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Algebraic curve rasterization method based on pixel precision

A pixel precision and rasterization technology, applied in image data processing, 2D image generation, instruments, etc., can solve the problems of low drawing efficiency and low precision of drawing curves, and achieve high processing efficiency, improve precision, and ensure correctness Effect

Inactive Publication Date: 2012-08-29
ZHEJIANG UNIV
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Problems solved by technology

[0009] The present invention provides a method for rasterizing algebraic curves based on pixel precision, which overcomes the problems of low drawing efficiency and low precision of drawing curves in the existing algebraic curve drawing method

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  • Algebraic curve rasterization method based on pixel precision
  • Algebraic curve rasterization method based on pixel precision
  • Algebraic curve rasterization method based on pixel precision

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Embodiment Construction

[0078] The specific implementation manner of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0079] Such as figure 1 Described a kind of algebraic curve rasterization method based on pixel precision, comprises the following steps:

[0080] (1) Input the algebraic curve to be drawn and its related information.

[0081] The input algebraic curve is a plane implicit algebraic curve, and its expression is as follows:

[0082] f(x,y)=∑a ij x i the y j =0

[0083] Among them, i and j are the degrees of x and y respectively, and the degrees of x and y are not higher than four; the relevant information of the algebraic curve includes a in the expression ij , a ij is the control coefficient corresponding to the algebraic curve.

[0084] (2) Limit the characteristic points of the curve within a pixel range, and obtain several characteristic regions containing the characteristic points of the curve.

[0085] The characteri...

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Abstract

The invention discloses an algebraic curve rasterization method based on pixel precision, comprising the following steps of: inputting an algebraic curve to be plotted and relevant information; limiting characteristic points of the curve into a pixel range to obtain a plurality of characteristic regions containing curve characteristic points; calculating crossed points of the curve and interfaces of the characteristic regions; constructing topology connecting information of the curve on the characteristic regions through the crossed points; determining the direction of the crossed points of the interfaces of the characteristic regions and utilizing a straight-line section to connect the adjacent characteristic regions to obtain a straight-line section fitting curve, wherein the straight-line section passes through the crossed points of the interfaces of the characteristic regions; and optimizing the straight-line section fitting curve, and plotting and displaying the curve. The algebraic curve rasterization method based on the pixel precision can obtain a high-quality curve through Newton iteration and guarantees the smoothness of the curve; and a numerical calculation process with complicated sub-resultant and high ordered equation rooting problems is omitted, and the curve can be conveniently plotted in real time.

Description

technical field [0001] The invention relates to computer algebraic curve and surface modeling technology, in particular to an algebraic curve rasterization method based on pixel precision. Background technique [0002] Algebraic curves and surfaces have a strong representation ability in geometric modeling, and they can express complex curves and surfaces with arbitrary topology better than parametric curves and surfaces. However, because it is far inferior to parametric curves in terms of intuitive control, and the number of control coefficients is large, there are not many studies on algebraic curves and surfaces. Algebraic B-spline curves make up for the shortcomings of unintuitive editing of power-based algebraic curves in terms of geometric intuition, and have the advantages of piecewise smoothness, local editing, intuitive geometric editing, and the ability to express complex topological shapes. [0003] In the research of drawing plane algebraic curves, the main diff...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06T11/00
Inventor 冯结青黄锦基
Owner ZHEJIANG UNIV
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