How can I find the midpoint of an arc with JavaScript?-CodePudding

I need to find the midpoint of the arc USING JavaScript .

I want to find M in terms of the following information:

A.X and A.Y, the coordinates of A B.X and B.Y, the coordinates of B Radius, the radius of the arc C.X and C.Y, the center of the arc How do I compute the coordinates of M?

I have a problem with the x sign

var a = {x:x1,y:y1}
  var b = {x:x2,y:y2}
  var c = {x:cx,y:cy}


  var theta1 = Math.atan(a.y / a.y);
  var theta2 = Math.atan(b.y / b.x)

  var theta = (theta1   theta2) / 2;

  var mx = r * Math.cos(theta);
  var my = r * Math.sin(theta);


  var positive
  if (cx > 0) {
    positive = 1
  } else {
    positive = -1
  }
  var midx = positive * (Math.abs(mx)   Math.abs(cx))
  var midy = my   cy
  writeBlock(cx, cy);
  writeBlock(mx, my, x1, y1, x2, y2);

CodePudding user response：

Here's how I would do it, using a unit circle to make things simple:

const A = { x: 0, y: 1 };
const B = { x: 1, y: 0 };
const C = { x: 0, y: 0 };

// get A and B as vectors relative to C
const vA = { x: A.x - C.x, y: A.y - C.y };
const vB = { x: B.x - C.x, y: B.y - C.y };

// angle between A and B
const angle = Math.atan2(vA.y, vA.x) - Math.atan2(vB.y, vB.x);

// half of that
const half = angle / 2;

// rotate point B by half of the angle
const s = Math.sin(half);
const c = Math.cos(half);

const xnew = vB.x * c - vB.y * s;
const ynew = vB.x * s   vB.y * c;

// midpoint is new coords plus C
const midpoint = { x: xnew   C.x, y: ynew   C.y };

console.log(midpoint); // { x: sqrt2 / 2, y: sqrt2 / 2 }

Please note that this assumes that point B is always "after" A (going clockwise) and it always assumes the arc is defined clockwise.

CodePudding user response：

Sum CA and CB vectors, making bisector D

Normalize bisector dividing by its length

Multiply normalized bisector by R

Add result to C to get M

Dx = A.x   B.x - 2*C.x
Dy = A.y   B.y - 2*C.y
Len = sqrt(Dx*Dx   Dy*Dy)
f = R / Len
Mx = C.x   Dx * f
My = C.y   Dy * f

(doesn't work for 180 degrees arc, for that case just rotate Dx by 90)