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3d7.mp
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% tex/conc/mp/3d7.mp 2005-3-10 Alan Kennington.
% $Id: tex/conc/mp/3d7.mp 8017ff16b3 2008-06-01 17:11:26Z Alan U. Kennington $
% 3d graphic: Sphere S^2 in perspective.
input 3dmax.mp
%%%%%%%%%%%%%%%%%%%%%%%%%
% figure 1 %
%%%%%%%%%%%%%%%%%%%%%%%%%
beginfig(1);
numeric A[][]; % The current 4x3 transformation matrix.
numeric p[][], q[][]; % Lists of 3-vectors.
pair w[]; % Coordinate pairs on the drawing canvas.
numeric s; % The screen scale factor.
path pat[];
% Multiplier and orientation angles for viewer.
dv := 5; % Distance of camera from centre of sphere.
ph_v := -40; % Angle phi.
th_v := 35; % Angle theta.
Z_set_rpt(p0)(dv, ph_v, th_v); % Position of viewer.
Z_set(p13)(0,0,1);
Z_add(p0)(p13);
Z_set(q0)(0, 0, 0); % Centre of picture.
% Z_add(q0)(p13);
% Set the viewing matrix for the viewer and the focus point.
A_set_pq(A)(p0)(q0);
% Some sort of magnification/zoom factor.
s := 350;
% Radius of the sphere.
R := 1;
axlength := 2;
azlength := 2.5;
yt := 0.5;
Z_set(p1)(axlength, 0, 0); % X axis.
Z_set(p2)(0, axlength + yt, 0); % Y axis.
Z_set(p3)(0, 0, azlength); % Z axis.
Z_set(p4)(0, 0, 0); % Origin.
A_calc_w(A)(w1)(p1)(s);
A_calc_w(A)(w2)(p2)(s);
A_calc_w(A)(w3)(p3)(s);
A_calc_w(A)(w4)(p4)(s);
% showvariable w;
pickup pencircle scaled 0.85pt;
drawarrow w4--w1;
drawarrow w4--w2;
drawarrow w4--w3;
np := 1;
nq := 1;
xt := 0.5; % Extension of lines.
for i=-np step 1 until np:
Z_set(p5)(i, -nq - xt, 0);
Z_set(p6)(i, nq + xt, 0);
A_calc_w(A)(w5)(p5)(s);
A_calc_w(A)(w6)(p6)(s);
draw w5--w6;
endfor
for j=-nq step 1 until nq:
Z_set(p5)(-np - xt, j, 0);
Z_set(p6)(np + xt, j, 0);
A_calc_w(A)(w5)(p5)(s);
A_calc_w(A)(w6)(p6)(s);
draw w5--w6;
endfor
pickup pencircle;
for i=-np step 1 until np:
for j=-nq step 1 until nq:
Z_set(p5)(i, j, 0);
A_calc_w(A)(w5)(p5)(s);
draw w5;
endfor
endfor
%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% Draw the constant-latitude lines.
nR := 12; % 12 points around the equator.
nlat := 9; % Number for dividing the latitude of 90 degrees.
Z_set(p11)(0,0,1); % Centre of the sphere.
A_draw_lat(A)(s)(p11)(R, nlat, nR, 0.6pt);
Z_set(p12)(0,0,-1); % Centre of the sphere.
A_draw_lat(A)(s)(p12)(R, nlat, nR, 0.3pt);
%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% Draw the longitude lines.
mR := 12; % 24 points along the longitude line.
nlong := 12; % Number for dividing the longitude of 180 degrees.
% Choose nlong = 1 to just draw the equator.
A_draw_long(A)(s)(p11)(R, nlong, mR, 0.6pt);
A_draw_long(A)(s)(p12)(R, nlong, mR, 0.3pt);
%- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% Draw the poles. (Superfluous!?)
pickup pencircle scaled 1.0pt;
Z_set(p10)(0,0,R*2); % North pole.
A_calc_w(A)(w20)(p10)(s);
draw w20;
Z_set(p10)(0,0,0); % South pole.
A_calc_w(A)(w20)(p10)(s);
draw w20;
endfig;
end