ImplicitSurfaceNetwork/surface_integral/include/polygon_winding_number.h

// polygon_winding.h
#pragma once

#include <vector>
#include <Eigen/Dense>
#include <string>
#include <iostream>

// Type aliases for convenience
using Point2d = Eigen::Vector2d;
using PolygonRing = std::vector<Point2d>;

/**
 * @brief Determines if a point is inside a polygon with holes using the non-zero winding rule.
 *
 * @param P The query point.
 * @param outer_ring The outer boundary of the polygon (should be counter-clockwise).
 * @param holes A list of inner rings (holes), each should be clockwise.
 * @return true if the point is inside (including boundary), false otherwise.
 */
bool point_in_polygon_with_holes(
    const Point2d& P,
    const PolygonRing& outer_ring,
    const std::vector<PolygonRing>& holes
);

/**
 * @brief Computes the winding number of a point with respect to a single closed ring.
 *
 * @param P The query point.
 * @param ring A closed polygonal ring (at least 3 vertices).
 * @return The winding number (positive for counter-clockwise turns).
 */
int compute_winding_number_ring(const Point2d& P, const PolygonRing& ring);


/**
 * @brief Validates the polygon input for correct orientation and sufficient vertices.
 *
 * @param query_point The query point (for logging purposes).
 * @param outer_ring The outer boundary ring.
 * @param holes The list of hole rings.
 * @param context Optional context string for logging.
 * @return true if valid, false otherwise.
 */
bool validate_polygon_input(
    const Point2d& query_point,
    const PolygonRing& outer_ring,
    const std::vector<PolygonRing>& holes,
    const std::string& context = ""
);


/**
 * @brief Computes the signed area of a polygon ring.
 *
 * @param ring The polygon ring (closed).
 * @return The signed area (positive if CCW, negative if CW).
 */
double compute_ring_area(const PolygonRing& ring);