sarmal.art
Back to Curve Catalog

Epicycloid (n=3)

Import

import { epicycloid3 } from "@sarmal/core/curves/epicycloid3";

A 3-pointed star shape created by a point on a circle rolling around the outside of another circle.

Equation

x=4cos⁡(t)−cos⁡(4t)y=4sin⁡(t)−sin⁡(4t)\begin{aligned}x = 4\cos(t) - \cos(4t) &\\y = 4\sin(t) - \sin(4t) &\end{aligned}

Parameters

Family Roulette
Period 2π
Default Speed 0.75
Skeleton static

Key Features

  • 3-pointed star shape
  • Created by exterior rolling circle
  • Classic epicycloid with n=3

Usage

Standard

import { createSarmal } from "@sarmal/core";
import { epicycloid3 } from "@sarmal/core/curves/epicycloid3";

const canvas = document.getElementById("spinner") as HTMLCanvasElement;
const sarmal = createSarmal(canvas, epicycloid3);

React

import { Sarmal } from "@sarmal/react";
import { epicycloid3 } from "@sarmal/core/curves/epicycloid3";

function App() {
  return <Sarmal curve={epicycloid3} />;
}