ViewDesignEngine/include/vde/foundation/exact_predicates_gmp.h

#pragma once
#include "vde/foundation/exact_predicates.h"

#ifdef VDE_USE_GMP
#include <gmpxx.h>

namespace vde::foundation::exact {

/**
 * @brief GMP 精确算术谓词后端
 *
 * 基于 GNU MP（多精度有理数）的精确几何谓词。
 * 使用高精度有理数运算，零舍入误差，适用于对鲁棒性要求极高的场景。
 *
 * @note 仅在定义了 VDE_USE_GMP 宏且链接了 GMP 库时可用
 * @warning GMP 版本比自适应双精度版本慢约 10-50 倍，仅在双精度不足以确定结果时使用
 *
 * @ingroup foundation
 */
struct GmpExact {
    /// GMP 有理数类型
    using Rational = mpq_class;

    /**
     * @brief 精确有理数二维定向测试
     *
     * 使用 GMP 有理数精确计算三点定向，零误差。
     *
     * @param a 第一个点
     * @param b 第二个点
     * @param c 第三个点
     * @return 定向结果（保证正确，无舍入误差）
     *
     * @code{.cpp}
     * // 对近共线点仍能给出确定结果
     * Point2D a(0, 0), b(1, 1e-15), c(2, 2e-15);
     * auto ori = GmpExact::orient_2d(a, b, c);
     * @endcode
     *
     * @see GmpExact::orient_3d, GmpExact::in_circle
     */
    static Orientation orient_2d(const Point2D& a, const Point2D& b, const Point2D& c) {
        Rational ax(a.x()), ay(a.y());
        Rational bx(b.x()), by(b.y());
        Rational cx(c.x()), cy(c.y());
        Rational det = (bx - ax) * (cy - ay) - (by - ay) * (cx - ax);
        int s = mpq_sgn(det.get_mpq_t());
        return s > 0 ? Orientation::CounterClockwise :
               s < 0 ? Orientation::Clockwise : Orientation::Collinear;
    }

    /**
     * @brief 精确有理数三维定向测试
     *
     * 判断点 d 相对于平面 abc 的位置，使用有理数精确运算。
     *
     * @param a,b,c 定义平面的三点
     * @param d 待测试点
     * @return 定向结果（零误差）
     *
     * @see GmpExact::orient_2d
     */
    static Orientation orient_3d(const Point3D& a, const Point3D& b,
                                  const Point3D& c, const Point3D& d) {
        Rational ax(a.x()), ay(a.y()), az(a.z());
        Rational bx(b.x()), by(b.y()), bz(b.z());
        Rational cx(c.x()), cy(c.y()), cz(c.z());
        Rational dx(d.x()), dy(d.y()), dz(d.z());

        Rational adx = ax - dx, ady = ay - dy, adz = az - dz;
        Rational bdx = bx - dx, bdy = by - dy, bdz = bz - dz;
        Rational cdx = cx - dx, cdy = cy - dy, cdz = cz - dz;

        Rational det = adx * (bdy * cdz - bdz * cdy)
                     + bdx * (cdy * adz - cdz * ady)
                     + cdx * (ady * bdz - adz * bdy);

        int s = mpq_sgn(det.get_mpq_t());
        return s > 0 ? Orientation::CounterClockwise :
               s < 0 ? Orientation::Clockwise : Orientation::Collinear;
    }

    /**
     * @brief 精确有理数圆内测试
     *
     * 判断点 d 是否在三角形 abc 的外接圆内，零误差。
     *
     * @param a,b,c 三角形三顶点
     * @param d 待测试点
     * @return 圆测试结果（零误差）
     *
     * @see GmpExact::orient_2d
     */
    static CircleTest in_circle(const Point2D& a, const Point2D& b,
                                const Point2D& c, const Point2D& d) {
        Rational ax(a.x()), ay(a.y());
        Rational bx(b.x()), by(b.y());
        Rational cx(c.x()), cy(c.y());
        Rational dx(d.x()), dy(d.y());

        Rational adx = ax - dx, ady = ay - dy;
        Rational bdx = bx - dx, bdy = by - dy;
        Rational cdx = cx - dx, cdy = cy - dy;

        Rational ab = adx * bdy - ady * bdx;
        Rational bc = bdx * cdy - bdy * cdx;
        Rational ca = cdx * ady - cdy * adx;
        Rational al = adx * adx + ady * ady;
        Rational bl = bdx * bdx + bdy * bdy;
        Rational cl = cdx * cdx + cdy * cdy;

        Rational det = al * bc + bl * ca + cl * ab;
        int s = mpq_sgn(det.get_mpq_t());
        return s > 0 ? CircleTest::Inside :
               s < 0 ? CircleTest::Outside : CircleTest::On;
    }
};

}  // namespace vde::foundation::exact

#endif // VDE_USE_GMP