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-// Copyright(c) 2008, Philippe Ivaldi.
-// Simplified by John Bowman 02Feb2011
-// http: //www.piprime.fr/
-// trembling.asy: handwriting package for the software Asymptote.
-
-// This program is free software; you can redistribute it and/or modify
-// it under the terms of the GNU Lesser General Public License as published by
-// the Free Software Foundation; either version 3 of the License, or
-//(at your option) any later version.
-
-// This program is distributed in the hope that it will be useful, but
-// WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
-// Lesser General Public License for more details.
-
-// You should have received a copy of the GNU Lesser General Public License
-// along with this program; if not, write to the Free Software
-// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-
-// COMMENTARY:
-
-// THANKS:
-
-// BUGS:
-// magnetic points are experimental...
-
-// CODE:
-
-real magneticRadius=1; // unit is bp in postscript coordinates.
-real trembleFuzz(){return min(1e-3,magneticRadius/10);}
-
-/* <asyxml> <variable type="real" signature="trembleAngle"> <code> </asyxml> */
-real trembleAngle=4, trembleFrequency=0.5, trembleRandom=2;
-/* <asyxml> </code> <documentation> Variables used by the routine 'tremble'.
- </documentation> </variable> </asyxml> */
-
-struct tremble
-{
- static real test=5;
-
- real angle,frequency,random,fuzz;
-
- pair[] single(pair[] P)
- {
- pair[] op;
- bool allow;
- for(int i=0; i < P.length-1; ++i) {
- allow=true;
- for(int j=i+1; j < P.length; ++j) {
- if(abs(P[i]-P[j]) < magneticRadius) {
- allow=false;
- break;
- }
- }
- if(allow) op.push(P[i]);
- }
- if(P.length > 0) op.push(P[P.length-1]);
- return op;
- }
-
- /* <asyxml> <function type="pair" signature="attract(pair,path,real)"> <code>
- </asyxml> */
- real atime(pair m, path g, real fuzz=trembleFuzz())
- {/* <asyxml> </code> <documentation> Return the time of the point on path g
- nearest to 'm'.
- 'fuzz' is the argument 'fuzz' of 'intersect'. </documentation> </function>
- </asyxml> */
- if(length(g) == 0) return 0.0;
- real[] t=intersect(m,g,fuzz);
- if(t.length > 0) return t[1];
- real ot;
- static real eps=sqrt(realEpsilon);
- real abmax=abs(max(g)-m), abmin=abs(min(g)-m);
- real initr=abs(m-midpoint(g));
- real maxR=2*max(abmax,abmin), step=eps, r=initr;
- real shx=1e-4;
- transform T=shift(m);
- path ig;
- if(t.length > 0) ot=t[1];
- real rm=0, rM=r;
- while(rM-rm > eps) {
- r=(rm+rM)/2;
- t=intersect(T*scale(r)*unitcircle,g,fuzz);
- if(t.length <= 0) {
- rm=r;
- } else {
- rM=r;
- ot=t[1];
- }
- }
- return ot;
- }
-
- /* <asyxml> <function type="path" signature="addnode(path,real)"> <code>
- </asyxml> */
- path addnode(path g, real t)
- {/* <asyxml> </code> <documentation> Add a node to 'g' at point(g,t).
- </documentation> </function> </asyxml> */
- real l=length(g);
- real rt=t % 1;
- if(l == 0 || (t > l && !cyclic(g)) || rt == 0) return g;
- if(cyclic(g)) t=t % l;
- int t0=floor(t);
- int t1=t0+1;
- pair z0=point(g,t0), z1=point(g,t1),
- c0=postcontrol(g,t0), c1=precontrol(g,t1),
- m0=(1-rt)*z0+rt*c0, m1=(1-rt)*c0+rt*c1,
- m2=(1-rt)*c1+rt*z1, m3=(1-rt)*m0+rt*m1,
- m4=(1-rt)*m1+rt*m2;
- guide og=subpath(g,0,t0)..controls m0 and m3..point(g,t);
- if(cyclic(g)) {
- if(t1 < l)
- og=og..controls m4 and m2..subpath(g,t1,l)&cycle;
- else og=og..controls m4 and m2..cycle;
- } else og=og..controls m4 and m2..subpath(g,t1,l);
- return og;
- }
-
- path addnodes(path g, real fuzz=trembleFuzz()...pair[] P)
- {
- pair[] P=single(P);
- if(length(g) == 0 || P.length == 0 || magneticRadius <= 0) return g;
- path og=g;
- for(pair tp: P) {
- real t=atime(tp,og,fuzz);
- real d=abs(tp-point(og,t));
- if(d < magneticRadius) og=addnode(og,t);
- }
- return og;
- }
-
- /* <asyxml> <function type="path" signature="addnodes(path,int)"> <code>
- </asyxml> */
- path addnodes(path g, int n)
- {/* <asyxml> </code> <documentation> Add 'n' nodes between each node of 'g'.
- </documentation> </function> </asyxml> */
- real l=length(g);
- if(n == 0 || l == 0) return g;
- path og=g;
- int np=0;
- for(int i=0; i < l; ++i) {
- real step=1/(n+1);
- for(int j=0; j < n; ++j) {
- og=addnode(og,i*(n+1)+j+step);
- step=1/(n-j);
- }
- }
- return og;
- }
-
- /* <asyxml> <function type="path"
- signature="tremble(path,real,real,real,real,pair[] )"> <code> </asyxml> */
- void operator init(real angle=trembleAngle, real frequency=trembleFrequency,
- real random=trembleRandom, real fuzz=trembleFuzz()) {
- this.angle=angle;
- this.frequency=frequency;
- this.random=random;
- this.fuzz=fuzz;
- }
-
- path deform(path g...pair[] magneticPoints) {
- /* <asyxml> </code> <documentation> Return g as it was handwriting.
- The postcontrols and precontrols of the nodes of g will be rotated
- by an angle proportional to 'angle'(in degrees).
- If frequency < 1, floor(1/frequency) nodes will be added to g to
- increase the control points.
- If frequency>= 1, one point for floor(frequency) will be used to deform
- the path.
- 'random' controls the randomized coefficient which will be multiplied
- by 'angle'.
- random is 0 means don't use randomized coefficient;
- The higher 'random' is, the more the trembling is randomized.
- </documentation> </function> </asyxml> */
- if(length(g) == 0) return g;
- g=addnodes(g,fuzz*abs(max(g)-min(g))...magneticPoints);
- path tg=g;
- frequency=abs(frequency);
- int f=abs(floor(1/frequency)-1);
- tg=addnodes(tg,f);
- int frequency=floor(frequency);
- int tf=(frequency == 0) ? 1 : frequency;
- int l=length(tg);
- guide og=point(tg,0);
- random=abs(random);
- int rsgn(real x){
- int d2=floor(100*x)-10*floor(10*x);
- if(d2 == 0) return 1;
- return 2 % d2 == 0 ? 1 : -1;
- }
- real randf()
- {
- real or;
- if(random != 0) {
- if(1 % tf != 0) or=0;
- else {
- real ur=unitrand();
- or=rsgn(ur)*angle*(1+ur^(1/random));
- }
- } else or=rsgn(unitrand())*1.5*angle;
- return or;
- }
-
- real first=randf();
- for(int i=1; i <= l; ++i) {
- pair P=point(tg,i);
- real a=randf();
- pair post=rotate(a,point(tg,i-1))*postcontrol(tg,i-1);
- pair pre=rotate((a+randf())/2,P)*precontrol(tg,i);
- if(i == l && (cyclic(tg)))
- og=og..controls post and pre..cycle;
- else
- og=og..controls post and pre..P;
- }
- return og;
- }
-}