MsqGeomPrim.hpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2008 Sandia National Laboratories.  Developed at the
    University of Wisconsin--Madison under SNL contract number
    624796.  The U.S. Government and the University of Wisconsin
    retain certain rights to this software.

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2008) [email protected]

  ***************************************************************** */

/** \file MsqGeomPrim.hpp
 *  \brief Classes for primitive geometry
 *  \author Jason Kraftcheck
 */

#ifndef MSQ_MSQ_GEOM_PRIM_HPP
#define MSQ_MSQ_GEOM_PRIM_HPP

#include "Mesquite.hpp"
#include "Vector3D.hpp"

namespace MBMesquite
{

/**\brief Line in R^3 */
class MESQUITE_EXPORT MsqLine
{
  private:
    Vector3D mPoint;
    Vector3D mDirection;  // unit direction

  public:
    MsqLine( const Vector3D& p_point, const Vector3D& p_dir ) : mPoint( p_point ), mDirection( p_dir / p_dir.length() )
    {
    }

    MsqLine() : mPoint( 0, 0, 0 ), mDirection( 0, 0, 0 ) {}

    static MsqLine two_point( const Vector3D& p1, const Vector3D& p2 )
    {
        return MsqLine( p1, p2 - p1 );
    }

    const Vector3D& point() const
    {
        return mPoint;
    }
    const Vector3D& direction() const
    {
        return mDirection;
    }

    //! Get point given parameter (mPoint + param * mDirection)
    Vector3D point( double param ) const
    {
        return point() + param * direction();
    }

    //! Get parameter value for location on line closest to input point.
    double closest( const Vector3D& from_point ) const
    {
        return mDirection % ( from_point - mPoint );
    }

    double distance( const Vector3D& from_point ) const
    {
        return ( point( closest( from_point ) ) - from_point ).length();
    }

    //! Find intersection between two lines
    //!\return false if no point intersection (skew, parallel, coincident, etc.)
    bool intersect( const MsqLine& other, double& param, double epsilon ) const;

    //! Find parameter of closest position on this line to another line
    bool closest( const MsqLine& other, double& param ) const;
};

/**\brief Circle in R^3 */
class MESQUITE_EXPORT MsqCircle
{
  private:
    Vector3D mCenter;
    Vector3D mNormal;  //!< unit normal
    double mRadius;

  public:
    MsqCircle() : mCenter( 0, 0, 0 ), mNormal( 0, 0, 0 ), mRadius( 0 ) {}

    MsqCircle( const Vector3D& p_center, const Vector3D& p_normal, double p_radius )
        : mCenter( p_center ), mNormal( p_normal / p_normal.length() ), mRadius( p_radius )
    {
    }

    //! Find circle passing through three points
    //!\return false if points are colinear, true otherwise.
    static bool three_point( const Vector3D& p1, const Vector3D& p2, const Vector3D& p3, MsqCircle& result );

    //! Find circle with center and two points
    //!\return false if points are colinear or not equidistant from center, true otherwise.
    static bool two_point( const Vector3D& center, const Vector3D& p1, const Vector3D& p2, MsqCircle& result );

    const Vector3D& center() const
    {
        return mCenter;
    }
    const Vector3D& normal() const
    {
        return mNormal;
    }
    double radius() const
    {
        return mRadius;
    }

    //! Get arbitrary radial vector (vector in plane with length equal to radius)
    Vector3D radial_vector() const;

    //! Find closest point on circle to input position.  Returns
    //! arbitrary location on circle if point is at center.
    Vector3D closest( const Vector3D& point ) const;

    //! Find closest point on circle to input position, and tangent
    //! at that point.  Fails and returns false if point is at center
    //! of circle.
    bool closest( const Vector3D& point, Vector3D& point_on_circle, Vector3D& tangent_at_point ) const;
};

/**\brief Plane */
class MESQUITE_EXPORT MsqPlane
{
  private:
    Vector3D mNormal;  //!< unit normal
    double mCoeff;

  public:
    MsqPlane( const Vector3D& p_normal, double coeff );
    MsqPlane( const Vector3D& p_normal, const Vector3D& p_point );
    //! ax+by+cz+d=0
    MsqPlane( double a, double b, double c, double d );

    //! get unit normal vector for plane
    const Vector3D& normal() const
    {
        return mNormal;
    }

    //! get coefficient term for plane
    double coefficient() const
    {
        return mCoeff;
    }

    //! Get point on plane closest to origin.
    Vector3D point() const
    {
        return -mCoeff * mNormal;
    }

    //! Get distance from point to plane
    double distance( const Vector3D& p_point ) const
    {
        return fabs( normal() % p_point + coefficient() );
    }

    //! Get closest location on plane to input position
    Vector3D closest( const Vector3D& p_point ) const
    {
        return p_point - normal() * ( normal() % p_point + coefficient() );
    }

    //! Find intersection of this plane with another.
    //!\return false if parallel or invalid plane, true otherwise
    bool intersect( const MsqPlane& plane, MsqLine& result ) const;

    //! Find point of itersection with a line
    //!\return false if parallel, true otherwise
    bool intersect( const MsqLine& line, double& line_param ) const;
};

/**\brief Sphere */
class MESQUITE_EXPORT MsqSphere
{
  private:
    Vector3D mCenter;
    double mRadius;

  public:
    MsqSphere( const Vector3D& p_center, double p_radius ) : mCenter( p_center ), mRadius( p_radius ) {}

    const Vector3D& center() const
    {
        return mCenter;
    }
    double radius() const
    {
        return mRadius;
    }

    //! Get location on sphere closest to input location.
    //! Returns arbitrary point if input location is at center.
    Vector3D closest( const Vector3D& point ) const;

    //! Get location on sphere closest to input location, and
    //! normal at closest point.
    //!\return false if input point is at center, true otherwise.
    bool closest( const Vector3D& point, Vector3D& point_on_sphere, Vector3D& normal_at_point ) const;

    double distance( const Vector3D& point ) const
    {
        return fabs( ( center() - point ).length() - radius() );
    }

    //! Intersect plane with sphere
    //!\return true if intersection exists, false otherwise.
    bool intersect( const MsqPlane& plane, MsqCircle& result ) const;

    //! Intersect spheres
    //!\return true if intersection exists, false otherwise.
    bool intersect( const MsqSphere& sphere, MsqCircle& result ) const;
};

}  // namespace MBMesquite

#endif