ParametricSurface.h
// Geometric Tools, LLC
// Copyright (c) 1998-2012
// Distributed under the Boost Software License, Version 1.0.
#pragma once
#include "Surface.h"
namespace NURBS
{
template <typename Real>
class ParametricSurface
{
public:
// Abstract base class.
ParametricSurface() {}
virtual ~ParametricSurface() {}
// The parametric domain is either rectangular or triangular. Valid (u,v)
// values for a rectangular domain satisfy
// umin <= u <= umax, vmin <= v <= vmax
// Valid (u,v) values for a triangular domain satisfy
// umin <= u <= umax, vmin <= v <= vmax,
// (vmax-vmin)*(u-umin)+(umax-umin)*(v-vmax) <= 0
Real GetUMin () const;
Real GetUMax () const;
Real GetVMin () const;
Real GetVMax () const;
bool IsRectangular () const;
// position and derivatives up to second order
virtual Vector3 P (Real u, Real v) = 0;
virtual Vector3 PU (Real u, Real v) = 0;
virtual Vector3 PV (Real u, Real v) = 0;
virtual Vector3 PUU (Real u, Real v) = 0;
virtual Vector3 PUV (Real u, Real v) = 0;
virtual Vector3 PVV (Real u, Real v) = 0;
// Compute a coordinate frame. The set {T0,T1,N} is a right-handed
// orthonormal set.
void GetFrame (Real u, Real v, Vector3& position,
Vector3& tangent0, Vector3& tangent1,
Vector3& normal) ;
// Differential geometric quantities. The returned scalars are the
// principal curvatures and the returned vectors are the corresponding
// principal directions.
void ComputePrincipalCurvatureInfo (Real u, Real v, Real& curv0,
Real& curv1, Vector3& dir0, Vector3& dir1);
protected:
ParametricSurface (Real umin, Real umax, Real vmin, Real vmax,
bool rectangular);
Real mUMin, mUMax, mVMin, mVMax;
bool mRectangular;
};
typedef ParametricSurface<float> ParametricSurfacef;
typedef ParametricSurface<double> ParametricSurfaced;
}