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@@ -1,3 +1,10 @@
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+// This file is part of libigl, a simple c++ geometry processing library.
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+//
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+// Copyright (C) 2019 Qingnan Zhou <qnzhou@gmail.com>
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+//
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+// This Source Code Form is subject to the terms of the Mozilla Public License
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+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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+// obtain one at http://mozilla.org/MPL/2.0/.
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#pragma once
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#ifndef IGL_PREDICATES_PREDICATES_H
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#define IGL_PREDICATES_PREDICATES_H
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@@ -13,12 +20,30 @@ namespace igl {
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COLLINEAR=0, COPLANAR=0, COCIRCULAR=0, COSPHERICAL=0, DEGENERATE=0
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};
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+ // Compute the orientation of the triangle formed by pa, pb, pc.
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+ //
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+ // Input:
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+ // pa, pb, pc 2D points.
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+ //
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+ // Output:
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+ // Return POSITIVE if pa, pb, pc is counterclockwise oriented.
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+ // NEGATIVE if they are clockwise oriented.
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+ // COLLINEAR if they are collinear.
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template<typename Vector2D>
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IGL_INLINE Orientation orient2d(
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const Eigen::MatrixBase<Vector2D>& pa,
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const Eigen::MatrixBase<Vector2D>& pb,
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const Eigen::MatrixBase<Vector2D>& pc);
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+ // Compute the orientation of the tetrahedron formed by pa, pb, pc, pd.
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+ //
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+ // Input:
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+ // pa, pb, pc, pd 3D points.
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+ //
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+ // Output:
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+ // Return POSITIVE if pd is "below" the oriented plane formed by pa, pb and pc.
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+ // NEGATIVE if pd is "above" the plane.
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+ // COPLANAR if pd is on the plane.
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template<typename Vector3D>
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IGL_INLINE Orientation orient3d(
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const Eigen::MatrixBase<Vector3D>& pa,
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@@ -26,6 +51,16 @@ namespace igl {
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const Eigen::MatrixBase<Vector3D>& pc,
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const Eigen::MatrixBase<Vector3D>& pd);
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+ // Decide whether a point is inside/outside/on a circle.
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+ //
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+ // Input:
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+ // pa, pb, pc 2D points that defines an oriented circle.
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+ // pd 2D query point.
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+ //
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+ // Output:
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+ // Return INSIDE if pd is inside of the circle defined by pa, pb and pc.
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+ // OUSIDE if pd is outside of the circle.
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+ // COCIRCULAR pd is exactly on the circle.
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template<typename Vector2D>
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IGL_INLINE Orientation incircle(
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const Eigen::MatrixBase<Vector2D>& pa,
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@@ -33,6 +68,16 @@ namespace igl {
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const Eigen::MatrixBase<Vector2D>& pc,
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const Eigen::MatrixBase<Vector2D>& pd);
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+ // Decide whether a point is inside/outside/on a sphere.
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+ //
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+ // Input:
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+ // pa, pb, pc, pd 3D points that defines an oriented sphere.
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+ // pe 3D query point.
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+ //
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+ // Output:
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+ // Return INSIDE if pe is inside of the sphere defined by pa, pb, pc and pd.
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+ // OUSIDE if pe is outside of the sphere.
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+ // COSPHERICAL pd is exactly on the sphere.
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template<typename Vector3D>
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IGL_INLINE Orientation insphere(
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const Eigen::MatrixBase<Vector3D>& pa,
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Qingnan Zhou