This file is indexed.

/usr/include/libwildmagic/Wm5RiemannianGeodesic.h is in libwildmagic-dev 5.13-1+b2.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)

#ifndef WM5RIEMANNIANGEODESIC_H
#define WM5RIEMANNIANGEODESIC_H

#include "Wm5MathematicsLIB.h"
#include "Wm5GMatrix.h"

namespace Wm5
{

template <typename Real>
class WM5_MATHEMATICS_ITEM RiemannianGeodesic
{
public:
    // Construction and destruction.  The input dimension must be two or
    // larger.
    RiemannianGeodesic (int dimension);
    virtual ~RiemannianGeodesic ();

    // Tweakable parameters.
    // 1. The integral samples are the number of samples used in the Trapezoid
    //    Rule numerical integrator.
    // 2. The search samples are the number of samples taken along a ray for
    //    the steepest descent algorithm used to refine the vertices of the
    //    polyline approximation to the geodesic curve.
    // 3. The derivative step is the value of h used for centered difference
    //    approximations df/dx = (f(x+h)-f(x-h))/(2*h) in the steepest
    //    descent algorithm.
    // 4. The number of subdivisions indicates how many times the polyline
    //    segments should be subdivided.  The number of polyline vertices
    //    will be pow(2,subdivisions)+1.
    // 5. The number of refinements per subdivision.  Setting this to a
    //    positive value appears necessary when the geodesic curve has a
    //    large length.
    // 6. The search radius is the distance over which the steepest descent
    //    algorithm searches for a minimum on the line whose direction is the
    //    estimated gradient.  The default of 1 means the search interval is
    //    [-L,L], where L is the length of the gradient.  If the search
    //    radius is r, then the interval is [-r*L,r*L].
    int IntegralSamples;  // default = 16
    int SearchSamples;    // default = 32
    Real DerivativeStep;  // default = 0.0001
    int Subdivisions;     // default = 7
    int Refinements;      // default = 8
    Real SearchRadius;    // default = 1.0

    // The dimension of the manifold.
    int GetDimension () const;

    // Returns the length of the line segment connecting the points.
    Real ComputeSegmentLength (const GVector<Real>& point0,
        const GVector<Real>& point1);

    // Compute the total length of the polyline.  The lengths of the segments
    // are computed relative to the metric tensor.
    Real ComputeTotalLength (int quantity, const GVector<Real>* path);

    // Returns a polyline approximation to a geodesic curve connecting the
    // points.  The caller is responsible for deleting the output array (it
    // is dynamically allocated).
    void ComputeGeodesic (const GVector<Real>& end0,
        const GVector<Real>& end1, int& quantity,
        GVector<Real>*& path);

    // Start with the midpoint M of the line segment (E0,E1) and use a
    // steepest descent algorithm to move M so that
    //     Length(E0,M) + Length(M,E1) < Length(E0,E1)
    // This is essentially a relaxation scheme that inserts points into the
    // current polyline approximation to the geodesic curve.
    bool Subdivide (const GVector<Real>& end0, GVector<Real>& mid,
        const GVector<Real>& end1);

    // Apply the steepest descent algorithm to move the midpoint M of the
    // line segment (E0,E1) so that
    //     Length(E0,M) + Length(M,E1) < Length(E0,E1)
    // This is essentially a relaxation scheme that inserts points into the
    // current polyline approximation to the geodesic curve.
    bool Refine (const GVector<Real>& end0, GVector<Real>& mid,
        const GVector<Real>& end1);

    // A callback that is executed during each call of Refine.
    typedef void (*RefineCallbackFunction)();
    RefineCallbackFunction RefineCallback;

    // Information to be used during the callback.
    int GetSubdivisionStep () const;
    int GetRefinementStep () const;
    int GetCurrentQuantity () const;

    // Curvature computations to measure how close the approximating
    // polyline is to a geodesic.

    // Returns the total curvature of the line segment connecting the points.
    Real ComputeSegmentCurvature (const GVector<Real>& point0,
        const GVector<Real>& point1);

    // Compute the total curvature of the polyline.  The curvatures of the
    // segments are computed relative to the metric tensor.
    Real ComputeTotalCurvature (int quantity, const GVector<Real>* path);

protected:
    // Support for ComputeSegmentCurvature.
    Real ComputeIntegrand (const GVector<Real>& pos,
        const GVector<Real>& der);

    // Compute the metric tensor for the specified point.  Derived classes
    // are responsible for implementing this function.
    virtual void ComputeMetric (const GVector<Real>& point) = 0;

    // Compute the Christoffel symbols of the first kind for the current
    // point.  Derived classes are responsible for implementing this function.
    virtual void ComputeChristoffel1 (const GVector<Real>& point) = 0;

    // Compute the inverse of the current metric tensor.  The function
    // returns 'true' iff the inverse exists.
    bool ComputeMetricInverse ();

    // Compute the derivative of the metric tensor for the current state.
    // This is a triply indexed quantity, the values computed using the
    // Christoffel symbols of the first kind.
    void ComputeMetricDerivative ();

    // Compute the Christoffel symbols of the second kind for the current
    // state.  The values depend on the inverse of the metric tensor, so
    // they may be computed only when the inverse exists.  The function
    // returns 'true' whenever the inverse metric tensor exists.
    bool ComputeChristoffel2 ();

    int mDimension;
    GMatrix<Real> mMetric;
    GMatrix<Real> mMetricInverse;
    GMatrix<Real>* mChristoffel1;
    GMatrix<Real>* mChristoffel2;
    GMatrix<Real>* mMetricDerivative;
    bool mMetricInverseExists;

    // Progress parameters that are useful to mRefineCallback.
    int mSubdivide, mRefine, mCurrentQuantity;

    // Derived tweaking parameters.
    Real mIntegralStep;      // = 1/(mIntegralQuantity-1)
    Real mSearchStep;        // = 1/mSearchQuantity
    Real mDerivativeFactor;  // = 1/(2*mDerivativeStep)
};

typedef RiemannianGeodesic<float> RiemannianGeodesicf;
typedef RiemannianGeodesic<double> RiemannianGeodesicd;

}

#endif