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draukdrauk
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Committing all of the public metapost files for the dg book.
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‎3d1.mp

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% tex/conc/mp/3d1.mp 2005-3-10 Alan Kennington.
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% $Id: tex/conc/mp/3d1.mp 8017ff16b3 2008-06-01 17:11:26Z Alan U. Kennington $
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% 3d graphic: x,y,z demo.
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input 3dmax.mp
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%%%%%%%%%%%%%%%%%%%%%%%%%
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% figure 1 %
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%%%%%%%%%%%%%%%%%%%%%%%%%
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beginfig(1);
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numeric A[][]; % The current 4x3 transformation matrix.
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numeric p[][], q[][]; % Lists of 3-vectors.
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pair w[]; % Coordinate pairs on the drawing canvas.
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numeric s; % The screen scale factor.
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Z_set(p0)(100, -100, 50); % Position of viewer.
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Z_set(q0)(0, 0, 0); % Centre of picture.
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A_set_pq(A)(p0)(q0);
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% A_print(A);
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s := 300;
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Z_set(p1)(1cm, 0cm, 0cm); % X axis.
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Z_set(p2)(0cm, 1cm, 0cm); % Y axis.
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Z_set(p3)(0cm, 0cm, 1cm); % Z axis.
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Z_set(p4)(0cm, 0cm, 0cm); % Origin.
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A_calc_w(A)(w1)(p1)(s);
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A_calc_w(A)(w2)(p2)(s);
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A_calc_w(A)(w3)(p3)(s);
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A_calc_w(A)(w4)(p4)(s);
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% showvariable w;
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drawarrow w4--w1;
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drawarrow w4--w2;
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drawarrow w4--w3;
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label.lrt(btex $x$ etex, w1);
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label.rt(btex $y$ etex, w2);
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label.top(btex $z$ etex, w3);
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endfig;
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end

‎3d10.mp

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% tex/conc/mp/3d10.mp 2016-8-31 Alan U. Kennington.
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% $Id: tex/conc/mp/3d10.mp 6ca9ae4555 2016-08-31 13:44:02Z Alan U. Kennington $
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% 3d graphic: Sphere S^2 in perspective.
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input 3dmax
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input mapmax
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input centmax
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%%%%%%%%%%%%%%%%%%%%%%%%%
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% figure 1 %
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%%%%%%%%%%%%%%%%%%%%%%%%%
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beginfig(1);
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numeric A[][]; % The current 4x3 transformation matrix.
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numeric p[][], q[][]; % Lists of 3-vectors.
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pair w[], midpt; % Coordinate pairs on the drawing canvas.
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numeric s; % The screen scale factor.
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path pat[];
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color vcol;
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% Multiplier and orientation angles for viewer.
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dv := 10; % Distance of camera from centre of sphere.
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ph_v := 45; % Angle phi.
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th_v := 40; % Angle theta.
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Z_set_rpt(p0)(dv, ph_v, th_v); % Position of viewer.
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Z_set(q0)(0, 0, 0); % Centre of picture.
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A_set_pq(A)(p0)(q0); % Set the perspective matrix.
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s := 700; % Some sort of magnification/zoom factor.
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R := 1; % Radius of the sphere.
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A_calc_w(A)(midpt)(q0)(s);
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%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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% Constant-latitude circles.
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nR := 12; % 12 points around the equator.
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nlat := 9; % Number for dividing the latitude of 90 degrees.
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% nlat := 3; % Number for dividing the latitude of 90 degrees.
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% Constant-longitude circles.
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mR := 20; % 40 points along the longitude line.
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% nlong := 12; % Number for dividing the longitude of 180 degrees.
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nlong := 6; % Number for dividing the longitude of 180 degrees.
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Z_set(p11)(0,0,0); % Centre of the sphere.
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% Draw the sphere.
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A_draw_lat_hide(A)(s)(p11)(R, nlat, nR, 0.6pt, 0.9pt)(p0);
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A_draw_long_hide(A)(s)(p11)(R, nlong, mR, 0.6pt, 0.9pt)(p0);
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% Add some vectors to demonstrate parallel transport.
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pickup pencircle scaled 1.4pt;
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vlen := 0.35; % Length of vector.
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vcol := 0.0white; % Colour of vector.
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% Phi = 0 degrees.
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A_north_draw(A)(s)(q0)(R, 0, 0, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 0, 30, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 0, 60, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 0, 90, vlen, vcol);
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% A_north_draw(A)(s)(q0)(R, 0, 90/4, vlen, vcol);
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% A_north_draw(A)(s)(q0)(R, 0, 90/2, vlen, vcol);
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% A_north_draw(A)(s)(q0)(R, 0, 3*90/4, vlen, vcol);
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% Phi = 90 degrees.
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A_north_draw(A)(s)(q0)(R, 90, 0, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 90, 30, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 90, 60, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 90, 90, vlen, vcol);
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% Phi = 30, 60 degrees.
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A_north_draw(A)(s)(q0)(R, 15, 0, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 30, 0, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 45, 0, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 60, 0, vlen, vcol);
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A_north_draw(A)(s)(q0)(R, 75, 0, vlen, vcol);
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% End point.
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pickup pencircle scaled 1.0pt;
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Z_set_rpt(p10)(R,0,90);
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A_calc_w(A)(w10)(p10)(s);
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w11 := w10 + (4,4)*5;
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w10 := w10 + (0.5pt,3pt);
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drawarrow w11{dir-170}..{dir-90}w10 withcolor 0.5white;
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label.rt(btex Finish here etex, w11);
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% Start point.
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pickup pencircle scaled 1.0pt;
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Z_set_rpt(p10)(R,0,0);
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A_calc_w(A)(w10)(p10)(s);
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w11 := w10 + (-4,-4)*5;
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S_arrowspaces(w11,w10,2pt,2.5pt,1,0.5white);
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label.bot(btex Start here etex, w11);
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pickup pencircle scaled 3.0pt;
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draw w10;
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pickup pencircle scaled 1.0pt;
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% Draw Muenchen.
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alon := 11+34/60;
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alat := 48+8/60;
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% Draw Bologna.
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% alon := 11+20/60;
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% alat := 44+29/60;
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% Draw Genova.
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% alon := 8+57/60;
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% alat := 44+25/60;
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Z_set_rpt(p10)(R,alon,alat);
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A_calc_w(A)(w10)(p10)(s);
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w11 := w10 + (-9,-3)*5;
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% S_arrowspaces(w11,w10,2pt,4pt,1,0.5white);
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S_arrowspaces(w11,w10,2pt,3pt,1,0.5white);
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label.lft(btex M\"unchen etex, w11);
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% label.lft(btex Bologna etex, w11);
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% label.lft(btex Genova etex, w11);
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pickup pencircle scaled 3.0pt;
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draw w10;
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% Draw Hanoi.
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pickup pencircle scaled 1.0pt;
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alon := 105+51/60;
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alat := 21+2/60;
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Z_set_rpt(p10)(R,alon,alat);
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A_calc_w(A)(w10)(p10)(s);
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w11 := w10 + (4,-2)*5;
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S_arrowspaces(w11,w10,1.5pt,3pt,1,0.5white);
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label.rt(btex H\`a N\d{\^o}i etex, w11);
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pickup pencircle scaled 3.0pt;
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draw w10;
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% Centre the picture bounding box.
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C_bbox_centre_set(currentpicture)(midpt);
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endfig;
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end

‎3d11.mp

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% tex/conc/mp/3d11.mp 2006-8-3 Alan Kennington.
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% $Id: tex/conc/mp/3d11.mp 8017ff16b3 2008-06-01 17:11:26Z Alan U. Kennington $
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% 3d graphic: Sphere S^2 in perspective.
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input 3dmax.mp
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input mapmax.mp
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%%%%%%%%%%%%%%%%%%%%%%%%%
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% figure 1 %
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%%%%%%%%%%%%%%%%%%%%%%%%%
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beginfig(1);
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numeric A[][]; % The current 4x3 transformation matrix.
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numeric p[][], q[][]; % Lists of 3-vectors.
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pair w[]; % Coordinate pairs on the drawing canvas.
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numeric s; % The screen scale factor.
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path pat[];
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% Multiplier and orientation angles for viewer.
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dv := 10; % Distance of camera from centre of sphere.
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ph_v := -45; % Angle phi.
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th_v := 40; % Angle theta.
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Z_set_rpt(p0)(dv, ph_v, th_v); % Position of viewer.
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Z_set(q0)(0, 0, 0); % Centre of picture.
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A_set_pq(A)(p0)(q0); % Set the perspective matrix.
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s := 700; % Some sort of magnification/zoom factor.
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R := 1; % Radius of the sphere.
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%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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% Constant-latitude circles.
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nR := 12; % 12 points around the equator.
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nlat := 9; % Number for dividing the latitude of 90 degrees.
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% nlat := 3; % Number for dividing the latitude of 90 degrees.
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% Constant-longitude circles.
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mR := 20; % 40 points along the longitude line.
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% nlong := 12; % Number for dividing the longitude of 180 degrees.
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nlong := 6; % Number for dividing the longitude of 180 degrees.
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Z_set(p11)(0,0,0); % Centre of the sphere.
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% Draw the sphere.
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A_draw_lat_hide(A)(s)(p11)(R, nlat, nR, 0.6pt, 1.2pt)(p0);
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A_draw_long_hide(A)(s)(p11)(R, nlong, mR, 0.6pt, 1.2pt)(p0);
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% Save the current picture bounding box.
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bbx := bboxmargin;
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bboxmargin := 0;
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pat1 := bbox currentpicture;
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% show pat1;
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% pickup pencircle scaled 0.4pt;
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% draw pat1;
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bboxmargin := bbx;
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% Draw Muenchen
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pickup pencircle scaled 1.0pt;
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alon := 11+34/60;
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alat := 48+8/60;
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Z_set_rpt(p10)(R,alon,alat);
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A_calc_w(A)(w10)(p10)(s);
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w11 := w10 + (7,2)*5;
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S_arrowspace(w11,w10,4pt,1,0.5white);
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label.rt(btex M\"unchen etex, w11);
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pickup pencircle scaled 3.0pt;
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draw w10;
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% Draw Havana.
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pickup pencircle scaled 1.0pt;
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alon := -(82+22/60);
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alat := 23+8/60;
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Z_set_rpt(p10)(R,alon,alat);
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A_calc_w(A)(w10)(p10)(s);
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w11 := w10 + (-7,2)*5;
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S_arrowspace(w11,w10,4pt,1,0.5white);
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label.lft(btex La Habana etex, w11);
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pickup pencircle scaled 3.0pt;
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draw w10;
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% Lie about the picture edges.
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% pat1 := bbox currentpicture;
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% show pat1;
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setbounds currentpicture to pat1;
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% pickup pencircle scaled 0.4pt;
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% draw pat1 dashed evenly;
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endfig;
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end

‎3d12.mp

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% tex/conc/mp/3d12.mp 2005-3-10 Alan Kennington.
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% $Id: tex/conc/mp/3d12.mp 8017ff16b3 2008-06-01 17:11:26Z Alan U. Kennington $
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% 3d graphic: standard injection for tensor product of sets.
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input 3dmax.mp
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%%%%%%%%%%%%%%%%%%%%%%%%%
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% figure 1 %
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%%%%%%%%%%%%%%%%%%%%%%%%%
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beginfig(1);
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numeric A[][]; % The current 4x3 transformation matrix.
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numeric p[][], q[][]; % Lists of 3-vectors.
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pair w[]; % Coordinate pairs on the drawing canvas.
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numeric s; % The screen scale factor.
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% Scale factor to make viewer further away and increase zoom proportionately.
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ss := 0.5;
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Z_set(p0)(25 * ss, -40 * ss, 10 * ss); % Position of viewer.
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Z_set(q0)(0, 0, 0); % Centre of picture.
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A_set_pq(A)(p0)(q0);
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% A_print(A);
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s := 800 * ss;
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axlength := 5;
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yt := 0.5;
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Z_set(p1)(axlength, 0, 0); % X axis.
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Z_set(p2)(0, axlength + yt, 0); % Y axis.
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Z_set(p3)(0, 0, 3/5*axlength); % Z axis.
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Z_set(p4)(0, 0, 0); % Origin.
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A_calc_w(A)(w1)(p1)(s);
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A_calc_w(A)(w2)(p2)(s);
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A_calc_w(A)(w3)(p3)(s);
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A_calc_w(A)(w4)(p4)(s);
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% showvariable w;
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drawarrow w4--w1;
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drawarrow w4--w2;
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drawarrow w4--w3;
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np := 4;
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nq := 4;
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xt := 0.5; % Extension of lines.
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for i=-np step 1 until np:
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Z_set(p5)(i, -nq - xt, 0);
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Z_set(p6)(i, nq + xt, 0);
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A_calc_w(A)(w5)(p5)(s);
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A_calc_w(A)(w6)(p6)(s);
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draw w5--w6;
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endfor
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for j=-nq step 1 until nq:
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Z_set(p5)(-np - xt, j, 0);
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Z_set(p6)(np + xt, j, 0);
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A_calc_w(A)(w5)(p5)(s);
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A_calc_w(A)(w6)(p6)(s);
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draw w5--w6;
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endfor
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pickup pencircle;
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for i=-np step 1 until np:
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for j=-nq step 1 until nq:
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Z_set(p5)(i, j, 0);
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A_calc_w(A)(w5)(p5)(s);
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draw w5;
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endfor
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endfor
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label.lrt(btex $\mathop{\times}\limits_{\alpha\in A}V_\alpha$ etex, w1+(0,5));
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% label.urt(btex $y$ etex, w2);
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label.top(btex $K$ etex, w3+(0,2));
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% Draw a vector at a particular point.
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Z_set(p7)(3, 4, 0);
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Z_set(p8)(3, 4, 1);
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A_calc_w(A)(w7)(p7)(s);
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A_calc_w(A)(w8)(p8)(s);
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% Sneeky trick to make the vertical line look more vertical!!
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% (I think this is called orthographic projection.)
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w8 := w7 + (0, ypart(w8-w7));
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pickup pencircle scaled 0.3pt;
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draw w7--w8 dashed evenly;
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pickup pencircle scaled 4pt;
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draw w8;
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label.top(btex $(u,1)$ etex, w8 + (0,3));
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endfig;
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end

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