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Gompertz curve trend extrapolation accurate intelligent extending method

A trend extrapolation, curve technology, applied in the field of 3D modeling

Inactive Publication Date: 2013-04-03
ANHUI UNIVERSITY OF TECHNOLOGY AND SCIENCE
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

The aforementioned two patents solve the seamless splicing between two curves, which has strong practicability in CAD; but they cannot extend the curve to the specified target by maintaining the original characteristics

Method used

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  • Gompertz curve trend extrapolation accurate intelligent extending method
  • Gompertz curve trend extrapolation accurate intelligent extending method
  • Gompertz curve trend extrapolation accurate intelligent extending method

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0028] See attached figure 2 , The expression of the Gompertz curve 101 to be extended in this embodiment is , ; The target object 104 expression is ; Trend extrapolation, precise intelligent extension, includes the following steps:

[0029] (1) Select 3 groups of 9 characteristic points on the Gompertz curve 101 to be extended: (-4.000, 0.100), (-3.436, 0.005), (-2.873, 0.033), (-2.309, 0.120), (-1.745) , 0.318), (-1.182, 0.664), (-0.618, 1.151), (-0.055, 1.740), (0.509, 2.371);

[0030] (2) Judging the application conditions of the Gompertz curve extension model: the selection of 9 point sequences Log first difference Chain ratio , Ignoring the calculation error is a constant, choose Gompertz curve intelligent extension;

[0031] (3) Determine the undetermined parameters: the extended model is , Using the method of the present invention to determine the undetermined parameter as 0.300+5.910×10 -11 , 0.600+2.666×10 -11 , 6.000+6.901×10 -10 ;

[0032] (4) Determine the Gomp...

Embodiment 2

[0037] See attached image 3 , The expression of the curve 201 to be extended in this embodiment is , ; The target object 204 expression is ; Trend extrapolation, precise intelligent extension, includes the following steps:

[0038] (1) Calculate the symmetry axis of the curve 201 and y Shaft angle =45°, establish a rectangular affine coordinate system with the origin of the coordinate , Select 9 points on the curve 201: (9.992, 0.000), (4.330, -0.001), (3.660, 0.007), (2.991, 0.044), (2.321, 0.167), (1.651, 0.439), ( 0.981, 0.889), (0.311, 1.489), (-0.359, 2.170), the 9 points are in the coordinate system The abscissa is an arithmetic sequence;

[0039] (2) Judging the application conditions of the Gompertz curve extension model: the selection of 9 point sequences Log first difference Chain ratio , Ignoring the calculation error is a constant, choose Gompertz curve intelligent extension;

[0040] (3) Determine the undetermined parameters: the extended model is , Using the...

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Abstract

The invention belongs to the field of three-dimensional (3D) modeling of computer drawing, in particular to polynomial surface drawing, and relates to a Gompertz curve trend extrapolation accurate intelligent extending method. The conventional computer-aided design (CAD) software cannot extend the Gompertz curve with the original characteristic to be inserted at a given object. The method is used for extending the Gompertz curve by using a Gompertz curve extending model and sequentially comprises the following steps: selecting an M=3m group feature point {xi,yi} from the Gompertz curve to be extended; judging the application condition of the Gompertz curve extending model; determining a parameter to be determined; determining the Gompertz curve extending model; calculating an intersection point of the extending model and a target object; and extending by using the Gompertz curve extending model. The method also can be applied to accurate intelligent extension of the Gompertz curve at any position of the plane. By the method, the extending part does not change the original curve characteristic; long-distance accurate intelligent extension is realized; the accuracy is high; the curve at the connection position is smooth; the general key problem that a non-circular curve of a universal CAD software cannot extend is solved; and the Gompertz curve extending function of the conventional CAD software is increased or perfected.

Description

Technical field [0001] The invention belongs to the field of 3D modeling for computer graphics, in particular polynomial surface drawing, and relates to a precise and intelligent extension method for Gompertz curve trend extrapolation. Background technique [0002] When using CAD software for two-dimensional or three-dimensional drawing or modeling, you often encounter the problem of curve extension or transition. Modern CAD software can maintain the original characteristics of straight lines or arcs for extension, but can do nothing for other non-circular curves. . Gompertz curve is a commonly used curve that can be used to extend or transition CAD curves. [0003] Chinese patent CN 101482979A discloses a smoothly optimized CAD method for continuous splicing of curvatures of NURBS spatial curves. Without changing the original part of the curve, the gap between two NURBS curves is filled and the extension of the curve is guaranteed. Optimal smoothness; Chinese patent CN 101299278...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/50
Inventor 刘有余柳昊张海峰
Owner ANHUI UNIVERSITY OF TECHNOLOGY AND SCIENCE
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