Curve drawing method based on secondary B spline iteration

A curve drawing and iterative technology, applied in the field of curve drawing, can solve problems such as low accuracy of approximation splines and local modification of interpolation splines

Inactive Publication Date: 2011-10-19
NANJING UNIV OF INFORMATION SCI & TECH
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AI Technical Summary

Problems solved by technology

However, both splines have certain shortcomings, for example, the interpolation spline cannot be modified locally, and the accuracy of the approximation spline is not high.
Therefore, in practical applications, if the product is required to have good accuracy and smoothness, and can be easily modified locally, the existing algorithm cannot meet the requirements.

Method used

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  • Curve drawing method based on secondary B spline iteration
  • Curve drawing method based on secondary B spline iteration
  • Curve drawing method based on secondary B spline iteration

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Embodiment Construction

[0040] The technical scheme of the present invention is described in detail below in conjunction with accompanying drawing:

[0041] The curve drawing method based on the second B-spline iteration of the present invention, its principle is as follows figure 1 As shown, it specifically includes the following steps:

[0042] Step A, input the supervector of the given periodic coordinate point ; the supervector here Refers to a series of coordinate points with x, y, and z axes as coordinates in a predetermined space. These coordinate points need to be on the drawn curve. Supervector The expression of is as follows,

[0043] ,

[0044] In the formula, Respectively the first, the second, ..., the first NThe coordinate vector of a given periodic coordinate point, N is the number of given periodic coordinate points, , , Respectively represent the first points at axis, axis, Coordinate components on the axis, 7 coordinate points given in advance in the p...

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Abstract

The invention discloses a curve drawing method based on secondary B spline iteration. In the method, a curve passing through each coordinate point is drawn by using a computer according to a given periodic coordinate point. The method comprises the following steps of: inputting a super vector of the given periodic coordinate point; performing boundary supplementation on the super vector with a boundary supplementation method to obtain a new super vector; computing an approximate B spline curve by taking the new super vector as an initial control point; recording a coordinate value on the approximate B spline curve; and computing an error super vector and judging whether next iteration is needed according to the condition of whether the error super vector meets a given accuracy requirement. Compared with the prior art, the method has the advantages of high convergence rate of a drawn curve, high convergence accuracy, convenience for local modification and the like.

Description

technical field [0001] The invention relates to a method for drawing curves by using a computer, in particular to a method for drawing curves based on quadratic B-spline iteration. Background technique [0002] The so-called curve approximation drawing technology is to use the computer to realize the drawing of the required curve, so that it is as close as possible to the actual required curve. The core problem of realizing the curve approximation drawing technology is to find an algorithm with high efficiency and accuracy, so that it can draw the curve needed in actual production conveniently and quickly. Curves are not only widely used in the design of precision machinery such as aircraft, ships, automobiles, and aerospace vehicles, but also important research content in the fields of computational mathematics such as data approximation, numerical differentiation, numerical solution of differential equations, computational geometry, and computer graphics. . In the 1990s,...

Claims

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Application Information

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IPC IPC(8): G06T11/20
Inventor蒋勇王介付李玉梅
OwnerNANJING UNIV OF INFORMATION SCI & TECH