lineSegmentIntersections method

List<Vector2> lineSegmentIntersections(
  1. LineSegment line, {
  2. double epsilon = double.minPositive,
})

Returns the locus of points in which the provided line segment intersect the circle.

This can be an empty list (if they don't intersect), one point (if the line is tangent) or two points (if the line is secant).

Implementation

List<Vector2> lineSegmentIntersections(
  LineSegment line, {
  double epsilon = double.minPositive,
}) {
  double sq(double x) => pow(x, 2).toDouble();

  final cx = absoluteCenter.x;
  final cy = absoluteCenter.y;

  final point1 = line.from;
  final point2 = line.to;

  final delta = point2 - point1;

  final A = sq(delta.x) + sq(delta.y);
  final B = 2 * (delta.x * (point1.x - cx) + delta.y * (point1.y - cy));
  final C = sq(point1.x - cx) + sq(point1.y - cy) - sq(radius);

  final det = B * B - 4 * A * C;
  final result = <Vector2>[];
  if (A <= epsilon || det < 0) {
    return [];
  } else if (det == 0) {
    final t = -B / (2 * A);
    result.add(Vector2(point1.x + t * delta.x, point1.y + t * delta.y));
  } else {
    final t1 = (-B + sqrt(det)) / (2 * A);
    final i1 = Vector2(
      point1.x + t1 * delta.x,
      point1.y + t1 * delta.y,
    );

    final t2 = (-B - sqrt(det)) / (2 * A);
    final i2 = Vector2(
      point1.x + t2 * delta.x,
      point1.y + t2 * delta.y,
    );

    result.addAll([i1, i2]);
  }
  result.removeWhere((v) => !line.containsPoint(v));
  return result;
}