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Epitrochoid

Import

import { epitrochoid7 } from "@sarmal/core/curves/epitrochoid7";

A roulette tracing 7 lobes with an animated distance parameter that creates organic, undulating motion.

Equation

x=7cos⁡(t)−dcos⁡(7t)y=7sin⁡(t)−dsin⁡(7t)where d=1.0+0.55sin⁡(0.5t)\begin{aligned}x = 7\cos(t) - d\cos(7t) &\\y = 7\sin(t) - d\sin(7t) &\\\text{where } d = 1.0 + 0.55\sin(0.5t) &\end{aligned}

Parameters

Family Roulette
Period 2π
Default Speed 1.4
Skeleton custom (stabilized)

Key Features

  • 7 lobes with flower-like symmetry
  • Dynamic distance parameter creates organic motion
  • Custom skeleton uses fixed d=1.275 for stability

Usage

Standard

import { createSarmal } from "@sarmal/core";
import { epitrochoid7 } from "@sarmal/core/curves/epitrochoid7";

const canvas = document.getElementById("spinner") as HTMLCanvasElement;
const sarmal = createSarmal(canvas, epitrochoid7);

React

import { Sarmal } from "@sarmal/react";
import { epitrochoid7 } from "@sarmal/core/curves/epitrochoid7";

function App() {
  return <Sarmal curve={epitrochoid7} />;
}