Method for trend extrapolation as well as accurate and intelligent extension for cubic curve
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A technology of trend extrapolation and curve, applied in the field of 3D modeling
Inactive Publication Date: 2013-04-03
ANHUI UNIVERSITY OF TECHNOLOGY AND SCIENCE
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The above two patents solve the seamless splicing between two curves, which is very practical in CAD, but cannot extend the curve to the specified target while maintaining the original characteristics, but it is often required...
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Embodiment 1
[0025] See attached figure 2 , the expression of cubic curve 101 to be extended in this embodiment is , ; The target object 104 expression is ;Trend extrapolation and precise intelligent extension include the following steps:
[0026] (1) Select 5 points on the cubic curve 101 to be extended: (-3.000, -3.500), (-2.339, -1.167), (-1.679, 0.114), (-1.018, 0.691), (-0.357, 0.909 ), the abscissa of the five points is an arithmetic sequence;
[0027] (2) Judging the application conditions of the cubic curve extension model: the above-mentioned selection of 5 point sequences The third order difference of , ignoring the calculation error is a constant, which can be intelligently extended by the cubic curve;
[0028] (3) Use the least square method to determine the undetermined parameters: the extended model is , use the least squares method to determine the undetermined parameters as 0.200+4.922×10 -14 , 0.200+7.481×10 -13 , 0.300+3.301×10 -11 , =1.000+6.201×...
Embodiment 2
[0034] See attached image 3 , the expression of curve 201 to be extended in this embodiment is
[0035] , ; The target object 204 expression is ;Trend extrapolation and precise intelligent extension include the following steps:
[0036] (1) Calculate the symmetry axis of the curve 201 and y Axis angle =-45°, establish a Cartesian affine coordinate system with the coordinate origin , select 5 points on the curve 201: (4.200, -2.000), (2.576, -1.444), (1.638, -0.889), (1.117, -0.333), (0.974, 0.223), the 5 points point in the coordinate system The middle abscissa is an arithmetic sequence;
[0037] (2) Judging the application conditions of the cubic curve extension model: the above-mentioned selection of 5 point sequences The third order difference of , ignoring the calculation error is a constant, and choose the intelligent extension of the cubic curve;
[0038] (3) Use the least square method to determine the undetermined parameters: the extended model is ,...
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Abstract
The invention belongs to the field of 3D (three-dimensional) modelling for computer drawing, in particular, polynomial surface drawing, and relates to a method for trend extrapolation as well as accurate and intelligent extension for a cubic curve. In case of extension for a cubic curve via the existing CAD (computer aided design) software, a spline curve is adopted to approximately draw, and the accuracy is low and the connected parts are unsmooth. In the method disclosed by the invention, the cubic curve is extended by adopting a cubic curve extension model; and the method sequentially comprises the following steps of: selecting odd points {xi, yi} on the to-be-extended cubic curve, and enabling xi to form an arithmetic progression; judging the application conditions of the cubic curve extension model; determining undetermined parameters by the least square method; determining the cubic curve extension model; calculating the intersection point of the extension model and a target object; and extending by virtue of the cubic curve extension model. The method disclosed by the invention can also be applied to accurate and intelligent extension for any position which is in the shape of a cubic curve in a plane. The original curve characteristics are not changed after the extension, and long-distance and high-accuracy extension can be realized; and odd discrete points forming an arithmetic progression are selected on the curve, so that the formulas of the undetermined parameters are simplified, and the operational precision is high.
Description
technical field [0001] The invention belongs to the field of 3D modeling for computer drawing, in particular to polynomial surface drawing, and relates to a precise intelligent extension method for cubic curve trend extrapolation. Background technique [0002] In part modeling or artistic modeling, it is often necessary to extend the cubic curve to complete the connection or transition of the curve. The existing CAD software does not have this function, and the designer has to use the spline curve to approximate the drawing. Not smooth. [0003] Chinese patent CN 101299278A discloses a CAD method based on extended product shape space curve splicing, which fills the original gap between the two curves without changing the original shape of the curve without adding a third curve. part, realizes a new curve splicing effect; Chinese patent CN 101482979A discloses a smooth and optimized CAD method for continuous splicing of NURBS space curve curvature, which fills two NURBS curv...
Claims
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