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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 | // 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: 5.0.0 (2010/01/01)
#ifndef WM5TORUS_H
#define WM5TORUS_H
#include "Wm5MathematicsLIB.h"
#include "Wm5Vector3.h"
namespace Wm5
{
template <typename Real>
class Torus3
{
public:
// Implementation of torus centered at (0,0,0) with z-axis as the
// axis of symmetry (axis about which circle is rotated to generate
// the torus).
//
// Algebraic form:
// Ro > 0 is radius from center of torus (outer radius)
// Ri > 0 is radius of tube of torus (inner radius)
// p^2 = x^2 + y^2 + z^2
// p^4 - 2*(Ro^2 + Ri^2)*p^2 + 4*Ro^2*z^2 + (Ro^2 - Ri^2)^2 = 0
//
// Parametric form:
// 0 <= s <= 1, 0 <= t <= 1
// Rc = Ro + Ri*cos(2*PI*t)
// x = Rc*cos(2*PI*s)
// y = Rc*sin(2*PI*s)
// z = Ri*sin(2*PI*t)
// Construction and destruction.
Torus3 (); // uninitialized
~Torus3 ();
Torus3 (Real outerRadius, Real innerRadius);
Vector3<Real> GetPosition (Real s, Real t) const;
Vector3<Real> GetNormal (Real s, Real t) const;
void GetParameters (const Vector3<Real>& position, Real& s,
Real& t) const;
Real OuterRadius, InnerRadius;
};
#include "Wm5Torus3.inl"
typedef Torus3<float> Torus3f;
typedef Torus3<double> Torus3d;
}
#endif
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