hermite与bezier曲线的绘制（Plotting Hermite and Bezier curves）.docVIP

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hermite与bezier曲线的绘制（Plotting Hermite and Bezier curves）.doc

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hermite与bezier曲线的绘制（Plotting Hermite and Bezier curves）

hermite与bezier曲线的绘制（Plotting Hermite and Bezier curves） Sender: william@cis_nctu (he is the owner), letter area: Programming Title: [reprint] drawing of Hermite and Bezier curves Mail Station: Jiaotong University Information section _BBS (May 25, 00:32:41 1995) Relay station: cis_nctu From: Chiu I-Nan * Area: 90 C language To: All Date: 03 May 95 22:37:26 Plotting Subj:, Hermite and Bezier curves ********************************************************************** * method of drawing Hermite and Bezier * * Author: Qiu Yinan (Chi,u, I-Nan) * * copyright notice: I agree to the following articles only for BBS stations, but must be circulated throughout * (including copyright statements and procedures), all rights reserved. Anything without my consent * The behavior of *, trafficking, published excerpts, or other copyright infringement all I * * all of them need to bear criminal responsibility and civil liability for compensation. * ********************************************************************** The Hermite and Bezier curves are the usual expressions for the three degree space curve Define the two curves: 1.Hermite curve The Hermite curve is the three curve obtained at a given point at both ends and at both points. Order three curve: 32 X (T) = Ax * t + Bx * t + Cx * t + D 32 Y (T) = Ay * t + By * t + Cy * t + D The given endpoints are (x1, Y1), (X2, Y2), and YR1 (XR1) at both ends, (XR2, YR2), Then: X (0) = x1, y (0) = Y1 X (1) = X2, y (1) = Y2 X (0) = XR1, y (0) = YR1 X (1) = XR2, y (1) = YR2 Draw (x (T), y (T)), 0 =t =1, that is, the Hermite curve. 2.Bezier curve The Bezier curve is the three curve obtained for a given point at both ends and another two reference points, and it can be said to be Hermite Another representation of a curve. Suppose the points at both ends are P1, P2, and two reference points Pr1 and Pr2 The Bezier curve is converted into a Hermite curve: R1 = 3* (Pr1-P1) R2 = 3* (P2-Pr2) R1 and R2 are the point vectors at both ends of the Hermi