数学图形(1.31) 圆环

若干种环圈的画法:

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biquartic

#http://www.mathcurve.com/courbes2d/biquartic/biquartic.shtml
vertices = 1000
t = from 0 to (2*PI)
r = 10

x = sin(3*t)*cos(t)
y = pow(sin(3*t)*sin(t), 2)

Cornoid

#http://www.mathcurve.com/courbes2d/cornoid/cornoid.shtml

vertices = 1000
t = from 0 to (2*PI)
r = 10

x = r*cos(t)*cos(2*t)
y = r*sin(t)*(2 + cos(2*t))

Dipole curve

#http://www.mathcurve.com/courbes2d/clairaut/clairaut.shtml
#(x^2 + y^2)^3 = (a^4)*(x^2)

vertices = 10000
t = from (-PI) to (PI)
r = 10

a = 10

p = a*sqrt(abs(cos(t)))

x = p*cos(t)
y = p*sin(t)

lemniscate

#http://www.mathcurve.com/courbes2d/lemniscate/lemniscate.shtml
vertices = 1000
t = from 0 to (2*PI)
r = 10
s = sin(t)
c = cos(t)
x = r*s/(1+c*c)
y = r*s*c/(1+c*c)

trisectrix

#http://www.mathcurve.com/courbes2d/trisectricedeceva/trisectricedeceva.shtml
vertices = 1000

t = from 0 to (2*PI)
a = 10

p = a*(1 + 2*cos(2*t))

x = p*cos(t)
y = p*sin(t)

 

#http://www.mathcurve.com/courbes2d/sextic/sexticrationnelle.shtml
vertices = 1000

t = from 0 to (2*PI)
a = 10

x = 2*sin(2*t)
y = cos(t) + cos(3*t)

x = x*a
y = y*a

#http://www.mathcurve.com/courbes2d/sextic/sexticrationnelle.shtml
vertices = 1000

t = from 0 to (2*PI)
a = 10

x = pow(cos(t), 3)/(2*pow(cos(t), 3) - 2*cos(t) + 1)
y = sin(2*t)*pow(sin(t/2), 2)/(2*pow(cos(t), 3) - 2*cos(t) + 1)

x = x*a
y = y*a