text: // This file is part of libigl, a simple c++ geometry processing library.
  //
  // Copyright (C) 2019 Qingnan Zhou <qnzhou@gmail.com>
  //
  // This Source Code Form is subject to the terms of the Mozilla Public License
  // v. 2.0. If a copy of the MPL was not distributed with this file, You can
  // obtain one at http://mozilla.org/MPL/2.0/.
  #pragma once
  #ifndef IGL_PREDICATES_PREDICATES_H
  #define IGL_PREDICATES_PREDICATES_H
  
  #include <igl/igl_inline.h>
  #include <Eigen/Core>
  
  namespace igl {
    namespace predicates {
      enum class Orientation {
        POSITIVE=1, INSIDE=1,
        NEGATIVE=-1, OUTSIDE=-1,
        COLLINEAR=0, COPLANAR=0, COCIRCULAR=0, COSPHERICAL=0, DEGENERATE=0
      };
  
      // Initialize internal variable used by predciates. Must be called before
      // using exact predicates. It is safe to call this function from multiple
      // threads.
      IGL_INLINE void exactinit();
  
      // Compute the orientation of the triangle formed by pa, pb, pc.
      //
      // Input:
      //   pa, pb, pc  2D points.
      //
      // Output:
      //   Return POSITIVE if pa, pb, pc are counterclockwise oriented.
      //          NEGATIVE if they are clockwise oriented.
      //          COLLINEAR if they are collinear.
      template<typename Vector2D>
      IGL_INLINE Orientation orient2d(
          const Eigen::MatrixBase<Vector2D>& pa,
          const Eigen::MatrixBase<Vector2D>& pb,
          const Eigen::MatrixBase<Vector2D>& pc);
  
      // Compute the orientation of the tetrahedron formed by pa, pb, pc, pd.
      //
      // Input:
      //   pa, pb, pc, pd  3D points.
      //
      // Output:
      //   Return POSITIVE if pd is "below" the oriented plane formed by pa, pb and pc.
      //          NEGATIVE if pd is "above" the plane.
      //          COPLANAR if pd is on the plane.
      template<typename Vector3D>
      IGL_INLINE Orientation orient3d(
          const Eigen::MatrixBase<Vector3D>& pa,
          const Eigen::MatrixBase<Vector3D>& pb,
          const Eigen::MatrixBase<Vector3D>& pc,
          const Eigen::MatrixBase<Vector3D>& pd);
  
      // Decide whether a point is inside/outside/on a circle.
      //
      // Input:
      //   pa, pb, pc  2D points that defines an oriented circle.
      //   pd          2D query point.
      //
      // Output:
      //   Return INSIDE if pd is inside of the circle defined by pa, pb and pc.
      //          OUSIDE if pd is outside of the circle.
      //          COCIRCULAR pd is exactly on the circle.
      template<typename Vector2D>
      IGL_INLINE Orientation incircle(
          const Eigen::MatrixBase<Vector2D>& pa,
          const Eigen::MatrixBase<Vector2D>& pb,
          const Eigen::MatrixBase<Vector2D>& pc,
          const Eigen::MatrixBase<Vector2D>& pd);
  
      // Decide whether a point is inside/outside/on a sphere.
      //
      // Input:
      //   pa, pb, pc, pd  3D points that defines an oriented sphere.
      //   pe              3D query point.
      //
      // Output:
      //   Return INSIDE if pe is inside of the sphere defined by pa, pb, pc and pd.
      //          OUSIDE if pe is outside of the sphere.
      //          COSPHERICAL pd is exactly on the sphere.
      template<typename Vector3D>
      IGL_INLINE Orientation insphere(
          const Eigen::MatrixBase<Vector3D>& pa,
          const Eigen::MatrixBase<Vector3D>& pb,
          const Eigen::MatrixBase<Vector3D>& pc,
          const Eigen::MatrixBase<Vector3D>& pd,
          const Eigen::MatrixBase<Vector3D>& pe);
    }
  }
  
  #ifndef IGL_STATIC_LIBRARY
  #  include "predicates.cpp"
  #endif
  
  #endif
  