\input preamble.tex % --------------------------------------------------------------------------- \begin{document} \begin{center} {\Huge \bf{I. Rational Quadratic Bezier Curves}} \bigskip \begin{lapdf}(16,20)(-8,-10) \Dgray \Dash(1) \Polygon(-8,0)(0,10)(8,0) \Stroke \Dash(0) \Red \Rcurve(64)(-8,0,7)(0,10,1)(8,0,7) \Stroke \Green \Rcurve(64)(-8,0,6)(0,10,1)(8,0,6) \Stroke \Blue \Rcurve(64)(-8,0,5)(0,10,1)(8,0,5) \Stroke \Cyan \Rcurve(64)(-8,0,4)(0,10,1)(8,0,4) \Stroke \Magenta \Rcurve(64)(-8,0,3)(0,10,1)(8,0,3) \Stroke \Yellow \Rcurve(64)(-8,0,2)(0,10,1)(8,0,2) \Stroke \Black \Rcurve(64)(-8,0,1)(0,10,1)(8,0,1) \Stroke \Red \Rcurve(64)(-8,0,1)(0,10,2)(8,0,1) \Stroke \Green \Rcurve(64)(-8,0,1)(0,10,3)(8,0,1) \Stroke \Blue \Rcurve(64)(-8,0,1)(0,10,4)(8,0,1) \Stroke \Cyan \Rcurve(64)(-8,0,1)(0,10,5)(8,0,1) \Stroke \Magenta \Rcurve(64)(-8,0,1)(0,10,6)(8,0,1) \Stroke \Yellow \Rcurve(64)(-8,0,1)(0,10,7)(8,0,1) \Stroke \Black \Rcurve(64)(-8,0,1)(0,10,0)(8,0,1) \Stroke \Red \Rcurve(64)(-8,0,7)(0,10,-1)(8,0,7) \Stroke \Green \Rcurve(64)(-8,0,6)(0,10,-1)(8,0,6) \Stroke \Blue \Rcurve(64)(-8,0,5)(0,10,-1)(8,0,5) \Stroke \Cyan \Rcurve(64)(-8,0,4)(0,10,-1)(8,0,4) \Stroke \Magenta \Rcurve(64)(-8,0,3)(0,10,-1)(8,0,3) \Stroke \Yellow \Rcurve(64)(-8,0,2)(0,10,-1)(8,0,2) \Stroke \Point(1)(-8,0) \Point(1)(+0,10) \Point(1)(+8,0) \Text(-8.0,0.2,rb){$P_0$} \Text(+0.2,+10.3,rb){$P_1$} \Text(+8.0,0.2,lb){$P_2$} \end{lapdf} \end{center} All curves share the same Bezier points, but they differ in the weights of the points. The black curve is a parabola {$w = 1$}. Above of this all curves are hyperbolas with increasing weigts, below of this are elliptic curves with decreasing weights. The line has a weight of {$w = 0$}. After this the weights are negative increasing. The curves are the complementare elliptical arcs to the positive counterparts. \newpage \unitlength1.16cm \begin{center} {\Huge \bf{II. Conic Curves}} \bigskip \begin{lapdf}(16,16)(0,0) \Dgray \Rcurve(64)(4,10.333,2)(0,3.4,1)(8,3.4,2) \Rcurve(80)(4,10.333,2)(0,3.4,-1)(8,3.4,2) \Stroke \Red \Rcurve(64)(4,9.7,2)(0,4.7,1)(8,4.7,2) \Rcurve(80)(4,9.7,2)(0,4.7,-1)(8,4.7,2) \Stroke \Green \Rcurve(64)(9.7,4,2)(4.7,0,1)(4.7,8,2) \Rcurve(80)(9.7,4,2)(4.7,0,-1)(4.7,8,2) \Stroke \Blue \Rcurve(64)(16,16,1)(8,8,5)(16,0,1) \Stroke \Cyan \Rcurve(64)(0,16,1)(8,8,5)(0,0,1) \Stroke \Magenta \Rcurve(64)(0,16,1)(8,0,1)(16,16,1) \Stroke \Yellow \Rcurve(64)(0,0,1)(8,16,1)(16,0,1) \Stroke \end{lapdf} \large Circle, Ellipse, Parabola, Hyperbola \end{center} \end{document}