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gunu_derivatives.h

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/* LIBGUL - Geometry Utility Library
 * Copyright (C) 1998-1999 Norbert Irmer
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Library General Public
 * License as published by the Free Software Foundation; either
 * version 2 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
 * Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with this library; if not, write to the
 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */
 
#ifndef GUNU_DERIVATIVES_H
#define GUNU_DERIVATIVES_H

namespace gunu {

using gul::Ptr;
using gul::point;
using gul::hpoint;
using gul::curve;
using gul::Min;

/*------------------------------------------------------------------------
  Calculate NURBS basis functions and their first 'n' derivatives.
  Only the non-vanishing basis functions are calculated (see "The NURBS Book")
------------------------------------------------------------------------*/  
template< class T >
void CalcDersBasisFuns( 
            const T u, const int i, const int p, const int n,
            const Ptr< T >& U, Ptr< Ptr< T > >& ders );

/*-------------------------------------------------------------------------
  Calculates the first 'd' derivatives of a curve at a point 'u'. The results
  are homogeneous points (like the control points), returned in 'CK[]'
  (see "The NURBS Book")
--------------------------------------------------------------------------- */
/*
template< class T, class EP >
GULAPI void BSPCurveDerivatives( 
           const T u, const int n, const int p, const gul::Ptr< T >& U,
           const gul::Ptr< EP >& Pw, const int d, gul::Ptr< EP >& CK );
*/

/*---------------------------------------------------------------------------
  Calculates mixed partial derivatives of a NURBS surface. Let 'k' and 'l' be
  the number of derivatives in 'u' and 'v' direction, then all mixed ders with
  'k+l <= d' are calculated. They are returned in 'SKL[k][l]'.  
  (see "The NURBS Book")
------------------------------------------------------------------------- */  
template< class T, class EP >
void BSPSurfaceDerivatives(
                const T u, const T v,
                const int nu, const int pu, const Ptr< T >& U,
                const int nv, const int pv, const Ptr< T >& V,
                const Ptr< Ptr< EP > >& Pw,
                const int d, Ptr< Ptr< EP > >& SKL );

/*-------------------------------------------------------------------------
  Calculates the first 'd' partial derivatives of the projection of a NURBS
  curve into euclidian space (3-dimensions), so the calculated ders are points
  in 3-dimensional space   
  (see "The NURBS Book")
------------------------------------------------------------------------- */  
template< class T, class HP, class EP >
GULAPI void CurveDerivatives(
                    const T u, const int n, const int p,
                    const Ptr< T >& U, const Ptr< HP >& Pw, const int d,
                    Ptr< EP >& CK );        

// VC currently (VC7) has problems with the ordering of function templates,
// so i cannot use the following, more specialized template 
#ifndef _MSC_VER
template< class T, class EP >
GULAPI void CurveDerivatives(
                    const T u, const int n, const int p,
                    const Ptr< T >& U, const Ptr<EP>& Pw, const int d,
                    Ptr<EP>& CK )  
{
  BSPCurveDerivatives(u,n,p,U,Pw,d,CK);
}
#endif

/*-------------------------------------------------------------------------
  Calculates the first 'd' mixed partial derivatives of the projection of a
  NURBS surface into euclidian space (3-dimensions), so the calculated ders
  are points in 3-dimensional space. They are returned in 'SKL[k][l]'.  
  (see "The NURBS Book")
------------------------------------------------------------------------- */
template< class T, class HP, class EP >          
void SurfaceDerivatives(
                const T u, const T v,
                const int nu, const int pu, const Ptr< T >& U,
                const int nv, const int pv, const Ptr< T >& V,
                const Ptr< Ptr < HP > >& Pw,
                const int d, Ptr< Ptr < EP > >& SKL );

/*---------------------------------------------------------------------
  Calculates the normal vector of a NURBS surface at u=0,v=0
---------------------------------------------------------------------*/
template< class T, class HP >
void CalcNormal_U0V0( 
           const int nu, const int pu, 
           const int nv, const int pv,
           const Ptr< Ptr< HP > >& Pw, point<T> *Normal );

/*---------------------------------------------------------------------
  Calculates the normal vector of a NURBS surface at u=1,v=0
---------------------------------------------------------------------*/
template< class T, class HP >
void CalcNormal_U1V0( 
           const int nu, const int pu, 
           const int nv, const int pv,
           const Ptr< Ptr< HP > >& Pw, point<T> *Normal );

/*---------------------------------------------------------------------
  Calculates the normal vector of a NURBS surface at u=0,v=1
---------------------------------------------------------------------*/
template< class T, class HP >
void CalcNormal_U0V1( 
           const int nu, const int pu, 
           const int nv, const int pv,
           const Ptr< Ptr< HP > >& Pw, point<T> *Normal );

/*---------------------------------------------------------------------
  Calculates the normal vector of a NURBS surface at u=1,v=1
---------------------------------------------------------------------*/
template< class T, class HP >
void CalcNormal_U1V1( 
           const int nu, const int pu, 
           const int nv, const int pv,
           const Ptr< Ptr< HP > >& Pw, point<T> *Normal );

}

#endif

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