graphics with PSTric..

This point, which we denote by z 1234 is a point on the curve as can be seenin the next (enlarged) picture.z 12z 1z 2z 123z1234z 34z 234£z z 3z 4Curvy TricksOpen and closed curvesInvisible endsCurve tweakingA new curveOnline L A T E X TutorialPart II – GraphicsPSTricksHow about the other points of the curve? Well, the process we’ve describedabove is repeated with the new control points z 1 , z 12 , z 123 , z 1234 andz 1234 , z 234 , z 34 , z 4 to get another point and so on ad infinitum. This processconverges rather quickly and the scaffolding is finally removed. 1¢¢ ¡¡¡1 For the mathematically inclined, it may be interesting to note that the curve can be algebraicallydescribed by the equationa Bernshteĭn polynomial of degree 3.z(t) = (1 − t) 3 z 1 + 3(1 − t) 2 tz 2 + 3(1 − t)t 2 z 3 + t 3 z 4E Krishnan, CV Radhakrishnan and AJ Alexconstitute the graphics tutorial team.Comments and suggestions may be mailed totutorialteam@tug.org.inc○2002, 2003, The Indian T E X Users GroupThis document is generated by PDFT E X withhyperref, pstricks, pdftricks and pdfscreenpackages in an intel PC running GNU/LINUXand is released under LPPLThe Indian T E X Users GroupFloor iii, sjp Buildings, Cotton HillsTrivandrum 695014, indiahttp://www.tug.org.in 16/16