Doplnena 2. geometricka prednaska.

[ads2.git] / 8-geom2 / 8-geom2.mp

diff --git a/8-geom2/8-geom2.mp b/8-geom2/8-geom2.mp
index 3720dc0de5044e772abfe96501fb51c690455474..5a443969000d0001a3e03b0a18e1ef72e54d0d12 100644 (file)
--- a/8-geom2/8-geom2.mp
+++ b/8-geom2/8-geom2.mp
@@ -27,18 +27,26 @@ beginfig(2);
        fill p--reverse(p shifted (A-0.8[A,B]))--cycle withcolor 0.8white;
        %fill p{dir (an+180)}..-0.35[A,B]..{dir an}cycle withcolor 0.8white;
        draw p withpen boldpen;
+
+       pair C; C := point(0.9) of p; 
+       drawarrow from(C,an+180,0.1cm)--from(C,an+180,1cm) withpen boldpen;
+       C := point(0.1) of p; 
+       drawarrow from(C,an+180,0.1cm)--from(C,an+180,1cm) withpen boldpen;
+       label.rt(btex $p$ etex, point(0.15) of p);
        
        draw A--B dashed evenly;
        drawemptyvertex(A); drawemptyvertex(B);
        label.llft(btex $a$ etex, A);
        label.urt(btex $b$ etex, B);
+       label(btex $B_a$ etex, A+2(-0.1cm,0.5cm));
+       label(btex $B_b$ etex, B+2(-0.1cm,0.5cm));
 endfig;
 
 figtag("voroneho_diagram");
 beginfig(3);
        u := 1.35cm;
        pair A[],B[];
-       A0 := origin; A1 := (-u,-u); A2 := (1.3u,-u); A3 := (1.5u,0.7u); A4 := (0.6u,0.8u); A5 := (0.2u,1.9u); A6 := (-1.3u,1u);
+       A0 := origin; A1 := (-u,-u); A2 := (1.3u,-u); A3 := (1.50821u,0.7u); A4 := (0.6u,0.8u); A5 := (0.2u,1.9u); A6 := (-1.3u,1u);
        def osa(expr a, b, an,l) = from(.5[a,b], angle(b-a)+an, l) enddef;
        vardef prusecik_os(expr p,q,r) =
                save b; pair b;
@@ -47,19 +55,83 @@ beginfig(3);
                b
        enddef;
        B[0] := prusecik_os(A0,A1,A2); B[1] := prusecik_os(A0,A1,A6); B[2] := prusecik_os(A0,A4,A6); B[3] := prusecik_os(A4,A5,A6);
-       B[4] := prusecik_os(A3,A4,A5); B[5] := prusecik_os(A0,A3,A4); B[6] := prusecik_os(A0,A2,A3);
+       B[4] := prusecik_os(A3,A4,A5); B[5] := prusecik_os(A0,A3,A4); B[6] := prusecik_os(A0,A2,A4);
        draw osa(A1,A2,-90,2cm)--B[0]--B[1]--osa(A1,A6,90,1.3cm) withpen boldpen;
        draw B[1]--B[2]--B[3]--osa(A6,A5,90,2cm) withpen boldpen;
        draw B[3]--B[4]--osa(A3,A5,-90,2.7cm) withpen boldpen;
        draw B[4]--B[5]--B[2] withpen boldpen;
        draw B[5]--B[6]--osa(A2,A3,-90,1.3cm) withpen boldpen;
        draw B[6]--B[0] withpen boldpen;
-
+       
        draw A0--A1--A2--A0--A6--A1 dashed evenly;
-       draw A6--A5--A4--A0--A3--A2 dashed evenly;
+       draw A6--A5--A4--A0 dashed evenly; draw A3--A2 dashed evenly;
        draw A3--A5 dashed evenly; draw A6--A4--A3 dashed evenly;
 
        for i:=0 upto 6: draw vertex(B[i]); endfor
        for i:=0 upto 6: drawemptyvertex(A[i]); endfor
 endfig;
+
+figtag("pasy_mnohouhelniku");
+beginfig(4);
+       u := 1.35cm;
+       pair A[],B[];
+       A0 := origin; A1 := (-u,-u); A2 := (1.3u,-u); A3 := (1.50821u,0.7u); A4 := (0.6u,0.8u); A5 := (0.2u,1.9u); A6 := (-1.3u,1u);
+       def osa(expr a, b, an,l) = from(.5[a,b], angle(b-a)+an, l) enddef;
+       vardef prusecik_os(expr p,q,r) =
+               save b; pair b;
+               b = whatever[osa(p,q, 90,1cm), osa(p,q,-90,1cm)];
+               b = whatever[osa(q,r, 90,1cm), osa(q,r,-90,1cm)];
+               b
+       enddef;
+       def drawline(expr p) = draw ((-2.3u,p)--(2.5u,p)) cutbefore (D0--D1) cutafter (D2--D3) enddef;
+       B[0] := prusecik_os(A0,A1,A2); B[1] := prusecik_os(A0,A1,A6); B[2] := prusecik_os(A0,A4,A6); B[3] := prusecik_os(A4,A5,A6);
+       B[4] := prusecik_os(A3,A4,A5); B[5] := prusecik_os(A0,A3,A4); B[6] := prusecik_os(A0,A2,A4);
+       
+       pair C; C := origin; for i:=0 upto 6: C := C + B[i]; endfor C := C/6;
+       pair D[];
+       D0 := C+(-2.25,2.25)*u; D1 := C+(-2.25,-2.25)*u; D2 := C+(2.25,-2.25)*u; D3 := C+(2.25,2.25)*u; 
+       
+       draw B[0]--B[1]--B[2]--B[3]--B[4]--B[5]--B[6]--B[0] withpen boldpen;
+       draw B[5]--B[2] withpen boldpen;
+       pair E; E := 0.6[B0,B4];
+       drawline(ypart(E));
+       drawline(ypart(E)) cutbefore (B2--B5) cutafter (B4--B5) dashed evenly withpen bolderpen;
+       drawemptyvertex(E);
+
+       for i:=0 upto 6: drawline(ypart(B[i])) dashed evenly; endfor
+       for i:=0 upto 6: draw vertex(B[i]); endfor
+endfig;
+
+figtag("upravy_stromu");
+beginfig(5);
+       u := 1cm;
+       draw (0,0.1u)--(2.05u,-2.05u)--(-2.05u,-2.05u)--cycle;
+       pair A[]; A0 := from(origin,-90,0.1u); A1 := from(A0, -70, 0.5u); A2 := from(A1, -110, 0.5u); A3 := from(A2, -80, 0.5u); A4 := from(A3, -120, 0.45u);
+       path p; p := createpath(A0--A1--A2--A3--A4);
+       path q; q := (p scaled 0.93 shifted (-0.15u,-0.15u))--(-1.85u,-1.95u)--cycle; fill q withcolor 0.8white; draw q;
+       q := (p scaled 0.93 shifted (0.15u,-0.15u))--(1.85u,-1.95u)--cycle; fill q withcolor 0.8white; draw q;
+       p := createpath(A0--from(A0,-110,0.1u)--A1--A2--A3--A4); draw p withpen boldpen;
+endfig;
+
+figtag("rychla_perzistence");
+beginfig(6);
+       u := 1cm;
+       def drawtable(expr p, lab, sa, sb) =
+               draw centersquare xscaled 2u yscaled (2u/3) shifted (p+(0,u/3));
+               draw centersquare xscaled 2u yscaled (2u/3) shifted (p-(0,u/3));
+               label(sa, p+(0,u/3));
+               label(sb, p-(0,u/3));
+               label.bot(lab, p-(0,2u/3));
+       enddef;
+
+       pair A[];
+       for i:=0 upto 2: A[i] := (0,2u) rotated 120i; endfor
+       drawtable(A1, btex $v$ etex, btex verze 2 etex, btex verze 1 etex);
+       drawtable(A2, btex $v'$ etex, btex verze 3 etex, "");
+       drawtable(A0, btex $u$ etex, btex verze 2 etex, btex verze 1 etex);
+
+       drawarrow from(A[2]+(0,u/3), 180, 7u/6)--from(A[1]+(0,u/3), 0, 7u/6);
+       drawarrow from(A[0]+(0,-u/3), 180, 7u/6)..{dir -90}from(A[1]+(-3u/4,2u/3), 90, u/6);
+       drawarrow from(A[0]+(0,u/3), 0, 7u/6)..{dir -90}from(A[2]+(3u/4,2u/3), 90, u/6);
+endfig;
 end