| // 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/. | |
| 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); | |
| } | |
| } | |