两个圆连线的切点

gistfile1.txt

/**
 * r: circle -> r, ellipse -> rx, ry 
*/
export const getCenterPoint = (x, y, r) => (r.rx ? {
  x: x + r.rx,
  y: y + r.ry,
  rx: r.rx,
  ry: r.ry,
} : {
  x: x + r,
  y: y + r,
  r: r,
});

export const getCircleTangentPoint = (from, to) => {
  var { x: fromX, y: fromY } = from;
  var { x: toX, y: toY, r } = to;
  var theta;
  var x;
  var y;
  if (fromY > toY) {
    theta = Math.atan2(fromX - toX, fromY - toY);
    y = Math.cos(theta) * r;
    x = Math.sin(theta) * r;
  } else {
    theta = Math.atan2(fromY - toY, fromX - toX);
    x = Math.cos(theta) * r;
    y = Math.sin(theta) * r;
  }
  return {
    x: toX + x,
    y: toY + y,
  };
};

export const getEllipseTangentPoint = (from, to) => {
  var { x: fromX, y: fromY } = from;
  var { x: toX, y: toY, rx, ry } = to;
  var x;
  var y;
  var distX;
  var distY;
  var g;

  distX = fromX - toX;
  distY = fromY - toY;
  g = distY / distX;
  x = (fromX < toX ? -1 : 1) * rx * ry / Math.sqrt(ry * ry + g * g * rx * rx);
  y = g * x;
  return {
    x: toX + x,
    y: toY + y,
  };
};

export const getTangentPoints = ([x1, y1, x2, y2, r1, r2, tension=30]) => {
  // p1 ---> p2
  var p1 = typeof r1 === 'object' ?
    getEllipseTangentPoint({
      ...getCenterPoint(x2, y2, r2),
    }, {
      ...getCenterPoint(x1, y1, r1),
    }) : getCircleTangentPoint({
      ...getCenterPoint(x2, y2, r2),
    }, {
      ...getCenterPoint(x1, y1, r1),
    });
  var p2 = typeof r2 === 'object' ?
    getEllipseTangentPoint({
      ...getCenterPoint(x1, y1, r1)
    }, {
      ...getCenterPoint(x2, y2, r2)
    }) : getCircleTangentPoint({
      ...getCenterPoint(x1, y1, r1)
    }, {
      ...getCenterPoint(x2, y2, r2)
    });
  var dx = (p1.x + p2.x) / 2;
  var dy = (p1.y + p2.y) / 2;
  var dist = ((x, y) => Math.sqrt(x * x + y * y))
                 (Math.abs(p1.x - p2.x), Math.abs(p1.y - p2.y));
  dx = dx + dist / tension;
  dy = dy - dist / tension;
  return [p1.x, p1.y, dx, dy, p2.x, p2.y];
};