O'(x C ,y C ,z C ) is the center point of the three...

Embodiment 2

[0068] Such as Figure 5 Shown, on the other hand, a kind of equiangular approximation method of three-dimensional ellipse of the present invention is a kind of equiangular approximation method that carries out data point densification to three-dimensional ellipse according to parametric equation (with angle as parameter), specifically comprises the following steps:

[0069] Step 201, obtaining the primitive information of the three-dimensional ellipse from the DXF file

[0070] Specifically, the center point coordinate O'(x C ,y C ,z C ), semi-major axis R L , semi-minor axis R S , starting angle θ S , End angle θ E (closed ellipse θ S = 0°, θ E =360°), and the normal of its plane

[0071] Step 202, using the vector method to derive the parameter equation of the three-dimensional ellipse

[0072] Such as Figures 6 to 7 As shown, according to the primitive information of the 3D ellipse, R L , R S are the semi-major axis and semi-minor axis of the three-dimensio...

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Abstract

The invention relates to an equiangular approximation method for a three-dimensional circle and a three-dimensional ellipse. The equiangular approximation method specifically comprises the steps of: deducing a parameter equation of the three-dimensional circle by adopting a vector method according to pixel information of the three-dimensional circle acquired from a DXF file, and deducing a parameter equation of the three-dimensional ellipse by adopting the vector method according to pixel information of the three-dimensional ellipse acquired from the DXF file; calculating point coordinates onthe three-dimensional circle by assigning a value at the interval of a certain angle increment Delta theta according to the parameter equation of the three-dimensional circle, and calculating point coordinates on the three-dimensional ellipse by assigning a value at the interval of a certain angle increment Delta theta according to the parameter equation of the three-dimensional ellipse; and importing the point coordinates into AutoCAD and comparing the point coordinates with an original image, wherein comparison results verify the correctness of the equiangular approximation method disclosedby the invention. The equiangular approximation method is an equiangular approximation method for performing data point densification on the three-dimensional circle and the three-dimensional ellipseaccording to the parameter equations (with angles as parameters), and carries out data point densification on the three-dimensional circle and the three-dimensional ellipse conveniently and efficiently through equiangular segmentation according to data features in the DXF file.

Description

technical field [0001] The invention relates to the field of numerical control automatic processing, in particular to an equiangular approximation method for a three-dimensional circle and an ellipse, in particular to an equiangular approximation method for densifying data points of a three-dimensional circle and an ellipse according to a parametric equation (taking angle as a parameter) . Background technique [0002] At present, the algorithms for approximating straight line segments of curves include equal distance method, equal chord length method, equal error method, etc. If the above approximation algorithm is extended to three-dimensional space, the calculation is more cumbersome. In CNC automatic machining, it is often necessary to obtain graphic information from DXF graphic files, and DXF graphic files store the center point coordinates O′(x C ,y C ,z C ) and starting angle θ S , End angle θ E and other information. Therefore, according to the characteristics ...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G05B19/19
CPCG05B19/19G05B2219/32317
Inventor 邵辉王磊兰欣
Owner HUAQIAO UNIVERSITY