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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);}
real trembleAngle=4, trembleFrequency=0.5, trembleRandom=2;
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;
}
real atime(pair m, path g, real fuzz=trembleFuzz())
{// Return the time of the point on path g nearest to m, within fuzz.
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;
}
path addnode(path g, real t)
{// Add a node to 'g' at point(g,t).
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;
}
path addnodes(path g, int n)
{// Add 'n' nodes between each node of 'g'.
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;
}
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) {
/* 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. */
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;
}
}
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