## pyx-checkins

 [PyX-checkins] SF.net SVN: pyx: [2621] trunk/pyx/design From: - 2006-04-27 11:39:36 Revision: 2621 Author: m-schindler Date: 2006-04-27 04:39:24 -0700 (Thu, 27 Apr 2006) ViewCVS: http://svn.sourceforge.net/pyx/?rev=2621&view=rev Log Message: ----------- cosmetics Modified Paths: -------------- trunk/pyx/design/beziers.tex Property Changed: ---------------- trunk/pyx/design/ trunk/pyx/pyx/font/ trunk/pyx/pyx/pykpathsea/ Property changes on: trunk/pyx/design ___________________________________________________________________ Name: svn:ignore - *.aux *.log *.dvi *.size + *.aux *.log *.dvi *.size *.eps Modified: trunk/pyx/design/beziers.tex =================================================================== --- trunk/pyx/design/beziers.tex 2006-04-27 07:59:47 UTC (rev 2620) +++ trunk/pyx/design/beziers.tex 2006-04-27 11:39:24 UTC (rev 2621) @@ -320,6 +320,252 @@ not be valid at all. % >>> +\section{Points with extremal curvature in B\'ezier curves} + +% <<< +Extremal curvatures are found at parameter values~$t$ that are determined by +% +\begin{gather} + 0 = \dot\kappa(t) = [\dot x^2(t) + \dot y^2(t)]^{-\frac{5}{2}}\: p(t) \quad\text{with}\\ + p(t) := (\dot x\dddot y - \dddot x\dot y)(\dot x^2 + \dot y^2) + - 3(\dot x\ddot y - \ddot x\dot y)(\dot x\ddot x + \ddot y\dot y) +\end{gather} +% +which is equivalent to setting the polynom $p(t)$ to zero. +It is more convenient to write this equation as a polynom of $t$ and $(1{-}t)$, +where the corresponding powers always add up to 6, +% ++ \begin{aligned} + 0 = p(t) = {} + &A_0 t^0 (1{-}t)^6 + + A_1 t^1 (1{-}t)^5 + + A_2 t^2 (1{-}t)^4 + + A_3 t^3 (1{-}t)^3 \\ + {}+{}&A_4 t^4 (1{-}t)^2 + + A_5 t^5 (1{-}t)^1 + + A_6 t^6 (1{-}t)^0. + \end{aligned} + +% +Using Pascal's triangle we can convert this into an ordinary polynom, +% +$$+ \setlength\arraycolsep{2pt} + \begin{array}{rrrrrrrrrrrrrrr} + 0 = p(t) = [& A_0 & & & & & & & & & & & & ] & t^0 \\ + {} + [& 6 A_0 &+& A_1 & & & & & & & & & & ] & t^1 \\ + {} + [& 15 A_0 &+& 5 A_1 &+& A_2 & & & & & & & & ] & t^2 \\ + {} + [& 20 A_0 &+& 10 A_1 &+& 4 A_2 &+& A_3 & & & & & & ] & t^3 \\ + {} + [& 15 A_0 &+& 10 A_1 &+& 6 A_2 &+& 3 A_3 &+& A_4 & & & & ] & t^4 \\ + {} + [& 6 A_0 &+& 5 A_1 &+& 4 A_2 &+& 3 A_3 &+& 2 A_4 &+& A_5 & & ] & t^5 \\ + {} + [& A_0 &+& A_1 &+& A_2 &+& A_3 &+& A_4 &+& A_5 &+& A_6] & t^6 + \end{array} +$$ +% +% Pascal's triangle: <<< +% ^0 ^1 ^2 ^3 ^4 ^5 ^6 +% | 1| 6|15|20|15| 6| 1| = (1-t)^6 +% | 1| 5|10|10| 5| 1| | = (1-t)^5 +% | 1| 4| 6| 4| 1| | | = (1-t)^4 +% | 1| 3| 3| 1| | | | = (1-t)^3 +% | 1| 2| 1| | | | | = (1-t)^2 +% | 1| 1| | | | | | = (1-t)^1 +% | 1| | | | | | | = (1-t)^0 +% +% | 1| 6|15|20|15| 6| 1| = t^0 (1-t)^6 +% | | 1| 5|10|10| 5| 1| = t^1 (1-t)^5 +% | | | 1| 4| 6| 4| 1| = t^2 (1-t)^4 +% | | | | 1| 3| 3| 1| = t^3 (1-t)^3 +% | | | | | 1| 2| 1| = t^4 (1-t)^2 +% | | | | | | 1| 1| = t^5 (1-t)^1 +% | | | | | | | 1| = t^6 (1-t)^0 +% +% ein Polynom, das so geschrieben werden kann, +% p = A0 * t^0 (1-t)^6 +% + A1 * t^1 (1-t)^5 +% + A2 * t^2 (1-t)^4 +% + A3 * t^3 (1-t)^3 +% + A4 * t^4 (1-t)^2 +% + A5 * t^5 (1-t)^1 +% + A6 * t^6 (1-t)^0 +% +% ist als reines Polynom in t +% p = [ 1*A0 ] * t^0 +% [ 6*A0 + 1*A1 ] * t^1 +% [15*A0 + 5*A1 + 1*A2 ] * t^2 +% [20*A0 + 10*A1 + 4*A2 + 1*A3 ] * t^3 +% [15*A0 + 10*A1 + 6*A2 + 3*A3 + 1*A4 ] * t^4 +% [ 6*A0 + 5*A1 + 4*A2 + 3*A3 + 2*A4 + 1*A5 ] * t^5 +% [ 1*A0 + 1*A1 + 1*A2 + 1*A3 + 1*A4 + 1*A5 + 1*A6] * t^6 +% +% >>> + +%% Rechnung fuer die Polynom-Koeffizienten <<< +% +% dx = 3(x1-x0)(1-t)^2 + 3(x3-x2)t^2 + 6 (x2-x1)t(1-t) +% dy = 3(y1-y0)(1-t)^2 + 3(y3-y2)t^2 + 6 (y2-y1)t(1-t) +% +% ddx = 6(x0-2*x1+x2)(1-t) + 6(x1-2*x2+x3)t +% ddy = 6(y0-2*y1+y2)(1-t) + 6(y1-2*y2+y3)t +% +% ----------------------------- +% jetzt multipliziere die einzelnen Terme: +% +% dddy*dx = dddy * ( 3 (x1-x0)(1-t)^2 + 3 (x3-x2)t^2 + 6 (x2-x1)t(1-t) ) +% dddx*dy = dddx * ( 3 (y1-y0)(1-t)^2 + 3 (y3-y2)t^2 + 6 (y2-y1)t(1-t) ) +% +% (dx)^2 = 9 (x1-x0)^2 (1-t)^4 +% + 9 (x3-x2)^2 t^4 +% + 36 (x2-x1)^2 t^2(1-t)^2 +% + 18 (x1-x0)(x3-x2) t^2(1-t)^2 +% + 36 (x1-x0)(x2-x1) t (1-t)^3 +% + 36 (x3-x2)(x2-x1) t^3(1-t) +% +% (dy)^2 = 9 (y1-y0)^2 (1-t)^4 +% + 9 (y3-y2)^2 t^4 +% + 36 (y2-y1)^2 t^2(1-t)^2 +% + 18 (y1-y0)(y3-y2) t^2(1-t)^2 +% + 36 (y1-y0)(y2-y1) t (1-t)^3 +% + 36 (y3-y2)(y2-y1) t^3(1-t) +% +% dx*ddx = 18 (x1-x0)(x0-2*x1+x2) (1-t)^3 +% + 18 (x3-x2)(x1-2*x2+x3) t^3 +% + 18 (x1-x0)(x1-2*x2+x3) t(1-t)^2 +% + 36 (x2-x1)(x0-2*x1+x2) t(1-t)^2 +% + 18 (x3-x2)(x0-2*x1+x2) t^2(1-t) +% + 36 (x2-x1)(x1-2*x2+x3) t^2(1-t) +% +% dy*ddy = 18 (y1-y0)(y0-2*y1+y2) (1-t)^3 +% + 18 (y3-y2)(y1-2*y2+y3) t^3 +% + 18 (y1-y0)(y1-2*y2+y3) t(1-t)^2 +% + 36 (y2-y1)(y0-2*y1+y2) t(1-t)^2 +% + 18 (y3-y2)(y0-2*y1+y2) t^2(1-t) +% + 36 (y2-y1)(y1-2*y2+y3) t^2(1-t) +% +% dx*ddy = 18 (x1-x0)(y0-2*y1+y2) (1-t)^3 +% + 18 (x3-x2)(y1-2*y2+y3) t^3 +% + 18 (x1-x0)(y1-2*y2+y3) t(1-t)^2 +% + 36 (x2-x1)(y0-2*y1+y2) t(1-t)^2 +% + 18 (x3-x2)(y0-2*y1+y2) t^2(1-t) +% + 36 (x2-x1)(y1-2*y2+y3) t^2(1-t) +% +% dy*ddx = 18 (y1-y0)(x0-2*x1+x2) (1-t)^3 +% + 18 (y3-y2)(x1-2*x2+x3) t^3 +% + 18 (y1-y0)(x1-2*x2+x3) t(1-t)^2 +% + 36 (y2-y1)(x0-2*x1+x2) t(1-t)^2 +% + 18 (y3-y2)(x0-2*x1+x2) t^2(1-t) +% + 36 (y2-y1)(x1-2*x2+x3) t^2(1-t) +% +% ----------------------------- +% subtrahiere/addiere: +% +% dddy*dx - dddx*dy = +% + 3 [dddy*(x1-x0) - dddx*(y1-y0)] (1-t)^2 +% + 3 [dddy*(x3-x2) - dddx*(y3-y2)] t^2 +% + 6 [dddy*(x2-x1) - dddx*(y2-y1)] t(1-t) +% +% (dx)^2 + (dy)^2 = +% + 9 [(x1-x0)^2 + (y1-y0)^2 ] (1-t)^4 +% + 9 [(x3-x2)^2 + (y3-y2)^2 ] t^4 +% + 36 [(x2-x1)^2 + (y2-y1)^2 ] t^2(1-t)^2 +% + 18 [(x1-x0)(x3-x2) + (y1-y0)(y3-y2)] t^2(1-t)^2 +% + 36 [(x1-x0)(x2-x1) + (y1-y0)(y2-y1)] t (1-t)^3 +% + 36 [(x3-x2)(x2-x1) + (y3-y2)(y2-y1)] t^3(1-t) +% +% +% dx*ddy - dy*ddx = +% + 18 [(x1-x0)(y0-2*y1+y2) - (y1-y0)(x0-2*x1+x2)] (1-t)^3 +% + 18 [(x3-x2)(y1-2*y2+y3) - (y3-y2)(x1-2*x2+x3)] t^3 +% + 18 [(x1-x0)(y1-2*y2+y3) - (y1-y0)(x1-2*x2+x3)] t (1-t)^2 +% + 36 [(x2-x1)(y0-2*y1+y2) - (y2-y1)(x0-2*x1+x2)] t (1-t)^2 +% + 18 [(x3-x2)(y0-2*y1+y2) - (y3-y2)(x0-2*x1+x2)] t^2(1-t) +% + 36 [(x2-x1)(y1-2*y2+y3) - (y2-y1)(x1-2*x2+x3)] t^2(1-t) +% +% dx*ddx + dy*ddy = +% + 18 [(x1-x0)(x0-2*x1+x2) + (y1-y0)(y0-2*y1+y2)] (1-t)^3 +% + 18 [(x3-x2)(x1-2*x2+x3) + (y3-y2)(y1-2*y2+y3)] t^3 +% + 18 [(x1-x0)(x1-2*x2+x3) + (y1-y0)(y1-2*y2+y3)] t (1-t)^2 +% + 36 [(x2-x1)(x0-2*x1+x2) + (y2-y1)(y0-2*y1+y2)] t (1-t)^2 +% + 18 [(x3-x2)(x0-2*x1+x2) + (y3-y2)(y0-2*y1+y2)] t^2(1-t) +% + 36 [(x2-x1)(x1-2*x2+x3) + (y2-y1)(y1-2*y2+y3)] t^2(1-t) +% +% ----------------------------- +% und multipliziere die grossen Terme miteinander +% +% [dddy*dx - dddx*dy] * [(dx)^2 + (dy)^2] = +% + 27 [dddy*(x1-x0) - dddx*(y1-y0)] [(x1-x0)^2 + (y1-y0)^2 ] t^0(1-t)^6 +% + 108 [dddy*(x1-x0) - dddx*(y1-y0)] [(x1-x0)(x2-x1) + (y1-y0)(y2-y1)] t^1(1-t)^5 +% + 54 [dddy*(x2-x1) - dddx*(y2-y1)] [(x1-x0)^2 + (y1-y0)^2 ] t^1(1-t)^5 +% + 108 [dddy*(x1-x0) - dddx*(y1-y0)] [(x2-x1)^2 + (y2-y1)^2 ] t^2(1-t)^4 +% + 54 [dddy*(x1-x0) - dddx*(y1-y0)] [(x1-x0)(x3-x2) + (y1-y0)(y3-y2)] t^2(1-t)^4 +% + 27 [dddy*(x3-x2) - dddx*(y3-y2)] [(x1-x0)^2 + (y1-y0)^2 ] t^2(1-t)^4 +% + 216 [dddy*(x2-x1) - dddx*(y2-y1)] [(x1-x0)(x2-x1) + (y1-y0)(y2-y1)] t^2(1-t)^4 +% + 108 [dddy*(x1-x0) - dddx*(y1-y0)] [(x3-x2)(x2-x1) + (y3-y2)(y2-y1)] t^3(1-t)^3 +% + 108 [dddy*(x3-x2) - dddx*(y3-y2)] [(x1-x0)(x2-x1) + (y1-y0)(y2-y1)] t^3(1-t)^3 +% + 108 [dddy*(x2-x1) - dddx*(y2-y1)] [(x1-x0)(x3-x2) + (y1-y0)(y3-y2)] t^3(1-t)^3 +% + 216 [dddy*(x2-x1) - dddx*(y2-y1)] [(x2-x1)^2 + (y2-y1)^2 ] t^3(1-t)^3 +% + 27 [dddy*(x1-x0) - dddx*(y1-y0)] [(x3-x2)^2 + (y3-y2)^2 ] t^4(1-t)^2 +% + 108 [dddy*(x3-x2) - dddx*(y3-y2)] [(x2-x1)^2 + (y2-y1)^2 ] t^4(1-t)^2 +% + 216 [dddy*(x2-x1) - dddx*(y2-y1)] [(x3-x2)(x2-x1) + (y3-y2)(y2-y1)] t^4(1-t)^2 +% + 54 [dddy*(x3-x2) - dddx*(y3-y2)] [(x1-x0)(x3-x2) + (y1-y0)(y3-y2)] t^4(1-t)^2 +% + 108 [dddy*(x3-x2) - dddx*(y3-y2)] [(x3-x2)(x2-x1) + (y3-y2)(y2-y1)] t^5(1-t)^1 +% + 54 [dddy*(x2-x1) - dddx*(y2-y1)] [(x3-x2)^2 + (y3-y2)^2 ] t^5(1-t)^1 +% + 27 [dddy*(x3-x2) - dddx*(y3-y2)] [(x3-x2)^2 + (y3-y2)^2 ] t^6(1-t)^0 +% +% [dx*ddy - dy*ddx] * [dx*ddx + dy*ddy] = +% + 18 18 [(x1-x0)(y0-2*y1+y2) - (y1-y0)(x0-2*x1+x2)] [(x1-x0)(x0-2*x1+x2) + (y1-y0)(y0-2*y1+y2)] t^0(1-t)^6 +% + 18 18 [(x1-x0)(y0-2*y1+y2) - (y1-y0)(x0-2*x1+x2)] [(x1-x0)(x1-2*x2+x3) + (y1-y0)(y1-2*y2+y3)] t^1(1-t)^5 +% + 18 36 [(x1-x0)(y0-2*y1+y2) - (y1-y0)(x0-2*x1+x2)] [(x2-x1)(x0-2*x1+x2) + (y2-y1)(y0-2*y1+y2)] t^1(1-t)^5 +% + 18 18 [(x1-x0)(y1-2*y2+y3) - (y1-y0)(x1-2*x2+x3)] [(x1-x0)(x0-2*x1+x2) + (y1-y0)(y0-2*y1+y2)] t^1(1-t)^5 +% + 36 18 [(x2-x1)(y0-2*y1+y2) - (y2-y1)(x0-2*x1+x2)] [(x1-x0)(x0-2*x1+x2) + (y1-y0)(y0-2*y1+y2)] t^1(1-t)^5 +% + 18 18 [(x1-x0)(y1-2*y2+y3) - (y1-y0)(x1-2*x2+x3)] [(x1-x0)(x1-2*x2+x3) + (y1-y0)(y1-2*y2+y3)] t^2(1-t)^4 +% + 18 36 [(x1-x0)(y1-2*y2+y3) - (y1-y0)(x1-2*x2+x3)] [(x2-x1)(x0-2*x1+x2) + (y2-y1)(y0-2*y1+y2)] t^2(1-t)^4 +% + 36 18 [(x2-x1)(y0-2*y1+y2) - (y2-y1)(x0-2*x1+x2)] [(x1-x0)(x1-2*x2+x3) + (y1-y0)(y1-2*y2+y3)] t^2(1-t)^4 +% + 36 36 [(x2-x1)(y0-2*y1+y2) - (y2-y1)(x0-2*x1+x2)] [(x2-x1)(x0-2*x1+x2) + (y2-y1)(y0-2*y1+y2)] t^2(1-t)^4 +% + 18 18 [(x1-x0)(y0-2*y1+y2) - (y1-y0)(x0-2*x1+x2)] [(x3-x2)(x0-2*x1+x2) + (y3-y2)(y0-2*y1+y2)] t^2(1-t)^4 +% + 18 36 [(x1-x0)(y0-2*y1+y2) - (y1-y0)(x0-2*x1+x2)] [(x2-x1)(x1-2*x2+x3) + (y2-y1)(y1-2*y2+y3)] t^2(1-t)^4 +% + 18 18 [(x3-x2)(y0-2*y1+y2) - (y3-y2)(x0-2*x1+x2)] [(x1-x0)(x0-2*x1+x2) + (y1-y0)(y0-2*y1+y2)] t^2(1-t)^4 +% + 36 18 [(x2-x1)(y1-2*y2+y3) - (y2-y1)(x1-2*x2+x3)] [(x1-x0)(x0-2*x1+x2) + (y1-y0)(y0-2*y1+y2)] t^2(1-t)^4 +% + 36 18 [(x2-x1)(y0-2*y1+y2) - (y2-y1)(x0-2*x1+x2)] [(x3-x2)(x0-2*x1+x2) + (y3-y2)(y0-2*y1+y2)] t^3(1-t)^3 +% + 36 36 [(x2-x1)(y0-2*y1+y2) - (y2-y1)(x0-2*x1+x2)] [(x2-x1)(x1-2*x2+x3) + (y2-y1)(y1-2*y2+y3)] t^3(1-t)^3 +% + 18 18 [(x3-x2)(y0-2*y1+y2) - (y3-y2)(x0-2*x1+x2)] [(x1-x0)(x1-2*x2+x3) + (y1-y0)(y1-2*y2+y3)] t^3(1-t)^3 +% + 18 36 [(x3-x2)(y0-2*y1+y2) - (y3-y2)(x0-2*x1+x2)] [(x2-x1)(x0-2*x1+x2) + (y2-y1)(y0-2*y1+y2)] t^3(1-t)^3 +% + 36 18 [(x2-x1)(y1-2*y2+y3) - (y2-y1)(x1-2*x2+x3)] [(x1-x0)(x1-2*x2+x3) + (y1-y0)(y1-2*y2+y3)] t^3(1-t)^3 +% + 36 36 [(x2-x1)(y1-2*y2+y3) - (y2-y1)(x1-2*x2+x3)] [(x2-x1)(x0-2*x1+x2) + (y2-y1)(y0-2*y1+y2)] t^3(1-t)^3 +% + 18 18 [(x1-x0)(y1-2*y2+y3) - (y1-y0)(x1-2*x2+x3)] [(x3-x2)(x0-2*x1+x2) + (y3-y2)(y0-2*y1+y2)] t^3(1-t)^3 +% + 18 36 [(x1-x0)(y1-2*y2+y3) - (y1-y0)(x1-2*x2+x3)] [(x2-x1)(x1-2*x2+x3) + (y2-y1)(y1-2*y2+y3)] t^3(1-t)^3 +% + 18 18 [(x1-x0)(y0-2*y1+y2) - (y1-y0)(x0-2*x1+x2)] [(x3-x2)(x1-2*x2+x3) + (y3-y2)(y1-2*y2+y3)] t^3(1-t)^3 +% + 18 18 [(x3-x2)(y1-2*y2+y3) - (y3-y2)(x1-2*x2+x3)] [(x1-x0)(x0-2*x1+x2) + (y1-y0)(y0-2*y1+y2)] t^3(1-t)^3 +% + 18 18 [(x3-x2)(y1-2*y2+y3) - (y3-y2)(x1-2*x2+x3)] [(x1-x0)(x1-2*x2+x3) + (y1-y0)(y1-2*y2+y3)] t^4(1-t)^2 +% + 18 36 [(x3-x2)(y1-2*y2+y3) - (y3-y2)(x1-2*x2+x3)] [(x2-x1)(x0-2*x1+x2) + (y2-y1)(y0-2*y1+y2)] t^4(1-t)^2 +% + 36 18 [(x2-x1)(y1-2*y2+y3) - (y2-y1)(x1-2*x2+x3)] [(x3-x2)(x0-2*x1+x2) + (y3-y2)(y0-2*y1+y2)] t^4(1-t)^2 +% + 18 18 [(x3-x2)(y0-2*y1+y2) - (y3-y2)(x0-2*x1+x2)] [(x3-x2)(x0-2*x1+x2) + (y3-y2)(y0-2*y1+y2)] t^4(1-t)^2 +% + 36 18 [(x2-x1)(y0-2*y1+y2) - (y2-y1)(x0-2*x1+x2)] [(x3-x2)(x1-2*x2+x3) + (y3-y2)(y1-2*y2+y3)] t^4(1-t)^2 +% + 18 36 [(x3-x2)(y0-2*y1+y2) - (y3-y2)(x0-2*x1+x2)] [(x2-x1)(x1-2*x2+x3) + (y2-y1)(y1-2*y2+y3)] t^4(1-t)^2 +% + 18 18 [(x1-x0)(y1-2*y2+y3) - (y1-y0)(x1-2*x2+x3)] [(x3-x2)(x1-2*x2+x3) + (y3-y2)(y1-2*y2+y3)] t^4(1-t)^2 +% + 36 36 [(x2-x1)(y1-2*y2+y3) - (y2-y1)(x1-2*x2+x3)] [(x2-x1)(x1-2*x2+x3) + (y2-y1)(y1-2*y2+y3)] t^4(1-t)^2 +% + 36 18 [(x2-x1)(y1-2*y2+y3) - (y2-y1)(x1-2*x2+x3)] [(x3-x2)(x1-2*x2+x3) + (y3-y2)(y1-2*y2+y3)] t^5(1-t)^1 +% + 18 18 [(x3-x2)(y1-2*y2+y3) - (y3-y2)(x1-2*x2+x3)] [(x3-x2)(x0-2*x1+x2) + (y3-y2)(y0-2*y1+y2)] t^5(1-t)^1 +% + 18 36 [(x3-x2)(y1-2*y2+y3) - (y3-y2)(x1-2*x2+x3)] [(x2-x1)(x1-2*x2+x3) + (y2-y1)(y1-2*y2+y3)] t^5(1-t)^1 +% + 18 18 [(x3-x2)(y0-2*y1+y2) - (y3-y2)(x0-2*x1+x2)] [(x3-x2)(x1-2*x2+x3) + (y3-y2)(y1-2*y2+y3)] t^5(1-t)^1 +% + 18 18 [(x3-x2)(y1-2*y2+y3) - (y3-y2)(x1-2*x2+x3)] [(x3-x2)(x1-2*x2+x3) + (y3-y2)(y1-2*y2+y3)] t^6(1-t)^0 +% +% Koeffizienten: 27 ist GGT +% 27 = 3^3 = 27 * 1 +% 54 = 3^3 * 2 = 27 * 2 +% 108 = 3^3 * 2^2 = 27 * 4 +% 216 = 3^3 * 2^3 = 27 * 8 +% +% 3*18*18 = 3^5 * 2^2 = 27 * 36 +% 3*36*18 = 3^5 * 2^3 = 27 * 72 +% 3*36*36 = 3^5 * 2^4 = 27 * 144 +% + +%% >>> + +% >>> + \end{document} % vim:foldmethod=marker:foldmarker=<<<,>>> Property changes on: trunk/pyx/pyx/font ___________________________________________________________________ Name: svn:ignore - *.pyc + *.pyc *.so Property changes on: trunk/pyx/pyx/pykpathsea ___________________________________________________________________ Name: svn:ignore - *.pyc + *.pyc *.so This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site. 
 [PyX-checkins] SF.net SVN: pyx: [2709] trunk/pyx/design From: - 2006-05-18 09:01:25 Revision: 2709 Author: m-schindler Date: 2006-05-18 02:01:18 -0700 (Thu, 18 May 2006) ViewCVS: http://svn.sourceforge.net/pyx/?rev=2709&view=rev Log Message: ----------- cosmetics Modified Paths: -------------- trunk/pyx/examples/drawing2/smoothed.py Property Changed: ---------------- trunk/pyx/design/ Property changes on: trunk/pyx/design ___________________________________________________________________ Name: svn:ignore - *.aux *.log *.dvi *.size *.eps + *.aux *.log *.toc *.dvi *.size *.eps *.pdf Modified: trunk/pyx/examples/drawing2/smoothed.py =================================================================== --- trunk/pyx/examples/drawing2/smoothed.py 2006-05-18 08:58:31 UTC (rev 2708) +++ trunk/pyx/examples/drawing2/smoothed.py 2006-05-18 09:01:18 UTC (rev 2709) @@ -4,7 +4,7 @@ p = path.line(0, 0, 2, 2) p.append(path.curveto(2, 0, 3, 0, 4, 0)) c.stroke(p) -c.stroke(p, [deformer.smoothed(0.5), color.rgb.blue]) -c.stroke(p, [deformer.smoothed(1.0), color.rgb.red]) +c.stroke(p, [deformer.smoothed(1.0), color.rgb.blue]) +c.stroke(p, [deformer.smoothed(2.0), color.rgb.red]) c.writeEPSfile("smoothed") c.writePDFfile("smoothed") This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.