Rasterization method of algebraic B-spline curve based on regularization conditions

Abstract

The invention discloses a rasterization method of an algebraic B-spline curve based on regularization conditions. The rasterization method of the algebraic B-spline curve based on the regularization conditions includes the steps of inputting the algebraic B-spline curve to be drawn and relevant information; processing the curve in a fragmentation manner, and converting the processed curve into a piecewise algebraic Bezier curve; confirming a curve segment needing to be displayed according to screen space parameters; subdividing a region corresponding to the curve segment needing to be displayed to obtain a control coefficient of each sub-region curve; detecting whether each sub-region satisfies the regularization conditions or not; and as for one sub-region satisfying the regularization conditions or with the region area smaller than one pixel, drawing the curve in the sub-region and displaying the curve on a screen. The curve can be defined in a simple region, and precision of the pixel is higher. Characteristic points can be refined step by step to achieve the precision of the pixel, calculation of the characteristic points with high complexity of time and space is avoided, and real-time rasterization drawing of the algebraic B-spline curve with complex topology is achieved.

Description

technical field [0001] The invention relates to computer algebraic curve and surface modeling technology, in particular to a method for rasterizing algebraic B-spline curves based on regularization conditions. Background technique [0002] Computer-aided geometric design began in the 1960s. Under the influence of computer development, in order to use computers to design more efficiently, people began to look for ways to represent curves or surfaces. With the development of computer technology, algebraic B-spline curves are more used in curve representation. The advantage of using algebraic B-spline curve representation method is that the control coefficient of algebraic B-spline curve has geometric meaning, and the shape of the curve can be intuitively controlled by changing the control coefficient during the editing process. [0003] In 1989, Professor Patrikalakis and Kriezis of MIT introduced piecewise continuous B-spline basis functions into the representation of algebr...

AI Technical Summary

Problems solved by technology

In the prior art, the algebraic curve drawing method mainly aimed at power-based polynomials uses the method of solving the subjunction of the curve to accurately calculate the feature points on the curve. This type of algorithm is slow to implement and cannot effectively draw the curve in segments , unable to meet the requirements of real-time rendering

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