Sine
Cartesian coordinates
x = 50 * t
y = 10 * sin (t * 360)
Rhodonea
Cartesian coordinates
theta = t * 360 * 4
x = 25 + (10-6) * cos (theta) +10 * cos ((10/6-1) * theta)
y = 25 + (10-6) * sin (theta) - 6 * sin ((10/6-1) * theta)
Involute
Cartesian coordinates
r = 1
ang = 360 * t
s = 2 * pi * r * t
x0 = s * cos (ang)
y0 = s * sin (ang)
x = x0 + s * sin (ang)
y = y0-s * cos (ang)
Logarithmic
Cartesian coordinates
z = 0
x = 10 * t
y = log (10 * t +0.0001)
Double Arc Epicycloid
Cartesian coordinate
l = 2.5
b = 2.5
x = 3 * b * cos (t * 360) + l * cos (3 * t * 360)
Y = 3 * b * sin (t * 360) + l * sin (3 * t * 360)
Star Southbound
Cartesian coordinate
a = 5
x = a * (cos (t * 360)) ^ 3
y = a * (sin (t * 360)) ^ 3
Leaf
Cartesian coordinates
a = 10
x = 3 * a * t / (1 + (t ^ 3))
y = 3 * a * (t ^ 2) / (1 + (t ^ 3))
Helix
Cartesian coordinates
x = 4 * cos (t * (5 * 360))
y = 4 * sin (t * (5 * 360))
z = 10 * t
Parabolic
Cartesian coordinates
x = (4 * t)
y = (3 * t) + (5 * t ^ 2)
z = 0
Eliptical Helix
Cartesian coordinates
X = 4 * cos (t * 3 * 360)
y = 2 * sin (t * 3 * 360)
z = 5
Disc Spiral 1
Cartesian coordinates
/* Inner Diameter
d = 10
/* Pitch
p = 5
/* Revolutions
r = 5
/* Height; use 0 for a 2D curve
h = 0
x = ((d/2 + p * r * t) * cos ((r * t) * 360))
y = ((d / 2 + p * r * t) * sin ((r * t) * 360))
z = t * h
Butterfly
a=cos(t*360)
b=sin(t*360)
c=cos(4*t*360)
d=(sin((1/12)*t*360))^5
x=b*(exp(a)-2*c+d)
y=a*(exp(a)-2*c+d)
Fish
a = cos (t * 360)
b = sin (t * 360)
/* As "c" increases the fish gets fatter until it transforms into a figure 8.
c = 10
x = (C*a-20*((b)^2)/1.5)
y = c * a * b
Cappa
/* "c" is a scaling variable
c=20
/* Revolutions
r=1
/* Height
h=0
x=c*cos(t*r*360)*sin(t*r*360)
y=c*cos(t*r*360)
z=t*h
Star
/* "a" & "b" are scaling variables
a=2
b=2
/* If, r=2/3 ----> astroid
/* If, r=2 ----> ellipse; when a=b, its a circle
/* r cannot equal 1
r=2/3
x=a*(cos(t*360))^(2/r)
y=b*(sin(t*360))^(2/r)
z=0
Bicorn
/* "c" is a scaling variable.
c=5
a=cos(t*360)
b=sin(t*360)
x=c*a
y=c*(a^2)*(2+a)/(3+b^2)
Talbots
/* "c" is a scaling variable.
c=10
a=cos(t*360)
b=sin(t*360)
x=C*a*(1+exp(2)*(b^2))
y=C*b*(1+exp(2)*(b^2))
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