## [PyX-checkins] pyx/design beziers.tex,1.4,1.5

 [PyX-checkins] pyx/design beziers.tex,1.4,1.5 From: Jörg Lehmann - 2005-09-01 20:45:57 Update of /cvsroot/pyx/pyx/design In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv17944 Modified Files: beziers.tex Log Message: some spelling fixes Index: beziers.tex =================================================================== RCS file: /cvsroot/pyx/pyx/design/beziers.tex,v retrieving revision 1.4 retrieving revision 1.5 diff -C2 -d -r1.4 -r1.5 *** beziers.tex 1 Sep 2005 19:25:51 -0000 1.4 --- beziers.tex 1 Sep 2005 20:45:49 -0000 1.5 *************** *** 3,9 **** \newcommand{\sign}{\operatorname{sign}} \begin{document} ! \section{Bezier curves with prescribed tangent directions and curvatures at the endpoints} ! Parameterization of the Bezier curve, for $x(t)$ and $y(t)$ equivalently, % \begin{align} --- 3,9 ---- \newcommand{\sign}{\operatorname{sign}} \begin{document} ! \section{B\'ezier curves with prescribed tangent directions and curvatures at the endpoints} ! Parameterization of the B\'ezier curve, for $x(t)$ and $y(t)$ equivalently, % \begin{align} *************** *** 165,169 **** % ! \section{Bounding boxes for bezier curves} The bounding box is defined by the minimal and maximal values of a --- 165,169 ---- % ! \section{Bounding boxes for B\'ezier curves} The bounding box is defined by the minimal and maximal values of a *************** *** 198,202 **** % $$! q = -\frac{1}{2}\left[\,b+\mathrm{sgn}(b)\sqrt{b^2-4ac}\right]$$ % --- 198,202 ---- % $$! q = -\frac{1}{2}\left[\,b+\mathrm{sgn}(b)\sqrt{b^2-4ac}\right]\, .$$ % *************** *** 209,213 **** % ! Again, for numerical failures (divisions by zero) just need to skip the particular solution. The minima and maxima for $x(t)$ can now occure at $t=0$, $t=t_1$, $t=t_2$ and $t=1$. --- 209,213 ---- % ! Again, for numerical failures (divisions by zero), we just need to skip the particular solution. The minima and maxima for $x(t)$ can now occure at $t=0$, $t=t_1$, $t=t_2$ and $t=1$. 

 [PyX-checkins] pyx/design beziers.tex,1.4,1.5 From: Jörg Lehmann - 2005-09-01 20:45:57 Update of /cvsroot/pyx/pyx/design In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv17944 Modified Files: beziers.tex Log Message: some spelling fixes Index: beziers.tex =================================================================== RCS file: /cvsroot/pyx/pyx/design/beziers.tex,v retrieving revision 1.4 retrieving revision 1.5 diff -C2 -d -r1.4 -r1.5 *** beziers.tex 1 Sep 2005 19:25:51 -0000 1.4 --- beziers.tex 1 Sep 2005 20:45:49 -0000 1.5 *************** *** 3,9 **** \newcommand{\sign}{\operatorname{sign}} \begin{document} ! \section{Bezier curves with prescribed tangent directions and curvatures at the endpoints} ! Parameterization of the Bezier curve, for $x(t)$ and $y(t)$ equivalently, % \begin{align} --- 3,9 ---- \newcommand{\sign}{\operatorname{sign}} \begin{document} ! \section{B\'ezier curves with prescribed tangent directions and curvatures at the endpoints} ! Parameterization of the B\'ezier curve, for $x(t)$ and $y(t)$ equivalently, % \begin{align} *************** *** 165,169 **** % ! \section{Bounding boxes for bezier curves} The bounding box is defined by the minimal and maximal values of a --- 165,169 ---- % ! \section{Bounding boxes for B\'ezier curves} The bounding box is defined by the minimal and maximal values of a *************** *** 198,202 **** % $$! q = -\frac{1}{2}\left[\,b+\mathrm{sgn}(b)\sqrt{b^2-4ac}\right]$$ % --- 198,202 ---- % $$! q = -\frac{1}{2}\left[\,b+\mathrm{sgn}(b)\sqrt{b^2-4ac}\right]\, .$$ % *************** *** 209,213 **** % ! Again, for numerical failures (divisions by zero) just need to skip the particular solution. The minima and maxima for $x(t)$ can now occure at $t=0$, $t=t_1$, $t=t_2$ and $t=1$. --- 209,213 ---- % ! Again, for numerical failures (divisions by zero), we just need to skip the particular solution. The minima and maxima for $x(t)$ can now occure at $t=0$, $t=t_1$, $t=t_2$ and $t=1$.