Last weekend, while practicing geometry node system in Blender, I created a bunch of procedural curves / shapes. You can download the blend file from my Gumroad page.
This post continues to document more curves in addition to what we covered in Set 1 (A-D), Set 2 (I-R) & Set 4 (S-Z).
You can find the actual formulas and definition from https://www.matematica.pt/en/useful/list-curves.php or https://en.wikipedia.org/
Below is the collection of nodes configuration and corresponding renders.
Astroid
Curve Equation
x2/3 + y2/3 = a2/3
Bicorn
Curve Equation
y2(a2 - x2) = (x2 + 2ay - a2)2
Cardioid
Curve Equation
(x2 + y2 - 2ax)2 = 4a2 (x2 + y2)
Conchoid
Curve Equation
(x - b)2 (x2 + y2) - a2x2 = 0
Catenary
Curve Equation
y = a cosh(x/a)
Circle
Curve Equation
x2 + y2 = a2
Cycloid
Curve Equation
x = at - h sin(t)
y = a - h cos(t)
Cayley’s Sextic
Curve Equation
4(x2 + y2 - ax)3 = 27a2 (x2 + y2)2
Cissoid of Diocles
Curve Equation
y2 = x3/(2a - x)
Devil’s Curve
Curve Equation
y4 - x4 + ay2 + bx2 = 0
