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

x^{2/3}+ y^{2/3}= a^{2/3}

## Bicorn

#### Curve Equation

y^{2}(a^{2}- x^{2}) = (x^{2}+ 2ay - a^{2})^{2}

## Cardioid

#### Curve Equation

(x^{2}+ y^{2}- 2ax)^{2}= 4a^{2}(x^{2}+ y^{2})

## Conchoid

#### Curve Equation

(x - b)^{2}(x^{2}+ y^{2}) - a^{2}x^{2}= 0

## Catenary

#### Curve Equation

y = a cosh(x/a)

## Circle

#### Curve Equation

x^{2}+ y^{2}= a^{2}

## Cycloid

#### Curve Equation

x = at - h sin(t)

y = a - h cos(t)

## Cayley’s Sextic

#### Curve Equation

4(x^{2}+ y^{2}- ax)^{3}= 27a^{2}(x^{2}+ y^{2})^{2}

## Cissoid of Diocles

#### Curve Equation

y^{2}= x^{3}/(2a - x)

## Devil’s Curve

#### Curve Equation

y^{4}- x^{4}+ ay^{2}+ bx^{2}= 0