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L'éditeur de formules de Carrara Studio - Page 24

Courbes planes et couleurs

1 - Papillon (voir Paul Bourke)

Formule fond Rendu
a=0.2;e=0.01;
pmin=-0.35;pmax=0.65;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=exp(cos(t))-2*cos(4*t)-cos(t/12);
x=a*r*cos(t);
y=a*r*sin(t);
green=1-(abs(x-p)<e&&abs(y-q)<e);
blue=1-(abs(x-2*p)<e&&abs(y-2*q)<e);
red=1-(abs(x-3*p)<e&&abs(y-3*q)<e); 		polairefond1.jpg
 
Formule fond Rendu
a=0.2;e=0.01;
pmin=-0.35;pmax=0.65;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=exp(cos(t))-2*cos(4*t)-cos(t/12);
x=a*r*cos(t);
y=a*r*sin(t);
green=(abs(x-p)<e&&abs(y-q)<e);
blue=(abs(x-2*p)<e&&abs(y-2*q)<e);
red=(abs(x-3*p)<e&&abs(y-3*q)<e);

2 - 

Formule fond Rendu
a=0.15;e=0.01;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
d=abs(cos(13*t))+abs(cos(17*t));
r=(d!=0?1/d:0);
x=a*r*cos(t);
y=a*r*sin(t);
green=1-(abs(mod(x,p))<e&&abs(mod(y,q))<e);
blue=1-(abs(mod(x,0.5*p))<e&&abs(mod(y,0.5*q))<e);
red=1-(abs(mod(x,0.75*p))<e&&abs(mod(y,0.75*q))<e); 		polairefond21.jpg
 
Formule fond Rendu
a=0.15;e=0.01;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
d=abs(cos(7*t))+abs(cos(11*t));
r=(d!=0?1/d:0);
x=a*r*cos(t);
y=a*r*sin(t);
green=1-(abs(mod(x,p))<e&&abs(mod(y,q))<e);
blue=1-(abs(mod(x,0.5*p))<e&&abs(mod(y,0.5*q))<e);
red=1-(abs(mod(x,0.75*p))<e&&abs(mod(y,0.75*q))<e) 		polairefond22.jpg

3 - 

Formule fond Rendu
a=0.4;e=0.05;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=1-sqrt(abs(sin(5*t)));
x=a*r*cos(t);
y=a*r*sin(t);
green=1-(abs(x-p)<e&&abs(y-q)<e);
blue=1-(abs(x-2*p)<e&&abs(y-2*q)<e);
red=1-(abs(x-3*p)<e&&abs(y-3*q)<e); 		polairefond31.jpg
 
Formule fond Rendu
a=0.4;e=0.05;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=1-sqrt(abs(sin(5*t)));
x=a*r*cos(t);
y=a*r*sin(t);
green=(abs(x-p)<e&&abs(y-q)<e);
blue=(abs(x-2*p)<e&&abs(y-2*q)<e);
red=(abs(x-3*p)<e&&abs(y-3*q)<e);

4 - 

Formule fond Rendu
a=1;n=2;e=0.01;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=a*cos(n*t);
x=r*cos(t);
y=r*sin(t);
green=1-(abs(mod(x,p))<e&&abs(mod(y,q))<e);
blue=1-(abs(mod(x,0.5*p))<e&&abs(mod(y,0.5*q))<e);
red=1; 		polairefond41.jpg
 
Formule fond Rendu
a=1;n=2;e=0.01;b=2.07;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=a*cos(n*t);
x=r*cos(t);
y=r*sin(t);
green=0.5*(1-(abs(mod(x,p))<e&&abs(mod(y,q))<e));
blue=1-(abs(mod(x,0.5*p))<e&&abs(mod(y,0.5*q))<e);
red=1-abs(pow(p*p,1/3)+pow(q*q,1/3)-pow(b*b,1/3))<e; 		polairefond42.jpg

5 - 

Formule fond Rendu
a=1;m=3;n=5;e=0.05;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=a*(1+m*cos(n*t));
x=r*cos(t);
y=r*sin(t);
green=1-(abs(mod(x,p))<e&&abs(mod(y,q))<e);
blue=1-(abs(mod(x,1.33*p))<e&&abs(mod(y,1.33*q))<e);
red=1-(abs(mod(x,1.66*p))<e&&abs(mod(y,1.66*q))<e); 		polairefond51.jpg
 
Formule fond Rendu
a=1;m=3;n=5;e=0.05;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=a*(1+m*cos(n*t));
x=r*cos(t);
y=r*sin(t);
green=abs(mod(x,p))<e&&abs(mod(y,q))<e;
blue=abs(mod(x,1.33*p))<e&&abs(mod(y,1.33*q))<e;
red=abs(mod(x,1.66*p))<e&&abs(mod(y,1.66*q))<e; 		polairefond52.jpg

6 - 

Formule fond Rendu
a=1;b=1;c=100;n=2;e=0.01;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=a*sqrt(1+cos(n*t));
x=r*cos(t);
y=r*sin(t);
red=1-(abs(mod(x,p))<e&&abs(mod(y,q))<e);
green=1-abs(p*p+q*q-b*b)<e;
blue=1-abs(p*(p*p+q*q)-c*(p*p-q*q))<e; 		polairefond61.jpg
 
Formule fond Rendu
a=1;b=1;c=100;n=7;e=0.01;
pmin=-0.5;pmax=0.5;
qmin=-0.5;qmax=0.5;
p=(pmax-pmin)*u+pmin;
q=(qmax-qmin)*v+qmin;
t=atan2(q,p);
r=a*sqrt(1+cos(n*t));
x=r*cos(t);
y=r*sin(t);
red=1-(abs(mod(x,p))<e&&abs(mod(y,q))<e);
green=1-abs(p*p+q*q-b*b)<e;
blue=1-abs(p*(p*p+q*q)-c*(p*p-q*q))<e; 		polairefond62.jpg