[Helper] Intersection between 2 Circles

[discoleo]

Helper Function

Intersection between 2 Circles:

• will be useful for radial arrows and other radial structures;

  solveCircleIntersection = function(mid1, mid2, r1, r2, digits=4, debug=TRUE) {
  xp = mid1[[1]]; yp = mid1[[2]];
  xc = mid2[[1]]; yc = mid2[[2]];
  d  = r1; r = r2;
  xs = xp + xc;
  xd = xp - xc; xd2 = xs*xd;
  yd = yp - yc;
  # P2:
  a  = 4*(xd^2 + yd^2);
  b1 = - 4*(xs^3 - 4*xp*xc*xs + yd^2*xs + (r^2 - d^2)*xd);
  b0 = d^4 + r^4 + xc^4 + xp^4 + yp^4 + yc^4 - 4*yp^3*yc - 4*yp*yc^3 + 6*yp^2*yc^2 +
      + 2*xp^2*yp^2 + 2*xp^2*yc^2 + 2*xc^2*yp^2 + 2*xc^2*yc^2 - 2*xp^2*xc^2 +
      + 2*(r^2 - d^2)*xd2 - 2*(r^2 + d^2)*yd^2 +
      - 4*yp*yc*xp^2 - 4*yp*yc*xc^2 - 2*d^2*r^2;
  # Det:
  D = b1^2 - 4*a*b0;
  if(debug) print(c(a, b1, b0, D));
  if(round(D, digits) == 0) D = 0;
  if(D < 0) return(NULL);
  D = sqrt(D);
  # Sol:
  x = ( - b1 + c(-D, D)) / (2*a);
  y =  yp^2 - yc^2 + xd2 - 2*xd*x + r^2 - d^2;
  div = 2*yd; # TODO: yp == yc;
  y = y / div;
  sol = data.frame(x=x, y=y);
  return(sol);
  }

Tests

• Note: more tests are needed;

  ### Circle Intersections
  midc = c(2,3)
  alpha = pi/5
  r = 3/2
  midp = c(midc[[1]] + r*cos(alpha), midc[[2]] + r*sin(alpha));
  p = solveCircleIntersection(midp, midc, 0.5, r)
  plot.base()
  shape::plotcircle(r, mid=midc)
  shape::plotcircle(0.5, mid=midp, lcol="red")
  points(p$x, p$y, col="green")

[DarianFlorianVoda]

Added.