Aus Online Mathematik Brückenkurs 1

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<noinclude>Dies ist eine Figur die in [[Lösung 4.2:9]] verwendet wird, und in der Programmierungssprache [http://en.wikipedia.org/wiki/Metapost Metapost] geschrieben ist. Die Figur kann editiert werden indem man auf "Editieren" drückt. <center> </noinclude> <metapost> verbatimtex \documentclass[12pt]{report} etex verbatimtex \usepackage{amsmath} etex verbatimtex \usepackage{mathpazo} etex verbatimtex \begin{document} etex %%% MACROS scfc := 1.2/1.5; % Colors color lightblue, gridblue, shadedblue, lightred, backgroundblue, lightgrey, darkgrey, graphcolor, lightgraphcolor; lightblue := (0.2,0.6,1); gridblue := 0.5[lightblue,white]; shadedblue := 0.5[lightblue,white]; lightred := (1,0.6,0.6); backgroundblue := 0.7[lightblue,white]; lightgrey := 0.5*white; lightgrey := 0.9*white; darkgrey := 0.6*white; graphcolor := lightblue; lightgraphcolor := 0.7[lightblue, white]; % Pens pen gridpen, axispen, graphpen, dotpen, bigdotpen, barpen; gridpen := pencircle scaled 0.12pt; axispen := pencircle scaled 0.4pt; graphpen := pencircle scaled 0.6pt; dotpen := pencircle scaled 2.8pt; bigdotpen := pencircle scaled 5pt; barpen := pencircle scaled 1.5pt; % Draw dimensions dot_radius := 1.2*2.8pt; graph_linewidth := 0.6pt; gridlength := 3pt; % Draw commands vardef startenddashed expr p = save t; numeric t[]; t1 := arctime 5bp of p; t2 := arctime (arclength p -5bp) of p; draw subpath(t1,t2) of p withpen pencircle scaled 0.4pt; draw subpath(t1,0) of p dashed dashpattern(off 10/9 bp on 5/9 bp); draw subpath(t2,length p) of p dashed dashpattern(off 10/9 bp on 5/9 bp); enddef; vardef startenddashed expr p = save t; numeric t[]; t1 := arctime 7bp of p; t2 := arctime (arclength p -7bp) of p; draw subpath(t1,t2) of p; draw subpath(t1,0) of p dashed dashpattern(off 12/9 bp on 9/9 bp); draw subpath(t2,length p) of p dashed dashpattern(off 12/9 bp on 9/9 bp); enddef; vardef startshy expr p = save q, t; path q; numeric t[]; q := fullcircle scaled (1.2*2.0pt) shifted point 0 of p; t := xpart (p intersectiontimes q); subpath(t,infinity) of p enddef; vardef endshy expr p = save q, t; path q; numeric t[]; q := fullcircle scaled (1.2*2.0pt) shifted point infinity of p; t := xpart (reverse p intersectiontimes q); reverse subpath(t,infinity) of reverse p enddef; vardef startendshy expr p = startshy endshy p %save q,r,s,t; path q,r; numeric s[],t[]; %q := fullcircle scaled (1.2*2.0pt) shifted point 0 of p; %r := fullcircle scaled (1.2*2.0pt) shifted point infinity of p; %s := xpart (p intersectiontimes q); %t := xpart (p intersectiontimes r); %subpath(s,t) of p enddef; vardef wiggle expr p = save i, d, w, dw, len, n, d, angledir, p_wiggly; d := 10pt; w := 0.5pt; dw := 0.03pt; len := arclength p; n := round(len/d); d := len/n; for i=1 upto n: t[i] := arctime i*d of p; endfor; path p_wiggly; angledir := 1; p_wiggly := point 0 of p .. for i=1 upto n-1: hide(angledir := -angledir;) point t[i] of p + (w+(uniformdeviate dw))*dir ((angle (direction t[i] of p))+90*angledir) .. endfor point infinity of p; p_wiggly enddef; vardef coordinate_system(text _t) = %save xmin, xmin_excess, xmax, xmax_excess, dx, _dx, % ymin, ymin_excess, ymax, ymax_excess, dy, _dy, % grid_excess; dx := 1.2*8.30219pt; % horizontal distance between grid lines dy := dx; % vertical distance between grid lines _dx := dx; _dy := dy; xmin := -3; xmax := 3; xmin_excess := 1.2*2pt; xmax_excess := 1.2*2pt; ymin := -3; ymax := 3; ymin_excess := 1.2*4pt; ymax_excess := 1.2*4pt; grid_excess := 1.2*2pt; _t; Lxmin := xmin*dx - xmin_excess; Lxmax := xmax*dx + xmax_excess; Lymin := ymin*dy - ymin_excess; Lymax := ymax*dy + ymax_excess; def map(expr x,y) = (x*dx,y*dy) enddef; vardef unmap(expr x,y) = save xnew, ynew; if x<>0: xnew := x/dx; else: xnew := 0; fi if y<>0: ynew := y/dy; else: ynew := 0; fi (xnew,ynew) enddef; def dmap(expr x,y) = (x*dx,y*dy) enddef; vardef draw_coordinate_axes(text _tt) = save xlabel, ylabel; picture xlabel, ylabel; xlabel := nullpicture; ylabel := nullpicture; _tt; save ahangle, ahlength; ahangle := 30; % Angle of the arrow tip ahlength := 1.2*5bp; % Length of the arrow tip drawarrow (Lxmin,0)--(Lxmax,0) withpen axispen; drawarrow (0,Lymin)--(0,Lymax) withpen axispen; label.rt(xlabel,(Lxmax,0)); label.top(ylabel,(0,Lymax-1pt)); enddef; vardef draw_grid_lines = for x=_dx step _dx until infinity: exitif x>Lxmax-grid_excess; draw (x,Lymin)--(x,Lymax) withcolor gridblue withpen gridpen; endfor for x=-_dx step -_dx until -infinity: exitif x<Lxmin+grid_excess; draw (x,Lymin)--(x,Lymax) withcolor gridblue withpen gridpen; endfor for y=_dy step _dy until infinity: exitif y>Lymax-grid_excess; draw (Lxmin,y)--(Lxmax,y) withcolor gridblue withpen gridpen; endfor for y=-_dy step -_dy until -infinity: exitif y<Lymin+grid_excess; draw (Lxmin,y)--(Lxmax,y) withcolor gridblue withpen gridpen; endfor enddef; vardef draw_gridmarks(text _tt) = save xmin, xmax, ymin, ymax; _tt; for x=1 upto infinity: exitif x>xmax; draw (x*dx,-gridlength/2)--(x*dx,gridlength/2) withpen axispen; endfor for x=-1 downto -infinity: exitif x<xmin; draw (x*dx,-gridlength/2)--(x*dx,gridlength/2) withpen axispen; endfor for y=1 upto infinity: exitif y>ymax; draw (-gridlength/2,y*dy)--(gridlength/2,y*dy) withpen axispen; endfor for y=-1 downto -infinity: exitif y<ymin; draw (-gridlength/2,y*dy)--(gridlength/2,y*dy) withpen axispen; endfor enddef; vardef drawangleline(expr alpha) = interim linecap := butt; draw map(0.03*cosd(alpha),0.03*sind(alpha))--map(cosd(alpha),sind(alpha)) withcolor background withpen barpen; draw startshy endshy startshy endshy reverse map(0,0)--map(cosd(alpha),sind(alpha)) withcolor black dashed evenly scaled 0.7 withpen barpen; linecap := rounded; drawdot map(cosd(alpha),sind(alpha)) withcolor background withpen bigdotpen; drawdot map(cosd(alpha),sind(alpha)) withcolor red withpen dotpen; enddef; vardef drawunitcircle = save theta; path p_circle; p_circle := map(1,0){dmap(0,1)} for theta = 5 step 5 until 355: ..map(cosd(theta),sind(theta)){dmap(cosd(theta+90),sind(theta+90))} endfor ..cycle; draw p_circle withcolor graphcolor withpen graphpen; enddef; vardef drawangle(expr r, alpha, beta) = save ahangle, ahlength, p_angle, theta; ahangle := 20; % Angle of the arrow tip ahlength := 4bp; % Length of the arrow tip path p_angle; if alpha<beta: p_angle := map(r*cosd(alpha),r*sind(alpha)) {dmap(cosd(alpha+90),sind(alpha+90))} for theta= alpha+5 step 5 until beta-5: ..map(r*cosd(theta),r*sind(theta)){dmap(cosd(theta+90),sind(theta+90))} endfor ..map(r*cosd(beta),r*sind(beta)){dmap(cosd(beta+90),sind(beta+90))}; draw startshy endshy startshy p_angle withcolor background withpen pencircle scaled 3pt; drawarrow endshy endshy p_angle withpen pencircle scaled 0.1pt; elseif alpha>beta: p_angle := map(r*cosd(alpha),r*sind(alpha)) {dmap(cosd(alpha-90),sind(alpha-90))} for theta= alpha-5 step -5 until beta+5: ..map(r*cosd(theta),r*sind(theta)){dmap(cosd(theta-90),sind(theta-90))} endfor ..map(r*cosd(beta),r*sind(beta)){dmap(cosd(beta-90),sind(beta-90))}; draw startshy endshy startshy p_angle withcolor background withpen pencircle scaled 3pt; drawarrow endshy endshy p_angle withpen pencircle scaled 0.1pt; fi enddef; vardef drawshortangle(expr r, alpha, beta) = save ahangle, ahlength, p_angle, theta; ahangle := 20; % Angle of the arrow tip ahlength := 4bp; % Length of the arrow tip path p_angle; if alpha<beta: p_angle := map(r*cosd(alpha),r*sind(alpha)) {dmap(cosd(alpha+90),sind(alpha+90))} for theta= alpha+5 step 5 until beta-5: ..map(r*cosd(theta),r*sind(theta)){dmap(cosd(theta+90),sind(theta+90))} endfor ..map(r*cosd(beta),r*sind(beta)){dmap(cosd(beta+90),sind(beta+90))}; draw startshy endshy startshy p_angle withcolor background withpen pencircle scaled 3pt; drawarrow endshy p_angle withpen pencircle scaled 0.1pt; elseif alpha>beta: p_angle := map(r*cosd(alpha),r*sind(alpha)) {dmap(cosd(alpha-90),sind(alpha-90))} for theta= alpha-5 step -5 until beta+5: ..map(r*cosd(theta),r*sind(theta)){dmap(cosd(theta-90),sind(theta-90))} endfor ..map(r*cosd(beta),r*sind(beta)){dmap(cosd(beta-90),sind(beta-90))}; draw startshy endshy startshy p_angle withcolor background withpen pencircle scaled 3pt; drawarrow endshy p_angle withpen pencircle scaled 0.1pt; fi enddef; enddef; randomseed := 0.687346; %%% END MACROS beginfig(1); numeric L, ap, qb, pq; L := 1.5*50pt; % Total horizontal length % Relations ap*sind(30)+qb = L; ap/4 = pq/12 = qb/5; % Define points A, B, P and Q pair A, B, P, Q; A := origin; P := ap*(dir (-90+30)); Q := P+pq*(dir 90); B := Q+qb*(dir 0); % Draw the path A--P--Q--B pickup pencircle scaled 0.4pt; draw A--P--Q--B withcolor darkgrey; pickup dotpen; drawdot A withcolor darkgrey; drawdot B withcolor darkgrey; % Draw the dashed triangle pair C; C = (xpart B, ypart A); path p_triangle; p_triangle := A--B--C--cycle; pickup pencircle scaled 0.4pt; draw p_triangle dashed evenly scaled 0.5 withcolor darkgrey; % Save the triangle picture p_left, p_right; p_left := currentpicture; p_right := currentpicture; % Draw horizontal distances pickup pencircle scaled 0.4pt; linecap := butt; ahangle := 20; ahlength := 3bp; numeric d[]; d1 := 8pt; d2 := 18pt; pair E,F,G; E = (xpart A, ypart B); F = (xpart P, ypart B); G = (xpart B, ypart B); draw E+(0,d1-1.5pt) -- E+(0,d1+1.5pt); draw F+(0,d1-1.5pt) -- F+(0,d1+1.5pt); draw G+(0,d1-1.5pt) -- G+(0,d1+1.5pt); drawdblarrow startshy endshy E+(0,d1)--F+(0,d1); drawdblarrow startshy endshy F+(0,d1)--G+(0,d1); label.top(btex \strut $x$ etex, 0.5[E,F]+(0,d1-4pt)); label.top(btex \strut $5$ etex, 0.5[F,G]+(0,d1-4pt)); draw E+(0,d1+d2-1.5pt) -- E+(0,d1+d2+1.5pt); draw G+(0,d1+d2-1.5pt) -- G+(0,d1+d2+1.5pt); drawdblarrow startshy endshy E+(0,d1+d2)--G+(0,d1+d2); label.top(btex \strut $a$ etex, 0.5[E,G]+(0,d1+d2-4pt)); % Draw the vertical distances pair E, F, G; E = (xpart B, ypart P); F = (xpart B, ypart A); G = (xpart B, ypart B); draw E+(d1-1.5pt,0) -- E+(d1+1.5pt,0); draw F+(d1-1.5pt,0) -- F+(d1+1.5pt,0); draw G+(d1-1.5pt,0) -- G+(d1+1.5pt,0); drawdblarrow startshy endshy E+(d1,0)--F+(d1,0); drawdblarrow startshy endshy F+(d1,0)--G+(d1,0); label.rt(btex \strut $y$ etex, 0.5[E,F]+(d1+2pt,0)); label.rt(btex \strut $b$ etex, 0.5[F,G]+(d1+2pt,0)); draw E+(d1+d2-1.5pt,0) -- E+(d1+d2+1.5pt,0); draw G+(d1+d2-1.5pt,0) -- G+(d1+d2+1.5pt,0); drawdblarrow startshy endshy E+(d1+d2,0)--G+(d1+d2,0); label.rt(btex \strut $12$ etex, 0.5[E,G]+(d1+d2+2pt,0)); endfig; end. </metapost> <noinclude></center></noinclude>

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