Method for quadratic curve trend extrapolation accuracy intelligent extension
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A quadratic curve and trend extrapolation technology, applied in the field of 3D modeling, can solve the problem that the curve cannot be extended to the specified target, and achieve the effect of high precision
Inactive Publication Date: 2013-03-13
ANHUI UNIVERSITY OF TECHNOLOGY AND SCIENCE
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Problems solved by technology
The aforementioned two patents solve the seamless splicing between two curves, which has strong practicability in CAD; however, the original characteristics of the curve cannot be extended to the specified target, which is also a problem often encountered in CAD applications
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Embodiment 1
[0025] Referring to accompanying drawing 2, the expression of the quadratic 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 9 points on the conic curve 101 to be extended: (-1.000, 0.500), (-0.884, 0.178), (-0.767, -0.090), (-0.651, -0.304), (-0.534, -0.464), (-0.418, -0.569), (-0.301, -0.620), (-0.185, -0.616), (-0.068, -0.559), the abscissa of the 9 points is an arithmetic sequence;
[0027] (2) Judging the application conditions of the quadratic curve extension model: the above-mentioned selection of 9 point sequences second difference of , ignoring the calculation error is a constant, and choose the intelligent extension of the quadratic 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...
Embodiment 2
[0034] Referring to accompanying drawing 3, the expression of curve 201 to be extended in this embodiment is , ; The target object 204 expression is ;Trend extrapolation and precise intelligent extension include the following steps:
[0035] (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 9 points on the curve 201: (1.000, 0.000), (0.875, -0.226), (0.750, -0.446), (0.625, -0.539), (0.500, -0.625), (0.375, - 0.664), (0.250, -0.656), (0.125, -0.602), (0.000, -0.500), the 9 points are in the coordinate system The middle abscissa is an arithmetic sequence;
[0036](2) Judging the application conditions of the quadratic curve extension model: the above-mentioned selection of 9 point sequences second difference of , ignoring the calculation error is a constant, and choose the intelligent extension of the quadratic curve;
[0037] (3) Use the least square method...
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Abstract
The invention belongs to the field of three-dimensional (3D) modeling for computer graphics, in particular relates to polynomial surface graphics, and relates to a method for quadratic curve trend extrapolation accuracy intelligent extension. The conventional computer-aided design (CAD) software cannot extend a quadratic curve to be intersected with a designated object under the condition of maintaining the original characteristics. The method adopts a quadratic curve extension model to extend the quadratic curve, and comprises the following steps that: a plurality of points {,} are selected from the quadratic curve to be extended and form an arithmetic progression; the application conditions of the quadratic curve extension model are judged; undetermined parameters are determined through a least square method; the quadratic curve extension model is determined; the intersection points of the extension model and a target object are calculated; and the quadratic curve extension model is utilized to extend. The method can also be applied to the accuracy intelligent extension of arbitrary quadratic curve-shaped positions in a plane. The characteristics of the original curve are not changed after the curve is extended, long-distance accurate extension can be realized, the general key problem that the general CAD software cannot extend non-circular curves is solved, and the quadratic curve extension function of the conventional CAD software is added or completed.
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 method for extrapolating and intelligently extending quadratic curve trends. Background technique [0002] With the vigorous development of modern CAD software technology, many excellent two-dimensional and three-dimensional design software with friendly interface and powerful functions have emerged, such as AutoCAD, CAXA, Pro / E, UG, CATIA, etc. These softwares all have the basic function of extend, which can extend a straight line or arc to intersect a specified object, and keep the original characteristics (straight line or arc) unchanged. However, the extend function of these softwares is incapable of dealing with non-circular curves. If the extend command is used for a non-circular curve, some software (such as AutoCAD) will not perform any action; although some software (such as CAXA) performs the extension, it doe...
Claims
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Application Information
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