Geometry

Overview


Curves


A simple way to plot a curve is with the use of the $from function, which will generate a list of numbers between two given endpoints.

The following code generates 100 points between 1 and 10. 


let points = $from(1,10,100);

The following code generates 100 x values between 1 and 10, and then creates a point with the given x value and a y value determined by the function f. 


let points = $from(1,10,100).map(p=>{
  return {
    x:p,
    y:f(x)
  }											
});

Cycloid


{% y(t) = (at - b sin(t), a - b cos(t)) %}
In order to properly chart this graph, we need the x values to be equally spaced. The interpolation library provides a function that takes a list of x and y values, and creates a new list with equally spaced x values and interpolated y values. 


let in1 = await import('/lib/interpolation/v1.0.0/interpolation.mjs');
let a = 1;
let b = 1;

let points = $from(1,10,1000).map(t=>{
  return {
    x: a*t - b*Math.sin(t),
    y: a - b*Math.cos(t)
  }											
});

let npoints = in1.equalSpaced(points.map(p=>[p.x,p.y]), 100);