/*
 * Copyright 2015 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 *
 * Initial import from skia:src/gpu/ganesh/geometry/GrTriangulator.h
 *
 * Copyright 2023 Rive
 */

#ifndef GrTriangulator_DEFINED
#define GrTriangulator_DEFINED

#if !defined(SK_ENABLE_OPTIMIZE_SIZE)

#include "rive/math/raw_path.hpp"
#include "rive/math/vec2d.hpp"
#include "rive/math/aabb.hpp"
#include "rive/pls/pls.hpp"
#include "rive/pls/buffer_ring.hpp"
#include "rive/pls/trivial_block_allocator.hpp"

namespace rive
{
#define TRIANGULATOR_LOGGING 0
#define TRIANGULATOR_WIREFRAME 0

/**
 * Provides utility functions for converting paths to a collection of triangles.
 */
class GrTriangulator
{
public:
    constexpr static int kArenaDefaultChunkSize = 16 * 1024;

    // Enums used by GrTriangulator internals.
    typedef enum
    {
        kLeft_Side,
        kRight_Side
    } Side;
    enum class EdgeType
    {
        kInner,
        kOuter,
        kConnector
    };

    // Structs used by GrTriangulator internals.
    struct Vertex;
    struct VertexList;
    struct Line;
    struct Edge;
    struct EdgeList;
    struct MonotonePoly;
    struct Poly;
    struct Comparator;

protected:
    GrTriangulator(const AABB& pathBounds, FillRule fillRule, TrivialBlockAllocator* alloc) :
        fPathBounds(pathBounds), fFillRule(fillRule), fAlloc(alloc)
    {}

    // There are six stages to the basic algorithm:
    //
    // 1) Linearize the path contours into piecewise linear segments:
    void pathToContours(const RawPath& path,
                        float tolerance,
                        const AABB& clipBounds,
                        VertexList* contours,
                        bool* isLinear) const;

    // 2) Build a mesh of edges connecting the vertices:
    void contoursToMesh(VertexList* contours, int contourCnt, VertexList* mesh, const Comparator&);

    // 3) Sort the vertices in Y (and secondarily in X):
    static void SortedMerge(VertexList* front,
                            VertexList* back,
                            VertexList* result,
                            const Comparator&);
    static void SortMesh(VertexList* vertices, const Comparator&);

    // 4) Simplify the mesh by inserting new vertices at intersecting edges:
    enum class SimplifyResult
    {
        kFailed,
        kAlreadySimple,
        kFoundSelfIntersection
    };

    [[nodiscard]] SimplifyResult simplify(VertexList* mesh, const Comparator&);

    // 5) Tessellate the simplified mesh into monotone polygons:
    virtual std::tuple<Poly*, bool> tessellate(const VertexList& vertices, const Comparator&);

    // 6) Triangulate the monotone polygons directly into a vertex buffer:
    void polysToTriangles(const Poly* polys,
                          FillRule overrideFillRule,
                          uint16_t pathID,
                          pls::BufferRing<pls::TriangleVertex>*) const;

    // The vertex sorting in step (3) is a merge sort, since it plays well with the linked list
    // of vertices (and the necessity of inserting new vertices on intersection).
    //
    // Stages (4) and (5) use an active edge list -- a list of all edges for which the
    // sweep line has crossed the top vertex, but not the bottom vertex.  It's sorted
    // left-to-right based on the point where both edges are active (when both top vertices
    // have been seen, so the "lower" top vertex of the two). If the top vertices are equal
    // (shared), it's sorted based on the last point where both edges are active, so the
    // "upper" bottom vertex.
    //
    // The most complex step is the simplification (4). It's based on the Bentley-Ottman
    // line-sweep algorithm, but due to floating point inaccuracy, the intersection points are
    // not exact and may violate the mesh topology or active edge list ordering. We
    // accommodate this by adjusting the topology of the mesh and AEL to match the intersection
    // points. This occurs in two ways:
    //
    // A) Intersections may cause a shortened edge to no longer be ordered with respect to its
    //    neighbouring edges at the top or bottom vertex. This is handled by merging the
    //    edges (mergeCollinearVertices()).
    // B) Intersections may cause an edge to violate the left-to-right ordering of the
    //    active edge list. This is handled by detecting potential violations and rewinding
    //    the active edge list to the vertex before they occur (rewind() during merging,
    //    rewind_if_necessary() during splitting).
    //
    // The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and
    // Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it
    // currently uses a linked list for the active edge list, rather than a 2-3 tree as the
    // paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also
    // become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N)
    // insertions and removals was greater than the cost of infrequent O(N) lookups with the
    // linked list implementation. With the latter, all removals are O(1), and most insertions
    // are O(1), since we know the adjacent edge in the active edge list based on the topology.
    // Only type 2 vertices (see paper) require the O(N) lookups, and these are much less
    // frequent. There may be other data structures worth investigating, however.
    //
    // Note that the orientation of the line sweep algorithms is determined by the aspect ratio of
    // the path bounds. When the path is taller than it is wide, we sort vertices based on
    // increasing Y coordinate, and secondarily by increasing X coordinate. When the path is wider
    // than it is tall, we sort by increasing X coordinate, but secondarily by *decreasing* Y
    // coordinate. This is so that the "left" and "right" orientation in the code remains correct
    // (edges to the left are increasing in Y; edges to the right are decreasing in Y). That is, the
    // setting rotates 90 degrees counterclockwise, rather that transposing.

    // Additional helpers and driver functions.
    void emitMonotonePoly(const MonotonePoly*,
                          uint16_t pathID,
                          pls::BufferRing<pls::TriangleVertex>*) const;
    void emitTriangle(Vertex* prev,
                      Vertex* curr,
                      Vertex* next,
                      int winding,
                      uint16_t pathID,
                      pls::BufferRing<pls::TriangleVertex>*) const;
    void emitPoly(const Poly*, uint16_t pathID, pls::BufferRing<pls::TriangleVertex>*) const;

    Poly* makePoly(Poly** head, Vertex* v, int winding) const;
    void appendPointToContour(const Vec2D& p, VertexList* contour) const;
    void appendQuadraticToContour(const Vec2D[3], float toleranceSqd, VertexList* contour) const;
    void generateCubicPoints(const Vec2D&,
                             const Vec2D&,
                             const Vec2D&,
                             const Vec2D&,
                             float tolSqd,
                             VertexList* contour,
                             int pointsLeft) const;
    bool applyFillType(int winding) const;
    MonotonePoly* allocateMonotonePoly(Edge* edge, Side side, int winding);
    Edge* allocateEdge(Vertex* top, Vertex* bottom, int winding, EdgeType type);
    Edge* makeEdge(Vertex* prev, Vertex* next, EdgeType type, const Comparator&);
    void setTop(Edge* edge,
                Vertex* v,
                EdgeList* activeEdges,
                Vertex** current,
                const Comparator&) const;
    void setBottom(Edge* edge,
                   Vertex* v,
                   EdgeList* activeEdges,
                   Vertex** current,
                   const Comparator&) const;
    void mergeEdgesAbove(Edge* edge,
                         Edge* other,
                         EdgeList* activeEdges,
                         Vertex** current,
                         const Comparator&) const;
    void mergeEdgesBelow(Edge* edge,
                         Edge* other,
                         EdgeList* activeEdges,
                         Vertex** current,
                         const Comparator&) const;
    Edge* makeConnectingEdge(Vertex* prev,
                             Vertex* next,
                             EdgeType,
                             const Comparator&,
                             int windingScale = 1);
    void mergeVertices(Vertex* src, Vertex* dst, VertexList* mesh, const Comparator&) const;
    static void FindEnclosingEdges(const Vertex& v,
                                   const EdgeList& edges,
                                   Edge** left,
                                   Edge** right);
    void mergeCollinearEdges(Edge* edge,
                             EdgeList* activeEdges,
                             Vertex** current,
                             const Comparator&) const;
    bool splitEdge(Edge* edge,
                   Vertex* v,
                   EdgeList* activeEdges,
                   Vertex** current,
                   const Comparator&);
    bool intersectEdgePair(Edge* left,
                           Edge* right,
                           EdgeList* activeEdges,
                           Vertex** current,
                           const Comparator&);
    Vertex* makeSortedVertex(const Vec2D&,
                             uint8_t alpha,
                             VertexList* mesh,
                             Vertex* reference,
                             const Comparator&) const;
#if 0
    void computeBisector(Edge* edge1, Edge* edge2, Vertex*) const;
#endif
    bool checkForIntersection(Edge* left,
                              Edge* right,
                              EdgeList* activeEdges,
                              Vertex** current,
                              VertexList* mesh,
                              const Comparator&);
    void sanitizeContours(VertexList* contours, int contourCnt) const;
    bool mergeCoincidentVertices(VertexList* mesh, const Comparator&) const;
    void buildEdges(VertexList* contours, int contourCnt, VertexList* mesh, const Comparator&);
    std::tuple<Poly*, bool> contoursToPolys(VertexList* contours, int contourCnt);
    std::tuple<Poly*, bool> pathToPolys(const RawPath&,
                                        float tolerance,
                                        const AABB& clipBounds,
                                        bool* isLinear);
    static int64_t CountPoints(const Poly* polys, FillRule overrideFillRule);
    size_t countMaxTriangleVertices(const Poly*) const;
    size_t polysToTriangles(const Poly*,
                            uint64_t maxVertexCount,
                            uint16_t pathID,
                            pls::BufferRing<pls::TriangleVertex>*) const;

    AABB fPathBounds;
    FillRule fFillRule;
    TrivialBlockAllocator* fAlloc;
    int fNumMonotonePolys = 0;
    int fNumEdges = 0;

    // Internal control knobs.
#if 0
    bool fRoundVerticesToQuarterPixel = false;
    bool fEmitCoverage = false;
#endif
    bool fPreserveCollinearVertices = false;
    bool fCollectGroutTriangles = false;

    // The grout triangles serve as a glue that erases T-junctions between a path's outer
    // curves and its inner polygon triangulation. Drawing a path's outer curves, grout
    // triangles, and inner polygon triangulation all together into the stencil buffer has the same
    // identical rasterized effect as stenciling a classic Redbook fan.
    //
    // The grout triangles track all the edge splits that led from the original inner polygon
    // edges to the final triangulation. Every time an edge splits, we emit a razor-thin grout
    // triangle consisting of the edge's original endpoints and the split point. (We also add
    // supplemental grout triangles to areas where abs(winding) > 1.)
    //
    //                a
    //               /
    //              /
    //             /
    //            x  <- Edge splits at x. New grout triangle is: [a, b, x].
    //           /
    //          /
    //         b
    //
    // The opposite-direction shared edges between the triangulation and grout triangles should
    // all cancel out, leaving just the set of edges from the original polygon.
    class GroutTriangleList
    {
    public:
        struct Node
        {
            Node(Vec2D a, Vec2D b, Vec2D c) : fPts{a, b, c} {}
            Vec2D fPts[3];
            Node* fNext = nullptr;
        };
        const Node* head() const { return fHead; }
        int count() const { return fCount; }

        void append(TrivialBlockAllocator* alloc, Vec2D a, Vec2D b, Vec2D c, int winding)
        {
            if (a == b || a == c || b == c || winding == 0)
            {
                return;
            }
            if (winding < 0)
            {
                std::swap(a, b);
                winding = -winding;
            }
            for (int i = 0; i < winding; ++i)
            {
                assert(fTail && !(*fTail));
                *fTail = alloc->make<Node>(a, b, c);
                fTail = &(*fTail)->fNext;
            }
            fCount += winding;
        }

        void concat(GroutTriangleList&& list)
        {
            assert(fTail && !(*fTail));
            if (list.fHead)
            {
                *fTail = list.fHead;
                fTail = list.fTail;
                fCount += list.fCount;
                list.fHead = nullptr;
                list.fTail = &list.fHead;
                list.fCount = 0;
            }
        }

    private:
        Node* fHead = nullptr;
        Node** fTail = &fHead;
        int fCount = 0;
    };

    mutable GroutTriangleList fGroutList;
};

/**
 * Vertices are used in three ways: first, the path contours are converted into a
 * circularly-linked list of Vertices for each contour. After edge construction, the same Vertices
 * are re-ordered by the merge sort according to the sweep_lt comparator (usually, increasing
 * in Y) using the same fPrev/fNext pointers that were used for the contours, to avoid
 * reallocation. Finally, MonotonePolys are built containing a circularly-linked list of
 * Vertices. (Currently, those Vertices are newly-allocated for the MonotonePolys, since
 * an individual Vertex from the path mesh may belong to multiple
 * MonotonePolys, so the original Vertices cannot be re-used.
 */

struct GrTriangulator::Vertex
{
    Vertex(const Vec2D& point, uint8_t alpha) :
        fPoint(point),
        fPrev(nullptr),
        fNext(nullptr),
        fFirstEdgeAbove(nullptr),
        fLastEdgeAbove(nullptr),
        fFirstEdgeBelow(nullptr),
        fLastEdgeBelow(nullptr),
        fLeftEnclosingEdge(nullptr),
        fRightEnclosingEdge(nullptr),
        fPartner(nullptr),
        fAlpha(alpha),
        fSynthetic(false)
#if TRIANGULATOR_LOGGING
        ,
        fID(-1.0f)
#endif
    {}
    Vec2D fPoint;              // Vertex position
    Vertex* fPrev;             // Linked list of contours, then Y-sorted vertices.
    Vertex* fNext;             // "
    Edge* fFirstEdgeAbove;     // Linked list of edges above this vertex.
    Edge* fLastEdgeAbove;      // "
    Edge* fFirstEdgeBelow;     // Linked list of edges below this vertex.
    Edge* fLastEdgeBelow;      // "
    Edge* fLeftEnclosingEdge;  // Nearest edge in the AEL left of this vertex.
    Edge* fRightEnclosingEdge; // Nearest edge in the AEL right of this vertex.
    Vertex* fPartner;          // Corresponding inner or outer vertex (for AA).
    uint8_t fAlpha;
    bool fSynthetic; // Is this a synthetic vertex?
#if TRIANGULATOR_LOGGING
    float fID; // Identifier used for logging.
#endif
    bool isConnected() const { return this->fFirstEdgeAbove || this->fFirstEdgeBelow; }
};

struct GrTriangulator::VertexList
{
    VertexList() : fHead(nullptr), fTail(nullptr) {}
    VertexList(Vertex* head, Vertex* tail) : fHead(head), fTail(tail) {}
    Vertex* fHead;
    Vertex* fTail;
    void insert(Vertex* v, Vertex* prev, Vertex* next);
    void append(Vertex* v) { insert(v, fTail, nullptr); }
    void append(const VertexList& list)
    {
        if (!list.fHead)
        {
            return;
        }
        if (fTail)
        {
            fTail->fNext = list.fHead;
            list.fHead->fPrev = fTail;
        }
        else
        {
            fHead = list.fHead;
        }
        fTail = list.fTail;
    }
    void prepend(Vertex* v) { insert(v, nullptr, fHead); }
    void remove(Vertex* v);
    void close()
    {
        if (fHead && fTail)
        {
            fTail->fNext = fHead;
            fHead->fPrev = fTail;
        }
    }
#if TRIANGULATOR_LOGGING
    void dump() const;
#endif
};

// A line equation in implicit form. fA * x + fB * y + fC = 0, for all points (x, y) on the line.
struct GrTriangulator::Line
{
    Line(double a, double b, double c) : fA(a), fB(b), fC(c) {}
    Line(Vertex* p, Vertex* q) : Line(p->fPoint, q->fPoint) {}
    Line(const Vec2D& p, const Vec2D& q) :
        fA(static_cast<double>(q.y) - p.y) // a = dY
        ,
        fB(static_cast<double>(p.x) - q.x) // b = -dX
        ,
        fC(static_cast<double>(p.y) * q.x - // c = cross(q, p)
           static_cast<double>(p.x) * q.y)
    {}
    double dist(const Vec2D& p) const { return fA * p.x + fB * p.y + fC; }
    Line operator*(double v) const { return Line(fA * v, fB * v, fC * v); }
    double magSq() const { return fA * fA + fB * fB; }
    void normalize()
    {
        double len = sqrt(this->magSq());
        if (len == 0.0)
        {
            return;
        }
        double scale = 1.0f / len;
        fA *= scale;
        fB *= scale;
        fC *= scale;
    }
    bool nearParallel(const Line& o) const
    {
        return fabs(o.fA - fA) < 0.00001 && fabs(o.fB - fB) < 0.00001;
    }

#if 0
    // Compute the intersection of two (infinite) Lines.
    bool intersect(const Line& other, Vec2D* point) const;
#endif
    double fA, fB, fC;
};

/**
 * An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and
 * "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf().
 * Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating
 * point). For speed, that case is only tested by the callers that require it (e.g.,
 * rewind_if_necessary()). Edges also handle checking for intersection with other edges.
 * Currently, this converts the edges to the parametric form, in order to avoid doing a division
 * until an intersection has been confirmed. This is slightly slower in the "found" case, but
 * a lot faster in the "not found" case.
 *
 * The coefficients of the line equation stored in double precision to avoid catastrophic
 * cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is
 * correct in float, since it's a polynomial of degree 2. The intersect() function, being
 * degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its
 * output may be incorrect, and adjusting the mesh topology to match (see comment at the top of
 * this file).
 */

struct GrTriangulator::Edge
{
    Edge(Vertex* top, Vertex* bottom, int winding, EdgeType type) :
        fWinding(winding),
        fTop(top),
        fBottom(bottom),
        fType(type),
        fLeft(nullptr),
        fRight(nullptr),
        fPrevEdgeAbove(nullptr),
        fNextEdgeAbove(nullptr),
        fPrevEdgeBelow(nullptr),
        fNextEdgeBelow(nullptr),
        fLeftPoly(nullptr),
        fRightPoly(nullptr),
        fLeftPolyPrev(nullptr),
        fLeftPolyNext(nullptr),
        fRightPolyPrev(nullptr),
        fRightPolyNext(nullptr),
        fUsedInLeftPoly(false),
        fUsedInRightPoly(false),
        fLine(top, bottom)
    {}
    int fWinding;    // 1 == edge goes downward; -1 = edge goes upward.
    Vertex* fTop;    // The top vertex in vertex-sort-order (sweep_lt).
    Vertex* fBottom; // The bottom vertex in vertex-sort-order.
    EdgeType fType;
    Edge* fLeft;          // The linked list of edges in the active edge list.
    Edge* fRight;         // "
    Edge* fPrevEdgeAbove; // The linked list of edges in the bottom Vertex's "edges above".
    Edge* fNextEdgeAbove; // "
    Edge* fPrevEdgeBelow; // The linked list of edges in the top Vertex's "edges below".
    Edge* fNextEdgeBelow; // "
    Poly* fLeftPoly;      // The Poly to the left of this edge, if any.
    Poly* fRightPoly;     // The Poly to the right of this edge, if any.
    Edge* fLeftPolyPrev;
    Edge* fLeftPolyNext;
    Edge* fRightPolyPrev;
    Edge* fRightPolyNext;
    bool fUsedInLeftPoly;
    bool fUsedInRightPoly;
    Line fLine;

    double dist(const Vec2D& p) const
    {
        // Coerce points coincident with the vertices to have dist = 0, since converting from
        // a double intersection point back to float storage might construct a point that's no
        // longer on the ideal line.
        return (p == fTop->fPoint || p == fBottom->fPoint) ? 0.0 : fLine.dist(p);
    }
    bool isRightOf(const Vertex& v) const { return this->dist(v.fPoint) < 0.0; }
    bool isLeftOf(const Vertex& v) const { return this->dist(v.fPoint) > 0.0; }
    void recompute() { fLine = Line(fTop, fBottom); }
    void insertAbove(Vertex*, const Comparator&);
    void insertBelow(Vertex*, const Comparator&);
    void disconnect();
    bool intersect(const Edge& other, Vec2D* p, uint8_t* alpha = nullptr) const;
};

struct GrTriangulator::EdgeList
{
    EdgeList() : fHead(nullptr), fTail(nullptr) {}
    Edge* fHead;
    Edge* fTail;
    void insert(Edge* edge, Edge* prev, Edge* next);
    void insert(Edge* edge, Edge* prev);
    void append(Edge* e) { insert(e, fTail, nullptr); }
    void remove(Edge* edge);
    void removeAll()
    {
        while (fHead)
        {
            this->remove(fHead);
        }
    }
    void close()
    {
        if (fHead && fTail)
        {
            fTail->fRight = fHead;
            fHead->fLeft = fTail;
        }
    }
    bool contains(Edge* edge) const { return edge->fLeft || edge->fRight || fHead == edge; }
};

struct GrTriangulator::MonotonePoly
{
    MonotonePoly(Edge* edge, Side side, int winding) :
        fSide(side),
        fFirstEdge(nullptr),
        fLastEdge(nullptr),
        fPrev(nullptr),
        fNext(nullptr),
        fWinding(winding)
    {
        this->addEdge(edge);
    }
    Side fSide;
    Edge* fFirstEdge;
    Edge* fLastEdge;
    MonotonePoly* fPrev;
    MonotonePoly* fNext;
    int fWinding;
    void addEdge(Edge*);
};

struct GrTriangulator::Poly
{
    Poly(Vertex* v, int winding);

    Poly* addEdge(Edge* e, Side side, GrTriangulator*);
    Vertex* lastVertex() const { return fTail ? fTail->fLastEdge->fBottom : fFirstVertex; }
    Vertex* fFirstVertex;
    int fWinding;
    MonotonePoly* fHead;
    MonotonePoly* fTail;
    Poly* fNext;
    Poly* fPartner;
    int fCount;
#if TRIANGULATOR_LOGGING
    int fID;
#endif
};

struct GrTriangulator::Comparator
{
    enum class Direction
    {
        kVertical,
        kHorizontal
    };
    Comparator(Direction direction) : fDirection(direction) {}
    bool sweep_lt(const Vec2D& a, const Vec2D& b) const;
    Direction fDirection;
};
} // namespace rive

#endif // SK_ENABLE_OPTIMIZE_SIZE

#endif // GrTriangulator_DEFINED