plot an involute curve in javascript

To plot an involute curve in javascript, you will need to first understand the mathematical definition of the curve. An involute curve is a curve traced by a point on a taut string as the string is unwound from a stationary circle.

To plot this curve, we can use parametric equations, where the x and y coordinates of the curve are defined by functions of a single parameter t.

Here is an example code snippet that plots an involute curve using the p5.js library in javascript:

index.tsx
let r = 50; // radius of the circle
let a = 0; // starting angle
let t = 0; // starting parameter t
let dt = 0.1; // increment for parameter t
let scaleFactor = 1; // scaling factor for the curve

function setup() {
  createCanvas(400, 400);
  angleMode(DEGREES);
}

function draw() {
  background(220);

  translate(width / 2, height / 2);
  scale(scaleFactor);

  // draw the circle
  noFill();
  stroke(0);
  ellipse(0, 0, r * 2, r * 2);

  // calculate the x and y coordinates of the curve
  let x = r * (cos(a) + a * sin(a));
  let y = r * (sin(a) - a * cos(a));

  // draw a point at the x and y coordinates
  noStroke();
  fill(255, 0, 0);
  ellipse(x, y, 5, 5);

  // draw a line from the center of the circle to the point on the curve
  stroke(0, 0, 255);
  line(0, 0, x, y);

  // update the angle and parameter t
  a += dt;
  t += dt;

  // increase the scaling factor to make the curve larger
  scaleFactor += 0.005;
}
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In this code, we start by defining the radius of the circle, the starting angle, the starting parameter t, and the increment for the parameter t. We also define a scaling factor to make the curve larger over time.

In the setup() function, we create a canvas and set the angle mode to degrees.

In the draw() function, we first set up the canvas by translating to the center and scaling by the scaling factor. We then draw the circle using the ellipse() function, and calculate the x and y coordinates of the point on the curve using the parametric equations for the involute curve.

We then draw a point at the x and y coordinates and a line from the center of the circle to the point on the curve using the ellipse() and line() functions.

Finally, we update the angle and parameter t, and increase the scaling factor to make the curve larger.

This code will produce a visual representation of an involute curve in javascript using the p5.js library.