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Awesome Procedural Curves Using Geometry Node in Blender – Set 1 (A-D)

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

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