circleIntersections method

List<Vector2> circleIntersections(
  1. Vector2 center,
  2. double radius
)

Returns the points where this segment crosses the edge of the circle with the given center and radius.

This can be an empty list (if they don't intersect), one point (if the segment only crosses the edge once) or two points (if the segment is secant, or tangent in which case the two points are equal). If from lies on the edge of the circle it doesn't count as an intersection.

Implementation

List<Vector2> circleIntersections(Vector2 center, double radius) {
  // A point on a line is `from + t*(to - from)`. We're trying to solve the
  // equation `‖point - center‖² == radius²`. Or, denoting `Δ₂₁ = to - from`
  // and `Δ₁₀ = from - center`, the equation is `‖t*Δ₂₁ + Δ₁₀‖² == radius²`.
  // Expanding the norm, this becomes a square equation in `t`:
  // `t²Δ₂₁² + 2tΔ₂₁Δ₁₀ + Δ₁₀² - radius² == 0`.
  _delta21
    ..setFrom(to)
    ..sub(from);
  _delta10
    ..setFrom(from)
    ..sub(center);
  final a = _delta21.length2;
  final b = 2 * _delta21.dot(_delta10);
  final c = _delta10.length2 - radius * radius;

  return solveQuadratic(a, b, c)
      .where((t) => t > 0 && t <= 1)
      .map((t) => from.clone()..addScaled(_delta21, t))
      .toList();
}