/usr/include/libwildmagic/Wm5ImplicitSurface.h is in libwildmagic-dev 5.13-1ubuntu3.
This file is owned by root:root, with mode 0o644.
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// 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 WM5IMPLICITSURFACE_H
#define WM5IMPLICITSURFACE_H
#include "Wm5MathematicsLIB.h"
#include "Wm5Matrix3.h"
#include "Wm5Surface.h"
namespace Wm5
{
template <typename Real>
class WM5_MATHEMATICS_ITEM ImplicitSurface : public Surface<Real>
{
public:
// Surface is defined by F(x,y,z) = 0. In all member functions it is
// the application's responsibility to ensure that (x,y,z) is a solution
// to F = 0.
// Abstract base class.
virtual ~ImplicitSurface ();
// The implicit function.
virtual Real F (const Vector3<Real>& pos) const = 0;
// First-order partial derivatives.
virtual Real FX (const Vector3<Real>& pos) const = 0;
virtual Real FY (const Vector3<Real>& pos) const = 0;
virtual Real FZ (const Vector3<Real>& pos) const = 0;
// Second-order partial derivatives.
virtual Real FXX (const Vector3<Real>& pos) const = 0;
virtual Real FXY (const Vector3<Real>& pos) const = 0;
virtual Real FXZ (const Vector3<Real>& pos) const = 0;
virtual Real FYY (const Vector3<Real>& pos) const = 0;
virtual Real FYZ (const Vector3<Real>& pos) const = 0;
virtual Real FZZ (const Vector3<Real>& pos) const = 0;
// Verify point is on surface (within the tolerance specified by epsilon).
bool IsOnSurface (const Vector3<Real>& pos, Real epsilon) const;
// First-order derivatives.
Vector3<Real> GetGradient (const Vector3<Real>& pos) const;
// Second-order derivatives.
Matrix3<Real> GetHessian (const Vector3<Real>& pos) const;
// Compute a coordinate frame. The set {T0,T1,N} is a right-handed
// orthonormal set.
void GetFrame (const Vector3<Real>& pos, Vector3<Real>& tangent0,
Vector3<Real>& tangent1, Vector3<Real>& normal) const;
// Differential geometric quantities. The returned scalars are the
// principal curvatures and the returned vectors are the corresponding
// principal directions.
bool ComputePrincipalCurvatureInfo (const Vector3<Real>& pos,
Real& curv0, Real& curv1, Vector3<Real>& dir0, Vector3<Real>& dir1);
protected:
ImplicitSurface ();
};
typedef ImplicitSurface<float> ImplicitSurfacef;
typedef ImplicitSurface<double> ImplicitSurfaced;
}
#endif
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