plane.h

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//
// Copyright 2016 Pixar
//
// Licensed under the Apache License, Version 2.0 (the "Apache License")
// with the following modification; you may not use this file except in
// compliance with the Apache License and the following modification to it:
// Section 6. Trademarks. is deleted and replaced with:
//
// 6. Trademarks. This License does not grant permission to use the trade
//    names, trademarks, service marks, or product names of the Licensor
//    and its affiliates, except as required to comply with Section 4(c) of
//    the License and to reproduce the content of the NOTICE file.
//
// You may obtain a copy of the Apache License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
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#ifndef PXR_BASE_GF_PLANE_H
#define PXR_BASE_GF_PLANE_H

/// \file gf/plane.h
/// \ingroup group_gf_BasicGeometry

#include "pxr/pxr.h"
#include "pxr/base/gf/vec3d.h"
#include "pxr/base/gf/api.h"

#include <iosfwd>
#include <vector>

PXR_NAMESPACE_OPEN_SCOPE

class GfRange3d;
class GfMatrix4d;
class GfVec4d;

/// \class GfPlane
/// \ingroup group_gf_BasicGeometry
///
/// Basic type: 3-dimensional plane
///
/// This class represents a three-dimensional plane as a normal vector
/// and the distance of the plane from the origin, measured along the
/// normal. The plane can also be used to represent a half-space: the
/// side of the plane in the direction of the normal.
///
class GfPlane
{
  public:

    /// The default constructor leaves the plane parameters undefined.
    GfPlane() {
    }

    /// This constructor sets this to the plane perpendicular to \p normal and
    /// at \p distance units from the origin. The passed-in normal is
    /// normalized to unit length first.
    GfPlane(const GfVec3d &normal, double distanceToOrigin) {
        Set(normal, distanceToOrigin);
    }

    /// This constructor sets this to the plane perpendicular to \p normal and
    /// that passes through \p point. The passed-in normal is normalized to
    /// unit length first.
    GfPlane(const GfVec3d &normal, const GfVec3d &point) {
        Set(normal, point);
    }

    /// This constructor sets this to the plane that contains the three given
    /// points. The normal is constructed from the cross product of (\p p1 -
    /// \p p0) (\p p2 - \p p0). Results are undefined if the points are
    /// collinear.
    GfPlane(const GfVec3d &p0, const GfVec3d &p1, const GfVec3d &p2) {
        Set(p0, p1, p2);
    }

    /// This constructor creates a plane given by the equation 
    /// \p eqn[0] * x + \p eqn[1] * y + \p eqn[2] * z + \p eqn[3] = 0.
    GfPlane(const GfVec4d &eqn) {
        Set(eqn);
    }

    /// Sets this to the plane perpendicular to \p normal and at \p distance
    /// units from the origin. The passed-in normal is normalized to unit
    /// length first.
    void                Set(const GfVec3d &normal, double distanceToOrigin) {
        _normal = normal.GetNormalized();
        _distance = distanceToOrigin;
    }

    /// This constructor sets this to the plane perpendicular to \p normal and
    /// that passes through \p point. The passed-in normal is normalized to
    /// unit length first.
    GF_API
    void                Set(const GfVec3d &normal, const GfVec3d &point);

    /// This constructor sets this to the plane that contains the three given
    /// points. The normal is constructed from the cross product of (\p p1 -
    /// \p p0) (\p p2 - \p p0). Results are undefined if the points are
    /// collinear.
    GF_API
    void                Set(const GfVec3d &p0,
                            const GfVec3d &p1,
                            const GfVec3d &p2);

    /// This method sets this to the plane given by the equation 
    /// \p eqn[0] * x + \p eqn[1] * y + \p eqn[2] * z + \p eqn[3] = 0.
    GF_API
    void                Set(const GfVec4d &eqn);

    /// Returns the unit-length normal vector of the plane.
    const GfVec3d &     GetNormal() const {
        return _normal;
    }

    /// Returns the distance of the plane from the origin.
    double              GetDistanceFromOrigin() const {
        return _distance;
    }

    /// Give the coefficients of the equation of the plane. Suitable
    /// to OpenGL calls to set the clipping plane.
    GF_API
    GfVec4d             GetEquation() const;

    /// Component-wise equality test. The normals and distances must match
    /// exactly for planes to be considered equal.
    bool                operator ==(const GfPlane &p) const {
        return (_normal   == p._normal &&
                _distance == p._distance);
    }

    /// Component-wise inequality test. The normals and distances must match
    /// exactly for planes to be considered equal.
    bool                operator !=(const GfPlane &p) const {
        return ! (*this == p);
    }

    /// Returns the distance of point \p from the plane. This distance will be
    /// positive if the point is on the side of the plane containing the
    /// normal.
    double              GetDistance(const GfVec3d &p) const {
        return p * _normal - _distance;
    }

    /// Return the projection of \p p onto the plane.
    GfVec3d             Project(const GfVec3d& p) const {
        return p - GetDistance(p) * _normal;
    }

    /// Transforms the plane by the given matrix.
    GF_API
    GfPlane &           Transform(const GfMatrix4d &matrix);

    /// Flip the plane normal (if necessary) so that \p p is in the positive
    /// halfspace.
    void                Reorient(const GfVec3d& p) {
        if (GetDistance(p) < 0) {
            _normal = -_normal;
            _distance = -_distance;
        }
    }

    /// Returns \c true if the given aligned bounding box is at least
    /// partially on the positive side (the one the normal points into) of the
    /// plane.
    GF_API
    bool IntersectsPositiveHalfSpace(const GfRange3d &box) const;

    /// Returns true if the given point is on the plane or within its positive
    /// half space.
    bool IntersectsPositiveHalfSpace(const GfVec3d &pt) const {
        return GetDistance(pt) >= 0.0;
    }

  private:
    /// The normal to the plane. Points in direction of half-space.
    GfVec3d             _normal;

    /// Distance from the plane to the origin.
    double              _distance;
};

/// Fits a plane to the given \p points. There must be at least three points in
/// order to fit the plane; if the size of \p points is less than three, this
/// issues a coding error.
///
/// If the \p points are all collinear, then no plane can be determined, and
/// this function returns \c false. Otherwise, if the fitting is successful,
/// it returns \c true and sets \p *fitPlane to the fitted plane. If \p points
/// contains exactly three points, then the resulting plane is the exact plane
/// defined by the three points. If \p points contains more than three points,
/// then this function determines the best-fitting plane for the given points.
/// The orientation of the plane normal is arbitrary with regards to the
/// plane's positive and negative half-spaces; you can use GfPlane::Reorient()
/// to flip the plane if necessary.
///
/// The current implementation uses linear least squares and thus defines
/// "best-fitting" as minimizing the sum of the squares of the vertical
/// distances between points and the plane surface.
GF_API
bool GfFitPlaneToPoints(const std::vector<GfVec3d>& points, GfPlane* fitPlane);

/// Output a GfPlane using the format [(nx ny nz) distance].
/// \ingroup group_gf_DebuggingOutput
GF_API std::ostream& operator<<(std::ostream&, const GfPlane&);

PXR_NAMESPACE_CLOSE_SCOPE

#endif // PXR_BASE_GF_PLANE_H