/**
 * Determine the relative orientation of three points in two-dimensional space.
 * The result is also an approximation of twice the signed area of the triangle defined by the three points.
 * This method is fast - but not robust against issues of floating point precision. Best used with integer coordinates.
 * Adapted from https://github.com/mourner/robust-predicates
 *
 * @param a - An endpoint of segment AB, relative to which point C is tested
 * @param b - An endpoint of segment AB, relative to which point C is tested
 * @param c - A point that is tested relative to segment AB
 *
 * @returns The relative orientation of points A, B, and C
 *          A positive value if the points are in counter-clockwise order (C lies to the left of AB)
 *          A negative value if the points are in clockwise order (C lies to the right of AB)
 *          Zero if the points A, B, and C are collinear.
 */
export declare function orient2dFast(a: Canvas.Point, b: Canvas.Point, c: Canvas.Point): number;

/**
 * Quickly test whether the line segment AB intersects with the line segment CD.
 * This method does not determine the point of intersection, for that use lineLineIntersection
 *
 * @param a - The first endpoint of segment AB
 * @param b - The second endpoint of segment AB
 * @param c - The first endpoint of segment CD
 * @param d - The second endpoint of segment CD
 *
 * @returns Do the line segments intersect?
 */
export declare function lineSegmentIntersects(
  a: Canvas.Point,
  b: Canvas.Point,
  c: Canvas.Point,
  d: Canvas.Point,
): boolean;

export interface LineIntersection {
  /** The x-coordinate of intersection */
  x: number;

  /** The y-coordinate of intersection */
  y: number;

  /** The vector distance from A to B on segment AB */
  t0: number;

  /** The vector distance from C to D on segment CD */
  t1?: number | undefined;
}

interface LineIntersectionOptions {
  /**
   * Return the optional vector distance from C to D on CD
   * @defaultValue `false`
   */
  t1?: boolean;
}

/**
 * An internal helper method for computing the intersection between two infinite-length lines.
 * Adapted from http://paulbourke.net/geometry/pointlineplane/
 *
 * @param a       - The first endpoint of segment AB
 * @param b       - The second endpoint of segment AB
 * @param c       - The first endpoint of segment CD
 * @param d       - The second endpoint of segment CD
 * @param options - Options which affect the intersection test
 *
 * @returns An intersection point, or null if no intersection occurred
 */
export declare function lineLineIntersection(
  a: Canvas.Point,
  b: Canvas.Point,
  c: Canvas.Point,
  d: Canvas.Point,
  options?: LineIntersectionOptions,
): LineIntersection | null;

/**
 * An internal helper method for computing the intersection between two finite line segments.
 * Adapted from http://paulbourke.net/geometry/pointlineplane/
 *
 * @param a       - The first endpoint of segment AB
 * @param b       - The second endpoint of segment AB
 * @param c       - The first endpoint of segment CD
 * @param d       - The second endpoint of segment CD
 * @param epsilon - A small epsilon which defines a tolerance for near-equality
 *                  (default: `1e-8`)
 *
 * @returns An intersection point, or null if no intersection occurred
 */
export declare function lineSegmentIntersection(
  a: Canvas.Point,
  b: Canvas.Point,
  c: Canvas.Point,
  d: Canvas.Point,
  epsilon?: number,
): LineIntersection | null;

export interface LineCircleIntersection {
  /** Is point A inside the circle? */
  aInside: boolean;

  /** Is point B inside the circle? */
  bInside: boolean;

  /** Is the segment AB contained within the circle? */
  contained: boolean;

  /** Is the segment AB fully outside the circle? */
  outside: boolean;

  /** Is the segment AB tangent to the circle? */
  tangent: boolean;

  /** Intersection points: zero, one, or two */
  intersections: [Canvas.Point?, Canvas.Point?];
}

/**
 * Determine the intersection between a candidate wall and the circular radius of the polygon.
 *
 * @param a       - The initial vertex of the candidate edge
 * @param b       - The second vertex of the candidate edge
 * @param center  - The center of the bounding circle
 * @param radius  - The radius of the bounding circle
 * @param epsilon - A small tolerance for floating point precision
 *                  (default: `1e-8`)
 *
 * @returns The intersection of the segment AB with the circle
 */
export declare function lineCircleIntersection(
  a: Canvas.Point,
  b: Canvas.Point,
  center: Canvas.Point,
  radius: number,
  epsilon?: number,
): LineCircleIntersection;

/**
 * Identify the point closest to C on segment AB
 *
 * @param c - The reference point C
 * @param a - Point A on segment AB
 * @param b - Point B on segment AB
 *
 * @returns The closest point to C on segment AB
 */
export declare function closestPointToSegment(c: Canvas.Point, a: Canvas.Point, b: Canvas.Point): Canvas.Point;

/**
 * Determine the points of intersection between a line segment (p0,p1) and a circle.
 * There will be zero, one, or two intersections
 * See https://math.stackexchange.com/a/311956
 *
 * @param p0      - The initial point of the line segment
 * @param p1      - The terminal point of the line segment
 * @param center  - The center of the circle
 * @param radius  - The radius of the circle
 * @param epsilon - A small tolerance for floating point precision
 *                  (default: `0`)
 */
export declare function quadraticIntersection(
  p0: Canvas.Point,
  p1: Canvas.Point,
  center: Canvas.Point,
  radius: number,
  epsilon?: number,
): [Canvas.Point?, Canvas.Point?];

declare type Points = Canvas.Point[] | number[];

/**
 * Calculate the centroid non-self-intersecting closed polygon.
 * See https://en.wikipedia.org/wiki/Centroid#Of_a_polygon.
 *
 * @param points    - The points of the polygon
 * @returns         - The centroid of the polygon
 */
export declare function polygonCentroid(points: Points): Canvas.Point;

/**
 * Test whether the circle given by the center and radius intersects the path (open or closed).
 *
 * @param points    - The points of the path
 * @param close     - If true, the edge from the last to the first point is tested
 * @param center    - The center of the circle
 * @param radius    - The radius of the circle
 * @returns         - Whether the circle intersect the path
 */
export declare function pathCircleIntersects(
  points: Points,
  close: boolean,
  center: Canvas.Point,
  radius: number,
): boolean;

/**
 * Test whether two circles (with position and radius) intersect.
 *
 * @param x0        - x center coordinate of circle A.
 * @param y0        - y center coordinate of circle A.
 * @param r0        - radius of circle A.
 * @param x1        - x center coordinate of circle B.
 * @param y1        - y center coordinate of circle B.
 * @param r1        - radius of circle B.
 * @returns         - True if the two circles intersect, false otherwise.
 */
export function circleCircleIntersects(x0: number, y0: number, r0: number, x1: number, y1: number, r1: number): boolean;