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Hypotrochoid Spirograph

Posted on July 18, 2012

Video Tutorial to Build a Spirograph based on Hypotrochoid Geometry
This tutorial was inspired by the project of Frances Fox one of my student’s at Pratt Institute in the Spring of 2012, who’s project was based on the art of Cristian Boian.

PartI : Model & Expression Setup

Part II : nParticle Setup

Part III : Paint Effects & Asset Creation

Part IV : Expressions to Create the Hypotrochoid Rose

Part V : Expression to even out the particle trail

Download Project Files


Wolfram Mathworld Hypotrochoid

Wolfram Mathworld Hypotrochoid Rose


Keep circleB tangent to circle A as the radii of each change

circleB.translateX = makeNurbCircleA.radius-makeNurbCircleB.radius

Make circleB automatically rotate the proper amount as it rolls around the inside of circleA

circleB.rotateY = -1*circleA.rotateY*makeNurbCircleA.radius/makeNurbCircleB.radius

Formulas to calculate radii of hypotrochoid relatve to an attribute “n”, in order to create a “rose”

makeNurbCircleA.radius = (2*AST_hypotrochoid_rose.n*curveH.scaleX)/(AST_hypotrochoid_rose.n+1)

makeNurbCircleB.radius = ((AST_hypotrochoid_rose.n-1)*curveH.scaleX)/(AST_hypotrochoid_rose.n+1)

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