% curves.m ----------------------------------------------------------
% This function shows an example (a bit contrived perhaps) where
% many GUI controls need to be crowded into a relatively small space.
% The ten controls above the graph (nine edit text objects and one
% popup text object) all are used to control how the parametric
% curves in the graph are displayed. If we used the traditional
% MatLab GUI objects, we would have had to make the graph much
% smaller to make room for all these controls. In addition, the
% plt('edit') objects provide a much easier way to modify the
% numeric values nearly matching the convenience of a slider object.
%
% After starting curves.m, right click on the curve name at the
% bottom of the figure to cycle thru the 36 different cool looking
% curve displays. (Left click on the curve name as well to select
% from the complete list of curves.) The equations in white above
% the curve name, are not only used as the x-axis label. These are
% the exact equations that are used to compute the points plotted
% on the graph. The vector t, and the constants a, b, and c that
% appear in these equations are defined by the controls above the
% graph. Experiment by both right and left clicking on these
% controls. For the cases when more than one trace is plotted, the
% first control on the left (called trace) indicates which trace is
% effected by the other nine controls above the graph. Note that
% when you left click on a control, it will increase or decrease
% depending on whether you click on the left or right side of the
% text string. Separate values for a, b, and c are saved for each
% trace of a multi-trace plot. This explains the variety of curves
% that can appear for a single set of equations (shown below the
% graph).
% ----- Author: ----- Paul Mennen
% ----- Email: ----- paul@mennen.org
function Out = curves(In)
qName = 1; % define columns of CRq
qT = 2;
qXlim = 3;
qYlim = 4;
qa = 5;
qb = 6;
qc = 7;
qSty = 8;
qXoff = 9;
qYoff = 10;
qEval = 11;
TXtrc = 1; % define user edit strings
TXa = 2;
TXb = 3;
TXc = 4;
TXxof = 5;
TXyof = 6;
TXstp = 7;
TXtmn = 8;
TXtmx = 9;
TXsty = 10;
startIdx = 31; % select the Spirograph curves as the initial choice
if ~nargin
% Curve Name [n tmin tmax] Xlim Ylim a b c Style Xoffset Yoffset
P2 = 2*pi;
CRq = ...
{'Arachnida ' [196 0 P2] [-5.6 1.2] [-1.4 1.4] [2 3 5] [3 2 4] 0 [1 8 1] [0 -2 -4] 0 ...
'r=sin(a*t)./sin(b*t);; x=r.*cos(t); y=r.*sin(t);';
'Archimedian Spiral ' [800 0 8*pi] [-26 47] [-29 23] [-1 -2 1 2] [30 600 1 .05] 0 1 [30 30 0 0] [10 10 0 0] ...
'r=b.*t.^a;; x=r.*cos(t); y=r.*sin(t);';
'Bell curve ' [800 -4 4] [-4 4] [-.1 1.1] [5 7 10 15 20 25] 0 0 1 0 0 ...
'x=t; a=a/10; y=exp(-x.^2/(2*a.^2));';
'Bicuspid curve ' [9999 -1 1] [-1.7 1.7] [-1.2 1.2] [1 1 -1 -1] [1 -1 1 -1] 0 9 0 0 ...
'x=a*sqrt(1+b*sqrt((1-t).^2.*(1-t.^2))); y=-t;; y(find(imag(x)))=Inf;';
'Bullet nose ' [300 0 P2] [-9 9] [-1.1 1.1] [3 4 5 6 8 10] 0 0 3 0 0 ...
'x=a*cot(t); y=cos(t);; y(find(abs(t-pi)<1e-6))=Inf;';
'Butteryfly curve ' [2000 0 24*pi] [-3.9 3.9] [-2.8 4.2] 24 5 4 1 0 0 ...
'r=exp(sin(t))-2*cos(c*t)+sin((2*t-pi)/a).^b;; x=r.*cos(t); y=r.*sin(t);';
'Catenary ' [200 -pi pi] [-1.7 1.7] [-.1 6] [15 10 7 4 2 1] 0 0 [1 1 1 1 1 6] 0 0 ...
'a=a/10; x=t; y=a*cosh(t/a);';
'Cissoid of Diocles ' [800 1.9 4.4] [-.3 10.2] [-13 13] [5 6 7 8 9 10] 0 0 1 [0 .5 1 1.5 2 2.5] 0 ...
'r=a*tan(t).*sin(t);; x=r.*cos(t); y=r.*sin(t);';
'Cochleoid ' [800 0 8*pi] [-.25 1.05] [-.1 .8] 0 0 0 1 0 0 ...
'r=sin(t)./t;; x=r.*cos(t); y=r.*sin(t);';
'Cocked hat curve ' [800 0 8*pi] [-1.5 1.5] [-3.5 14] [-2 -1 0 1 2 5] 0 0 1 0 [0 1.5 3 4.5 6 7] ...
'x=sin(t); y=cos(t).^2.*(a+cos(t))./(1+sin(t).^2);';
'Conchoid of Nicomedes' [800 0 P2] [-15 15] [-3.3 5.4] [4 3 2 1 2 1] [1 1 1 1 3 2] 0 1 0 0 ...
'r=a+b*csc(t);; x=r.*cos(t); y=r.*sin(t);';
'Cranioid ' [800 0 P2] [-17 17] [-9 21] 6 13 16 8 0 0 ...
'r=a*sin(t)+b*sqrt(1-c*cos(t).^2/20);; x=r.*cos(t); y=r.*sin(t);'
'Cycloid ' [800 0 18] [1.7 16] [-2.3 5.3] [10 7 4 13 16 -10] [10 7 4 13 16 10] 0 [8 3 3 1 1 8] 0 [3 .5 1 2 -1 -2] ...
'x=t-a*sin(t)/10; y=1-b*cos(t)/10;'
'Devil''s curve ' [800 0 P2] [-3 3] [-3 3] [1 1 1 1 2 3] [1.4 2 3 4 3 4] 0 1 0 0 ...
'v=sin(t).^2; w=cos(t).^2; r=sqrt((a*v-b*w)./(v-w));; x=r.*cos(t); y=r.*sin(t);'
'Dumbbell curve ' [801 -1 1] [-2 2] [-.6 2] [0 23 7 30 37 53] 0 0 1 [0 1 -1 0 -1 1] [0 1 1 0 1 1] ...
'r=sqrt(t.^2+t.^4-t.^6); w=acos(t./r)+(a*pi/30); x=r.*cos(w); y=r.*sin(w);'
'Ellipse & evolute ' [800 0 6*pi] [-31 31] [-1.1 1.1] [30 27 24 21 18 15] 0 0 1 0 0 ...
'v=bitor(floor(t/pi),1); x=a.*cos(t).^v; y=sin(t).^v;';
'Epispiral ' [800 0 P2] [-25 25] [-13 13] [2 3 4] 11 0 [1 8 1] [-16 -3 14] 0 ...
'r=abs(sec(a*t));; x=r.*cos(t); y=r.*sin(t); y(find(abs(complex(x,y))>b))=Inf;';
'Epitrochoid ' [800 0 10*pi] [-38 36] [-22 29] [8 5 14 2 2 2] [5 3 1 1 2 3] [5 5 1 1 2 3] [1 1 6 1 8 1] [-18 18 18 1 -16 2] [0 0 0 -15 0 19] ...
'w=(1+a/b)*t; x=(a+b)*cos(t)-c*cos(w); y=(a+b)*sin(t)-c*sin(w);'
'Euler''s spiral ' [600 -6 6] [-1.1 1.1] [-.77 .77] 0 0 0 1 0 0 ...
'[x y] = fresnel(t);';
'Fish Curve ' [300 0 P2] [-1.24 1.2] [-.7 .7] 1 0 0 11 0 0 ...
'p=sin(t); q=cos(t); x=a*q-a*p.^2/sqrt(2); y=a*p.*q;';
'Folium of Descartes ' [801 -6 6] [-3.2 3.7] [-2.9 2.5] 1 0 0 8 0 0 ...
't=t.^3; v=1+t.^3; x=3*a*t./v; y=3*a*t.^2./v;';
'Fourier Series ' [800 -2 12] [-2 12] [-2.5 11.5] [2 2 1 2 4 1] [1 0 1 1 1 1] [2 1 1 1 1 2] [1 1 8 1 1 8] 0 [10 7.6 4.4 2.2 0 -1.2] ...
'x=t; v=0:25; w=1+a*v; v=b*v; y=((-1).^v./(w.^c))*sin(w''*t);';
'Gear Curve ' [800 0 P2] [-3 3] [-2.2 2.2] [1 1.4 1.8] 8 [4 9 15] 1 0 0 ...
'r=a+tanh(b*sin(c*t))/b;; x=r.*cos(t); y=r.*sin(t);';
'Hypocycloid ' [800 0 14*pi] [-11 8] [-6 6] [3 5 4 5 pi] [1 1 1 3 1] 0 [8 1 1 1 1] [6 0 -7 0 -7] 0 ...
'v=a-b; p=t*v/b; x=v*cos(t)-b*cos(p); y=v*sin(t)+b*sin(p);';
'Limacon ' [200 0 P2] [-40 150] [-80 80] [48 42 20 3] [48 32 40 48] 0 [1 8 1 1] [-15 0 0 85] 0 ...
'r=a+b*cos(t);; x=r.*cos(t); y=r.*sin(t);';
'Lissajous curves ' [400 0 P2] [-9 11] [-1.2 1.2] [1 5 1 1] [2 4 2 3] [99 99 2 1] [1 1 8 8] [6 0 -7 9] 0 ...
'x=a.*sin(b*t+pi/c); y=sin(t);';
'Maclaurin Trisectrix ' [800 1.8 4.5] [-.9 1.6] [-1.5 1.5] [-5 -3 -1 1 3 5] 0 0 1 0 0 ...
'r=sin(3*t)./sin(2*t); w=t+a*pi/60; x=r.*cos(w); y=r.*sin(w);';
'Rose ' [800 0 14*pi] [-3 3.1] [-2.1 2] [2 3 4 1 2 exp(1)] [1 1 1 3 3 1] 0 1 [-2 0 2 -2 0 2] [1 1.2 1 -.8 -1 -1] ...
'r=sin(a*t/b);; x=r.*cos(t); y=r.*sin(t);';
'Scarabaeus ' [800 0 P2] [-6 12] [-4 4] [2 3 1 1] [3 2 1 3] [2 2 2 7] 1 [0 6 4 11] 0 ...
'r=a*cos(c*t)-b*cos(t);; x=r.*cos(t); y=r.*sin(t);';
'Serpentine curve ' [800 -9 9] [-9 9] [-.6 .6] [1 2 3 4 5 6] 0 0 1 0 0 ...
'x=t; y=a*x./(a^2+x.^2);';
'Spirograph ' [800 0 P2] [-3 17] [-5 9] [3 10 10 7 14 5] [1 1 1 2 2 3] [2 3 4 4 6 6] [6 1 1 1 1 8] [0 6 13 0 6 13] [6 6 6 0 0 0] ...
'x=b*cos(t)+a*cos(c*t)/10; y=b*sin(t)-a*sin(c*t)/10;';
'Square wave ' [400 -2 8] [-2 8] [-1.3 6.5] [6 5 4 3 2 1] 0 0 1 0 [0 1 2 3 4 5] ...
'x=t; v=1 : 2 : 2*a-1; y=4./(pi*v)*sin(v''*t);';
'Strophoid ' [800 0 P2] [-7.4 13.4] [-15 15] [8 9 10 11 12 13] 0 0 1 0 0 ...
'r=a*cos(2*t).*sec(t);; x=r.*cos(t); y=r.*sin(t);';
'Talbot''s curve ' [800 0 P2] [-16 110] [-15 15] [4 5 6 7 8 9] 13 0 1 [0 23 40 60 80 99] 0 ...
's=sin(t); c=a^2-b^2; x=(a^2+c*s.^2).*cos(t)/a; y=(a^2-2*c+c*s.^2).*s/b;';
'Teardrop ' [400 0 P2] [-1.1 1.1] [-.9 .9] [16 11 7 4 2 1] 0 0 [1 1 1 1 1 8] 0 0 ...
'x=cos(t); y=sin(t).*sin(t/2).^a;';
'Witch of Agnesi ' [800 -4 4] [-4 4] [0 5.6] [3 3.5 4 4.5 5 5.5] 0 0 1 0 0 ...
'x=t; y=a./(1+x.^2);'
};
names = CRq(:,1);
for k=1:length(names)
sz = length(CRq{k,qa});
for m=qb:qYoff % expand shorter vectors to the size of a
if length(CRq{k,m})<sz CRq{k,m} = zeros(1,sz)+CRq{k,m}; end;
end;
end;
CRlines = plt(1,ones(1,6),'LabelX','','Position',[10 45 930 680],...
'FigBKc',[.1 .2 .1],'Options','Ticks-X-Y',...
'FigName','Curves','AxisPos',[1 1.45 1 .9 1 .9 1 1]);
ax = gca;
set(ax,'TickLen',[0 0]);
CRb = flipud(get(findobj(gcf,'user','TraceID'),'child'));
xl = get(ax,'Xlabel');
fontsz = get(xl,'fontsize'); set(xl,'fontsize',1.4*fontsz,'color','white');
tx = {'Trace' 'a' 'b' 'c' 'Xoffset' 'Yoffset' 't Steps' 't Min' 't Max' 'Style' };
x = 0;
for k=1:length(tx)
text(0,0,tx{k},'units','norm','pos',[x 1.07],'color',[.8 .8 .8],'horiz','center');
cb = ['curves(' int2str(k) ')'];
if k==TXsty
CRi(k) = plt('pop','offset',[-.015 -.47],'choices',...
{' line';' --';' :';' -.';' +';' o';' *';' .';' x';' s';' d';' ^';' v';' >';' <';' p';' h'},...
'callbk',cb,'horiz','center','location',[x-.012 .943 .042 .5]);
else CRi(k) = plt('edit','units','norm','position',[x 1.035],'callbk',cb);
end;
x = x + .1;
end;
plt('edit',CRi(TXtrc),'min',1);
axes(ax);
CRa = text(0,0,'\leftarrow right click on curve name',...
'fontsize',1.4*fontsz,'color',[0 1 1],'units','norm','pos',[.35 -.135]);
CRp = plt('pop','choices',CRq(:,1),'index',31,'location',[.27 .01 .24 1],...
'fontsize',2*fontsz,'callbk','curves(0)');
set(gcf,'user',{CRlines CRq CRp CRi CRa CRb});
curves(0);
else
a = get(gcf,'user');
CRlines = a{1}; CRq = a{2}; CRp = a{3}; CRi = a{4}; CRa = a{5}; CRb = a{6};
cs = plt('pop',CRp,'get','index');
if cs ~= startIdx set(CRa,'visible','off'); end;
tr = plt('edit',CRi(1),'get','value');
if In<=TXtrc % here for curve name and trace number callbacks
if ~In % if curve callback, reset to trace number 1
tr = 1; plt('edit',CRi(1),'value',1,'max',length(CRq{cs,qa}));
plt('edit',CRi(TXstp),'value',CRq{cs,qT}(1));
plt('edit',CRi(TXtmn),'value',CRq{cs,qT}(2));
plt('edit',CRi(TXtmx),'value',CRq{cs,qT}(3));
end;
plt('edit',CRi(TXa), 'value',CRq{cs,qa}(tr));
plt('edit',CRi(TXb), 'value',CRq{cs,qb}(tr));
plt('edit',CRi(TXc), 'value',CRq{cs,qc}(tr));
plt('edit',CRi(TXxof),'value',CRq{cs,qXoff}(tr));
plt('edit',CRi(TXyof),'value',CRq{cs,qYoff}(tr));
plt('pop', CRi(TXsty),'index',CRq{cs,qSty}(tr));
else
if In==TXsty CRq{cs,qSty}(tr) = plt('pop',CRi(In),'get','index');
else v = plt('edit',CRi(In),'get','value');
switch In
case TXa, CRq{cs,qa}(tr) = v;
case TXb, CRq{cs,qb}(tr) = v;
case TXc, CRq{cs,qc}(tr) = v;
case TXxof, CRq{cs,qXoff}(tr) = v;
case TXyof, CRq{cs,qYoff}(tr) = v;
case TXstp, CRq{cs,qT}(1) = v;
case TXtmn, CRq{cs,qT}(2) = v;
case TXtmx, CRq{cs,qT}(3) = v;
end % end switch In
end; % if In==TXsty
end; % end if In<=TXtrc
ax = get(CRlines(1),'parent');
tiny = 1e-32;
t = CRq{cs,qT};
step = (t(3)-t(2))/t(1); t = tiny + t(2):step:t(3);
set(ax,'xlim',CRq{cs,qXlim},'ylim',CRq{cs,qYlim});
aa = CRq{cs,qa}; bb = CRq{cs,qb}; cc = CRq{cs,qc};
Xoff = CRq{cs,qXoff}; Yoff = CRq{cs,qYoff}; Style = CRq{cs,qSty};
StyCH = plt('pop',CRi(TXsty),'get','choices');
n = length(aa);
set(CRlines,'x',0,'y',0);
func = CRq{cs,qEval};
f = ['\bf' func]; p = findstr(f,';;');
if length(p) f = f(1:p(1)); end;
f1 = {'.' ';' '=' '*' '+' '-' '/' };
f2 = {'' ' \bf' ' = \rm' ' \cdot ' ' + ' ' - ' ' / '};
for k=1:length(f1) f=strrep(f,f1{k},f2{k}); end;
set(get(ax,'Xlabel'),'str',f);
for m = 1:n
a = aa(m); b = bb(m); c = cc(m); STYix = Style(m);
if STYix==1 sty = '-'; else sty = StyCH{STYix}; end;
if STYix<5 mrk = 'none'; else mrk = sty; sty = 'none'; end;
eval(func);
set(CRlines(m),'x',x+Xoff(m),'y',y+Yoff(m),'Marker',mrk,'LineStyle',sty);
s = ['trace ' int2str(m)];
if m==tr & n>1 s = [s '<<']; end;
set(CRb(m),'string',s);
end;
for m = (n+1):6 set(CRb(m),'string',''); end;
plt('grid',ax);
end; % end if ~nargin
%end function curves
function [fcos,fsin]=fresnel(xx) % computes the cos and sin fresnel integrals
acc = 1e-15; % accuracy required
sx = sign(xx); xx = abs(xx); % apply signs at the end
fcos = xx; fsin = xx; % pre-allocate outputs
for n = 1:length(xx)
x = xx(n);
px = pi*x; t = px*x/2; t2 = -t.^2;
if ~x c=0; s=0;
elseif x < 2.5
r = x; c = r;
for k=1:50 r = r * t2 * (4*k-3) / polyval([16 -4 -2 0],k);
c = c + r;
if abs(r) < abs(c)*acc break; end;
end;
s = x*t/3; r = s;
for k=1:50 r = r * t2 * (4*k-1) / polyval([16 20 6 0],k);
s = s + r;
if abs(r) < abs(s)*acc break; end;
end;
elseif x < 4.5;
m = fix(42 + 1.75*t);
su = 0; c = 0; s = 0; f1 = 0; f0 = 1e-100;
for k = m:-1:0 f = (2*k+3) * f0 / t - f1;
if mod(k,2) s=s+f; else c=c+f; end;
su = su + (2*k+1) * f^2; f1 = f0; f0 = f;
end;
q = sqrt(su); c = c*x/q; s=s*x/q;
else;
r = 1; f = 1;
for k=1:20 r = r * polyval([1 -1 .75],k) / t2;
f = f + r;
end;
r = 1 / (px*x);
g = r;
for k=1:12 r = r * polyval([1 0 -.0625],k) / t2;
g = g + r;
end;
t0 = t - fix(t/(2*pi)) * 2*pi;
c = .5 + (f*sin(t0) - g * cos(t0)) / px;
s = .5 - (f*cos(t0) + g * sin(t0)) / px;
end; % end if ~x
fcos(n) = c; fsin(n) = s;
end; % end for n = 1:length(xx)
fcos = sx .* fcos;
fsin = sx .* fsin;
% end function fresnel
