L'éditeur de formules de Carrara Studio - Page 16

Rubans

1 - Avec les courbes de Lissajous

Formule objet	Formule texture	Rendu
a=3;b=3;c=3; m1=1;m2=2;m3=3; e=0.0001; p=2*(PI-e)*u+e; q=2*(v-0.5); xc=a*sin(m1*p); yc=b*sin(m2*p); zc=c*sin(m3*p); xv=a*m1*cos(m1*p); yv=b*m2*cos(m2*p); zv=c*m3*cos(m3*p); xa=-a*m1*m1*sin(m1*p); ya=-b*m2*m2*sin(m2*p); za=-c*m3*m3*sin(m3*p); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.2*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

Formule objet	Formule texture	Rendu
a=3;b=3;c=3; m1=1;m2=4;m3=3; e=0.0001; p=2*(PI-e)*u+e; q=2*(v-0.5); xc=a*sin(m1*p); yc=b*sin(m2*p); zc=c*sin(m3*p); xv=a*m1*cos(m1*p); yv=b*m2*cos(m2*p); zv=c*m3*cos(m3*p); xa=-a*m1*m1*sin(m1*p); ya=-b*m2*m2*sin(m2*p); za=-c*m3*m3*sin(m3*p); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.2*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

Formule objet	Formule texture	Rendu
a=3;b=3;c=3; m1=1;m2=4;m3=2; e=0.0001; p=2*(PI-e)*u+e; q=2*(v-0.5); xc=a*sin(m1*p); yc=b*sin(m2*p); zc=c*sin(m3*p); xv=a*m1*cos(m1*p); yv=b*m2*cos(m2*p); zv=c*m3*cos(m3*p); xa=-a*m1*m1*sin(m1*p); ya=-b*m2*m2*sin(m2*p); za=-c*m3*m3*sin(m3*p); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.2*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

2 - Avec le noeud de trèfle

Formule objet	Formule texture	Rendu
a=3;b=3;c=3; p=2*PI*u; q=2*(v-0.5); 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=a*(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=-c*18*sin(3*p); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.5*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

3 - Avec le noeud de huit

Formule objet	Formule texture	Rendu
a=1;b=1;c=1; p=2*PI*u; q=2*(v-0.5); xc=a*(3*cos(p)+5*cos(3*p)); yc=b*(3*sin(p)+5*sin(3*p)); zc=c*(2*sin(5*p/2)*sin(3*p)+2*sin(4*p)-2*sin(6*p)); xv=a*(-3*sin(p)-15*sin(3*p)); yv=b*(3*cos(p)+15*cos(3*p)); zv=c*(8*cos(4*p)-12*cos(6*p)-(1/2)*sin(p/2)+(11/2)*sin(11*p/2)); xa=a*(-3*cos(p)-45*cos(3*p)); ya=b*(-3*sin(p)-45*sin(3*p)); za=c*(-(1/4)*cos(p/2)+(121/4)*cos(11*p/2)-32*sin(4*p)+72*sin(6*p)); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.2*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

4 - Avec la fenêtre de Viviani

Formule objet	Formule texture	Rendu
a=2; p=4*PI*u; q=2*(v-0.5); 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/2)*sin(p/2); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.5*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

5 - Avec une hélice

Formule objet	Formule texture	Rendu
a=2;c=0.5; p=8*PI*u; q=2*(v-0.5); 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; xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.2*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

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*(v-0.5); 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; xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.2*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

7 - 

e2 = 0.05

m = 2	m = 3	m = 4	m = 5

e2 = 0.2

m = 2	m = 3	m = 4	m = 5

8 - Avec une spirale logarithmique

Formule objet	Formule texture	Rendu
a=3;c=3;m=0.02; p=20*PI*u; q=2*(v-0.5); xc=a*exp(m*p)*cos(p); yc=a*exp(m*p)*sin(p); zc=c*exp(m*p); xv=a*(-sin(p)+m*cos(p))*exp(m*p); yv=a*(cos(p)+m*sin(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); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=0.2*q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

9 - 

Formule objet	Formule texture	Rendu
a=3;c=3;m=2;n=3; p=2*PI*u; q=2*(v-0.5); xc=a*p*cos(p); yc=a*p*sin(p); zc=c*(cos((m+n)*p)+cos((m-n)*p)); xv=a*(cos(p)-p*sin(p)); yv=a*(sin(p)-p*cos(p)); zv=c*(-(m+n)*sin((m+n)*p)-(m-n)*sin((m-n)*p)); xa=a*(-2*sin(p)-p*cos(p)); ya=a*(2*cos(p)-p*sin(p)); za=c*(-pow(m+n,2)*cos((m+n)*p)-pow(m-n,2)*cos((m-n)*p)); xb=yv*za-ya*zv; yb=zv*xa-za*xv; zb=xv*ya-xa*yv; nb=sqrt(pow(xb,2)+pow(yb,2)+pow(zb,2)); xb1=xb/nb; yb1=yb/nb; zb1=zb/nb; r=q; x=xc+r*xb1; y=yc+r*yb1; z=zc+r*zb1;	mt=100; p=2*PI*u; red=abs(cos(mt*p)); blue=1-red; green=0;

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