OpenNest-Engines/OpenNest.Engine.Qwen38FlashNext/Engine/Convex.cs

using System;
using System.Collections.Generic;
using OpenNest.Geometry;

namespace OpenNest.Engine.Qwen38FlashNext.Engine;

using Math = System.Math;

/// <summary>
/// Axis-aligned bounding box with no allocation and inclusive intersection tests.
/// </summary>
internal readonly struct Bounds
{
    public Bounds(double minX, double minY, double maxX, double maxY)
    {
        MinX = minX;
        MinY = minY;
        MaxX = maxX;
        MaxY = maxY;
    }

    public double MinX { get; }
    public double MinY { get; }
    public double MaxX { get; }
    public double MaxY { get; }

    public bool Intersects(in Bounds other, double margin = 0) =>
        other.MinX <= MaxX + margin
        && MinX <= other.MaxX + margin
        && other.MinY <= MaxY + margin
        && MinY <= other.MaxY + margin;
}

/// <summary>
/// A convex contour as flat coordinate arrays (closed: last point != first), with
/// O(log n) strict-inside and exact vertical/horizontal span queries. This is the
/// engine's own working representation for No-Fit-Polygon geometry; nothing here is
/// shared with the built-in nesters.
/// </summary>
internal sealed class ConvexContour
{
    // Numerical inset: points within this depth of the boundary count as outside, so a
    // placement resting on the NFP (hull contact) is accepted.
    public const double Surface = 1e-6;

    private readonly double[] _x;
    private readonly double[] _y;

    private ConvexContour(double[] x, double[] y, Bounds bounds)
    {
        _x = x;
        _y = y;
        Bounds = bounds;
        _ = FindStart();
    }

    public Bounds Bounds { get; }
    public int Count => _x.Length;

    /// <summary>Index of the lexicographic (Y, X) minimum vertex.</summary>
    public int Start { get; private set; }

    public double X(int i) => _x[i];
    public double Y(int i) => _y[i];

    public static ConvexContour FromVertices(IList<Vector> points)
    {
        var n = points.Count;
        if (n > 1 && points[0].Equals(points[n - 1]))
            n--;
        if (n < 3)
            throw new ArgumentException("Convex contour needs at least three vertices.");

        var x = new double[n];
        var y = new double[n];
        var minX = double.MaxValue;
        var minY = double.MaxValue;
        var maxX = double.MinValue;
        var maxY = double.MinValue;
        for (var i = 0; i < n; i++)
        {
            x[i] = points[i].X;
            y[i] = points[i].Y;
            if (x[i] < minX)
                minX = x[i];
            if (x[i] > maxX)
                maxX = x[i];
            if (y[i] < minY)
                minY = y[i];
            if (y[i] > maxY)
                maxY = y[i];
        }
        return new ConvexContour(x, y, new Bounds(minX, minY, maxX, maxY));
    }

    /// <summary>Regular 2^k-gon approximating a disk of the given radius (convex CCW).</summary>
    public static ConvexContour Disk(double radius, int segments = 32)
    {
        var x = new double[segments];
        var y = new double[segments];
        for (var i = 0; i < segments; i++)
        {
            var angle = 2 * Math.PI * i / segments;
            x[i] = radius * Math.Cos(angle);
            y[i] = radius * Math.Sin(angle);
        }
        return new ConvexContour(x, y, new Bounds(-radius, -radius, radius, radius));
    }

    public ConvexContour Translated(double dx, double dy)
    {
        var n = _x.Length;
        var x = new double[n];
        var y = new double[n];
        for (var i = 0; i < n; i++)
        {
            x[i] = _x[i] + dx;
            y[i] = _y[i] + dy;
        }
        return new ConvexContour(x, y, new Bounds(Bounds.MinX + dx, Bounds.MinY + dy, Bounds.MaxX + dx, Bounds.MaxY + dy));
    }

    public double MinX => Bounds.MinX;
    public double MinY => Bounds.MinY;
    public double MaxX => Bounds.MaxX;
    public double MaxY => Bounds.MaxY;

    /// <summary>
    /// Containment with a <see cref="Surface"/> band: points strictly outside return
    /// false; points inside - OR within the band of an edge - return true, so anchors
    /// resting on the NFP (the usual corner-candidate case) fall through to the exact
    /// material gate instead of being certified by the fast path. The inset may never
    /// exceed the circumscribed spacing disk's chord slack (Disk radius r/cos(pi/24)),
    /// so a hull contact that still clears the true spacing passes the gate.
    /// </summary>
    public bool ContainsPoint(double px, double py)
    {
        var n = _x.Length;
        var sx = _x[Start];
        var sy = _y[Start];

        // Polar-angle wedge from the start vertex (CCW order: first -> last).
        var first = Mod(Start + 1, n);
        var last = Mod(Start - 1, n);
        var head = Cross(sx, sy, _x[first], _y[first], px, py);
        if (head < -Surface)
            return false;
        var tail = Cross(sx, sy, _x[last], _y[last], px, py);
        if (tail > Surface)
            return false;
        // Within the band of the two wedge rays: conservative inside.
        if (head <= Surface || tail >= -Surface)
            return true;

        // Binary search for the fan triangle (start, vk, vk+1) bracketing the ray
        // start->p; vk is CCW-ordered so polar angle rises monotonically first->last.
        var lo = 0; // offset (from first) of the last vertex at-or-before p's angle
        var hi = n - 2; // offset of last
        while (hi - lo > 1)
        {
            var mid = (lo + hi) / 2;
            var index = Mod(Start + 1 + mid, n);
            if (Cross(sx, sy, _x[index], _y[index], px, py) >= -Surface)
                lo = mid;
            else
                hi = mid;
        }

        var a = Mod(Start + 1 + lo, n);
        var b = Mod(Start + 1 + lo + 1, n);
        var edgeAB = Cross(_x[a], _y[a], _x[b], _y[b], px, py);
        if (edgeAB < -Surface)
            return false;
        // Strictly inside the fan triangle, or inside the band of the far edge.
        return edgeAB <= Surface
            || Cross(sx, sy, _x[a], _y[a], px, py) >= -Surface
                && Cross(_x[b], _y[b], sx, sy, px, py) >= -Surface;
    }

    /// <summary>
    /// The vertical span [lo, hi] of the contour's cross-section at x, when x is
    /// strictly inside its x-range (inset by <see cref="Surface"/>); false otherwise.
    /// </summary>
    public bool VerticalSpanAt(double x, out double lo, out double hi)
    {
        lo = 0;
        hi = 0;
        if (x < MinX + Surface || x > MaxX - Surface)
            return false;

        lo = double.MaxValue;
        hi = double.MinValue;
        var n = _x.Length;
        var j = n - 1;
        for (var i = 0; i < n; i++)
        {
            var x0 = _x[j];
            var x1 = _x[i];
            if ((x0 <= x && x1 >= x) || (x1 <= x && x0 >= x))
            {
                var y0 = _y[j];
                var y1 = _y[i];
                double y;
                if (x1 == x0)
                    y = Math.Min(y0, y1);
                else
                    y = y0 + (y1 - y0) * (x - x0) / (x1 - x0);
                if (y < lo)
                    lo = y;
                if (y > hi)
                    hi = y;
            }
            j = i;
        }
        return lo <= hi;
    }

    /// <summary>The horizontal span at y, inset like <see cref="VerticalSpanAt"/>.</summary>
    public bool HorizontalSpanAt(double y, out double lo, out double hi)
    {
        lo = 0;
        hi = 0;
        if (y < MinY + Surface || y > MaxY - Surface)
            return false;

        lo = double.MaxValue;
        hi = double.MinValue;
        var n = _x.Length;
        var j = n - 1;
        for (var i = 0; i < n; i++)
        {
            var y0 = _y[j];
            var y1 = _y[i];
            if ((y0 <= y && y1 >= y) || (y1 <= y && y0 >= y))
            {
                var x0 = _x[j];
                var x1 = _x[i];
                double x;
                if (y1 == y0)
                    x = Math.Min(x0, x1);
                else
                    x = x0 + (x1 - x0) * (y - y0) / (y1 - y0);
                if (x < lo)
                    lo = x;
                if (x > hi)
                    hi = x;
            }
            j = i;
        }
        return lo <= hi;
    }

    private int Mod(int i, int n)
    {
        var m = i % n;
        return m < 0 ? m + n : m;
    }

    private int FindStart()
    {
        var best = 0;
        for (var i = 1; i < _y.Length; i++)
            if (
                _y[i] < _y[best] - 1e-12
                || (Math.Abs(_y[i] - _y[best]) <= 1e-12 && _x[i] < _x[best])
            )
                best = i;
        Start = best;
        return best;
    }

    private static double Cross(double ax, double ay, double bx, double by, double px, double py) =>
        (bx - ax) * (py - ay) - (by - ay) * (px - ax);
}

/// <summary>
/// No-Fit-Polygon geometry for this engine: the Minkowski sum of two convex contours
/// (the classic linear edge-merge), used to build convex NFPs as
/// placedHull (+) disk(spacing) (+) reflect(candidateHull). The engine's placement
/// search consumes these contours directly; it never tessellates part material or
/// delegates to the built-in NFP machinery.
/// </summary>
internal static class NfpGeometry
{
    /// <summary>
    /// Point-symmetric reflection (rotation by 180 degrees). Negating every vertex
    /// preserves CCW winding, so the vertex order must NOT be reversed - reversing it
    /// would hand the edge-merge a CW contour and corrupt the NFP.
    /// </summary>
    public static ConvexContour Reflect(ConvexContour contour)
    {
        var n = contour.Count;
        var points = new List<Vector>(n);
        for (var i = 0; i < n; i++)
            points.Add(new Vector(-contour.X(i), -contour.Y(i)));
        return ConvexContour.FromVertices(points);
    }

    /// <summary>
    /// Minkowski sum of two convex CCW contours via angular edge merge, starting from
    /// the sum of each contour's lexicographic (Y, X) minimum vertex. Edges are chosen
    /// by relative angle (cross product); the invariant that the two frontier edges are
    /// always less than 180 degrees apart holds because both walks start at the lowest
    /// vertex and each convex polygon turns by less than 180 degrees per vertex.
    /// </summary>
    public static ConvexContour Minkowski(ConvexContour a, ConvexContour b)
    {
        var na = a.Count;
        var nb = b.Count;
        var edges = new List<(double x, double y)>(na + nb);

        // Edge vectors walking CCW from each start vertex.
        var edgeA = new (double x, double y)[na];
        for (var k = 0; k < na; k++)
        {
            var p = (a.Start + k) % na;
            var q = (a.Start + k + 1) % na;
            edgeA[k] = (a.X(q) - a.X(p), a.Y(q) - a.Y(p));
        }
        var edgeB = new (double x, double y)[nb];
        for (var k = 0; k < nb; k++)
        {
            var p = (b.Start + k) % nb;
            var q = (b.Start + k + 1) % nb;
            edgeB[k] = (b.X(q) - b.X(p), b.Y(q) - b.Y(p));
        }

        var ka = 0;
        var kb = 0;
        while (ka < na || kb < nb)
        {
            if (ka >= na)
            {
                edges.Add(edgeB[kb++]);
                continue;
            }
            if (kb >= nb)
            {
                edges.Add(edgeA[ka++]);
                continue;
            }

            var ea = edgeA[ka];
            var eb = edgeB[kb];
            var cross = ea.x * eb.y - ea.y * eb.x;
            var scale =
                (ea.x * ea.x + ea.y * ea.y) * (eb.x * eb.x + eb.y * eb.y) + 1e-300;
            if (Math.Abs(cross) <= 1e-9 * Math.Sqrt(scale))
            {
                // Same direction: emit the summed edge.
                edges.Add((ea.x + eb.x, ea.y + eb.y));
                ka++;
                kb++;
            }
            else if (cross > 0)
            {
                // cross(ea, eb) > 0: eb is CCW-after ea, so ea is the more clockwise
                // edge and must be emitted first to keep the merge in angular order.
                edges.Add(ea);
                ka++;
            }
            else
            {
                edges.Add(eb);
                kb++;
            }
        }

        var result = new List<Vector>(edges.Count + 1);
        var px = a.X(a.Start) + b.X(b.Start);
        var py = a.Y(a.Start) + b.Y(b.Start);
        result.Add(new Vector(px, py));
        foreach (var (ex, ey) in edges)
        {
            px += ex;
            py += ey;
            result.Add(new Vector(px, py));
        }
        if (result.Count > 1 && result[0].Equals(result[^1]))
            result.RemoveAt(result.Count - 1);
        return ConvexContour.FromVertices(result);
    }
}