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L'éditeur de formules de Carrara Studio - Page 18

Tubes

1 - Avec les courbes de Lissajous

Formule objet Formule texture Rendu
a=3;b=3;c=3;
m1=1;m2=2;m3=3;
p=2*PI*u;
q=2*PI*v;
xc=a*sin(m1*p);
yc=b*sin(m2*p);
zc=c*sin(m3*p);
xt=a*m1*cos(m1*p);
yt=b*m2*cos(m2*p);
zt=c*m3*cos(m3*p);
xn=-yt;
yn=xt;
zn=0;
nn=sqrt(pow(xn,2)+pow(yn,2)+pow(zn,2));
xn1=xn/nn;
yn1=yn/nn;
zn1=zn/nn;
xb=-xt*zt;
yb=-yt*zt;
zb=xt*xt+yt*yt;
nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2));
xb1=xb/nb;
yb1=yb/nb;
zb1=zb/nb;
r1=0.5;r2=0.5;
x=xc+r1*cos(q)*xn1+r2*sin(q)*xb1;
y=yc+r1*cos(q)*yn1+r2*sin(q)*yb1;
z=zc+r1*cos(q)*zn1+r2*sin(q)*zb1; 		mt=100;
p=2*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 lissajoustube11.jpg
 
Formule objet Formule texture Rendu
a=3;b=3;c=3;
m1=1;m2=4;m3=2;
p=2*PI*u;
q=2*PI*v;
xc=a*sin(m1*p);
yc=b*sin(m2*p);
zc=c*sin(m3*p);
xt=a*m1*cos(m1*p);
yt=b*m2*cos(m2*p);
zt=c*m3*cos(m3*p);
xn=-yt;
yn=xt;
zn=0;
nn=sqrt(pow(xn,2)+pow(yn,2)+pow(zn,2));
xn1=xn/nn;
yn1=yn/nn;
zn1=zn/nn;
xb=-xt*zt;
yb=-yt*zt;
zb=xt*xt+yt*yt;
nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2));
xb1=xb/nb;
yb1=yb/nb;
zb1=zb/nb;
r1=0.5;r2=0.5;
x=xc+r1*cos(q)*xn1+r2*sin(q)*xb1;
y=yc+r1*cos(q)*yn1+r2*sin(q)*yb1;
z=zc+r1*cos(q)*zn1+r2*sin(q)*zb1; 		mt=100;
p=2*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 lissajoustube12.jpg
 
Formule objet Formule texture Rendu
a=3;b=3;c=3;
m1=1;m2=4;m3=3;
p=2*PI*u;
q=2*PI*v;
xc=a*sin(m1*p);
yc=b*sin(m2*p);
zc=c*sin(m3*p);
xt=a*m1*cos(m1*p);
yt=b*m2*cos(m2*p);
zt=c*m3*cos(m3*p);
xn=-yt;
yn=xt;
zn=0;
nn=sqrt(pow(xn,2)+pow(yn,2)+pow(zn,2));
xn1=xn/nn;
yn1=yn/nn;
zn1=zn/nn;
xb=-xt*zt;
yb=-yt*zt;
zb=xt*xt+yt*yt;
nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2));
xb1=xb/nb;
yb1=yb/nb;
zb1=zb/nb;
r1=0.5;r2=0.5;
x=xc+r1*cos(q)*xn1+r2*sin(q)*xb1;
y=yc+r1*cos(q)*yn1+r2*sin(q)*yb1;
z=zc+r1*cos(q)*zn1+r2*sin(q)*zb1; 		mt=100;
p=2*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 lissajoustube13.jpg

2 - Avec le noeud de trèfle

Formule objet Formule texture Rendu
a=3;b=3;c=3;
p=2*PI*u;
q=2*PI*v;
xc=a*(cos(p)+2*cos(2*p));
yc=b*(sin(p)-2*sin(2*p));
zc=2*c*sin(3*p);
 xv=a*(-sin(p)-4*sin(2*p));
yv=b*(cos(p)-4*cos(2*p));
zv=6*c*cos(3*p);
xa=a*(-cos(p)-8*cos(2*p));
ya=b*(-sin(p)+8*sin(2*p));
za=-18*c*sin(3*p);
xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);		 mt=100;
p=2*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 noeudtrefletube2.jpg

3 - Avec les noeuds toriques

Formule objet
a=5;b=2;c=3;m=2;n=5;
p=2*PI*u;
q=2*PI*v;
xc=(a+b*cos(n*p))*cos(m*p);
yc=(a+b*cos(n*p))*sin(m*p);
zc=c*sin(n*p);
 xv=-b*n*sin(n*p)*cos(m*p)-m*(a+b*cos(n*p))*sin(m*p);
yv=-b*n*sin(n*p)*sin(m*p)+m*(a+b*cos(n*p))*cos(m*p);
zv=c*n*cos(n*p);
xa=-cos(m*p)*(a* m*m+b *(m*m+n*n)* cos(n* p))+2* b* m *n *sin(m *p)* sin(n *p);
ya=-(a* m*m+b *(m*m+n*n)* cos(n *p))* sin(m *p)-2 *b* m* n* cos(m *p)* sin(n* p);
 za=-c*n*n*sin(n*p);
xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);
 
Formule texture Rendu pour a != 0 , m = 2 et n = 5
mt=100;
p=2*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 noeudtorique3.jpg
 
Rendu pour a != 0 , m = 2 et n = 7 Rendu pour a != 0 , m = 3 et n = 8
noeudtorique32.jpg noeudtorique33.jpg

4 - Avec la fenêtre de Viviani

Formule objet Formule texture Rendu
a=2;
p=4*PI*u;
q=2*PI*v;
xc=a*(1+cos(p));
yc=a*sin(p);
zc=2*a*sin(p/2);
 xv=-a*sin(p);
yv=a*cos(p);
zv=a*cos(p/2);
xa=-a*cos(p);
ya=-a*sin(p);
za=-a*sin(p/2)/2;
xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);		 mt=100;
p=4*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 vivianitube4.jpg

5 - Avec les hélices

Formule objet Formule texture Rendu
a=3;c=3;
p=8*PI*u;
q=2*PI*v;
xc=a*cos(p);
yc=a*sin(p);
zc=c*p;
 xv=-a*sin(p);
yv=a*cos(p);
zv=c;
xa=-a*cos(p);
ya=-a*sin(p);
za=0;
xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);		 mt=100;
p=8*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 helicetube0.jpg

6 - Avec la spirale conique de Pappus

Formule objet Formule texture Rendu
a=0.5;t=PI/4;
ct=cos(t);st=sin(t);
p=8*PI*u;
q=2*PI*v;
xc=a*st*p*cos(p);
yc=a*st*p*sin(p);
zc=a*ct*p;
 xv=a*st*(cos(p)-p*sin(p));
yv=a*st*(sin(p)+p*cos(p));
zv=a*ct;
xa=a*st*(-2*sin(p)-p*cos(p));
ya=a*st*(2*cos(p)-p*sin(p));
za=0;
xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);		 mt=100;
p=8*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 pappustube5.jpg

7 - Horoptère

Formule objet Formule texture Rendu
a=3;b=3;
p=20*(u-0.5);
q=2*PI*v;
dc=1+p*p;
xc=2*a/dc;
yc=b*p;
zc=2*a*p/dc;
 xv=-4*a*p/(dc*dc);
yv=b;
zv=2*a*(1-p*p)/(dc*dc);
xa=4*a*(-3*pow(p,4)-2*pow(p,2)+1)/pow(dc,4);
ya=0;
za=2*a*(2*pow(p,5)-4*pow(p,3)-6*p)/pow(dc,4);
xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);		 mt=100;
p=20*(u-0.5);
red=abs(cos(mt*p));
blue=1-red;
green=0;		 horopteretube7.jpg

8 - Avec une spirale logarithmique

Formule objet Formule texture Rendu
a=3;c=3;m=0.02;
p=20*PI*u;
q=2*PI*v;
xc=a*exp(m*p)*cos(p);
yc=a*exp(m*p)*sin(p);
zc=c*exp(m*p);
 xv=a*(m*cos(p)-sin(p))*exp(m*p);
yv=a*(m*sin(p)+cos(p))*exp(m*p);
zv=c*m*exp(m*p);
xa=a*(m*m-m*sin(p)-cos(p)*exp(m*p));
ya=a*(m*m+m*cos(p)-sin(p)*exp(m*p));
za=c*m*m*exp(m*p);
 xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);		 mt=100;
p=20*PI*u;
red=abs(cos(mt*p));
blue=1-red;
green=0;		 spiralogtube8.jpg

9 - 

Formule objet Formule texture Rendu
a=3;c=3;m=2;
p=4*PI*(u-0.5);
q=2*PI*v;
xc=a*p*cos(p);
yc=a*p*sin(p);
zc=c*cos(m*p);
 xv=a*(cos(p)-p*sin(p));
yv=a*(sin(p)+p*cos(p));
zv=-c*m*sin(m*p);
xa=a*(-2*sin(p)-p*cos(p));
ya=a*(2*cos(p)-p*sin(p));
za=-c*m*m*cos(m*p);
xva=yv*za-ya*zv;
yva=zv*xa-za*xv;
zva=xv*ya-xa*yv;
sva=xv*xva+yv*yva+zv*zva;
nv=sqrt(pow(xv,2)+pow(yv,2)+pow(zv,2));
nva=sqrt(pow(xva,2)+pow(yva,2)+pow(zva,2));
xn1=(nv*xa-(sva/nv)*xv)/nva;
yn1=(nv*ya-(sva/nv)*yv)/nva;
zn1=(nv*za-(sva/nv)*zv)/nva;
xb1=xva/nva;
yb1=yva/nva;
zb1=zva/nva;
r=0.5;
x=xc+r*(cos(q)*xn1+sin(q)*xb1);
y=yc+r*(cos(q)*yn1+sin(q)*yb1);
z=zc+r*(cos(q)*zn1+sin(q)*zb1);		 mt=100;
p=4*PI*(u-0.5);
red=abs(cos(mt*p));
blue=1-red;
green=0;		 spiralcostube9.jpg

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