text: /******************************************************************************
   * $Id$
   *
   * Project:  DXF Translator
   * Purpose:  Low level spline interpolation.
   * Author:   David F. Rogers
   *
   ******************************************************************************
  
  This code is derived from the code associated with the book "An Introduction
  to NURBS" by David F. Rogers.  More information on the book and the code is
  available at:
  
    http://www.nar-associates.com/nurbs/
  
  
  Copyright (c) 2009, David F. Rogers
  All rights reserved.
  
  Redistribution and use in source and binary forms, with or without 
  modification, are permitted provided that the following conditions are met:
  
      * Redistributions of source code must retain the above copyright notice, 
        this list of conditions and the following disclaimer.
      * Redistributions in binary form must reproduce the above copyright notice,
        this list of conditions and the following disclaimer in the documentation
        and/or other materials provided with the distribution.
      * Neither the name of David F. Rogers nor the names of its contributors
        may be used to endorse or promote products derived from this software 
        without specific prior written permission.
  
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE 
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
  POSSIBILITY OF SUCH DAMAGE.
  */
  
  #include <stdio.h>
  #include <vector>
  
  /* used by ogrdxflayer.cpp */
  void rbspline(int npts,int k,int p1,double b[],double h[], double p[]);
  void rbsplinu(int npts,int k,int p1,double b[],double h[], double p[]);
  
  /************************************************************************/
  /*                               knotu()                                */
  /************************************************************************/
  
  /*  Subroutine to generate a B-spline uniform (periodic) knot vector.
  
      c            = order of the basis function
      n            = the number of defining polygon vertices
      nplus2       = index of x() for the first occurrence of the maximum knot vector value
      nplusc       = maximum value of the knot vector -- $n + c$
      x[]          = array containing the knot vector
  */
  
  static void knotu(int n,int c,int x[])
  
  {
    int nplusc, /* nplus2, */i;
  
      nplusc = n + c;
      /* nplus2 = n + 2; */
  
      x[1] = 0;
      for (i = 2; i <= nplusc; i++){
          x[i] = i-1;
      }
  }
  
  /************************************************************************/
  /*                                knot()                                */
  /************************************************************************/
  
  /*
      Subroutine to generate a B-spline open knot vector with multiplicity
      equal to the order at the ends.
  
      c            = order of the basis function
      n            = the number of defining polygon vertices
      nplus2       = index of x() for the first occurrence of the maximum knot vector value
      nplusc       = maximum value of the knot vector -- $n + c$
      x()          = array containing the knot vector
  */
  
  static void knot(int n,int c,int x[])
  
  {
      int nplusc,nplus2,i;
  
      nplusc = n + c;
      nplus2 = n + 2;
  
      x[1] = 0;
      for (i = 2; i <= nplusc; i++){
          if ( (i > c) && (i < nplus2) )
              x[i] = x[i-1] + 1;
          else
              x[i] = x[i-1];
      }
  }
  
  /************************************************************************/
  /*                               rbasis()                               */
  /************************************************************************/
  
  /*  Subroutine to generate rational B-spline basis functions--open knot vector
  
  	C code for An Introduction to NURBS
  	by David F. Rogers. Copyright (C) 2000 David F. Rogers,
  	All rights reserved.
  	
  	Name: rbais
  	Language: C
  	Subroutines called: none
  	Book reference: Chapter 4, Sec. 4. , p 296
  
  	c        = order of the B-spline basis function
      d        = first term of the basis function recursion relation
      e        = second term of the basis function recursion relation
  	h[]	     = array containing the homogeneous weights
      npts     = number of defining polygon vertices
      nplusc   = constant -- npts + c -- maximum number of knot values
      r[]      = array containing the rationalbasis functions
                 r[1] contains the basis function associated with B1 etc.
      t        = parameter value
      temp[]   = temporary array
      x[]      = knot vector
  */	
  
  static void rbasis(int c,double t,int npts, int x[], double h[], double r[])
  
  {
      int nplusc;
      int i,k;
      double d,e;
      double sum;
      std::vector<double> temp;
  
      nplusc = npts + c;
  
      temp.resize( nplusc+1 );
  
  /* calculate the first order nonrational basis functions n[i]	*/
  
      for (i = 1; i<= nplusc-1; i++){
      	if (( t >= x[i]) && (t < x[i+1]))
              temp[i] = 1;
          else
              temp[i] = 0;
      }
  
  /* calculate the higher order nonrational basis functions */
  
      for (k = 2; k <= c; k++){
      	for (i = 1; i <= nplusc-k; i++){
              if (temp[i] != 0)    /* if the lower order basis function is zero skip the calculation */
                  d = ((t-x[i])*temp[i])/(x[i+k-1]-x[i]);
              else
                  d = 0;
  
      	    if (temp[i+1] != 0)     /* if the lower order basis function is zero skip the calculation */
                  e = ((x[i+k]-t)*temp[i+1])/(x[i+k]-x[i+1]);
              else
                  e = 0;
  
      	    temp[i] = d + e;
          }
      }
  
      if (t == (double)x[nplusc]){		/*    pick up last point	*/
          temp[npts] = 1;
      }
  
  /* calculate sum for denominator of rational basis functions */
  
      sum = 0.;
      for (i = 1; i <= npts; i++){
          sum = sum + temp[i]*h[i];
      }
  
  /* form rational basis functions and put in r vector */
  
      for (i = 1; i <= npts; i++){
      	if (sum != 0){
              r[i] = (temp[i]*h[i])/(sum);}
          else
              r[i] = 0;
      }
  }
  
  /************************************************************************/
  /*                              rbspline()                              */
  /************************************************************************/
  
  /*  Subroutine to generate a rational B-spline curve using an uniform open knot vector
  
  	C code for An Introduction to NURBS
  	by David F. Rogers. Copyright (C) 2000 David F. Rogers,
  	All rights reserved.
  	
  	Name: rbspline.c
  	Language: C
  	Subroutines called: knot.c, rbasis.c, fmtmul.c
  	Book reference: Chapter 4, Alg. p. 297
  
      b[]         = array containing the defining polygon vertices
                    b[1] contains the x-component of the vertex
                    b[2] contains the y-component of the vertex
                    b[3] contains the z-component of the vertex
  	h[]			= array containing the homogeneous weighting factors 
      k           = order of the B-spline basis function
      nbasis      = array containing the basis functions for a single value of t
      nplusc      = number of knot values
      npts        = number of defining polygon vertices
      p[,]        = array containing the curve points
                    p[1] contains the x-component of the point
                    p[2] contains the y-component of the point
                    p[3] contains the z-component of the point
      p1          = number of points to be calculated on the curve
      t           = parameter value 0 <= t <= npts - k + 1
      x[]         = array containing the knot vector
  */
  
  void rbspline(int npts,int k,int p1,double b[],double h[], double p[])
  
  {
      int i,j,icount,jcount;
      int i1;
      int nplusc;
  
      double step;
      double t;
      double temp;
      std::vector<double> nbasis;
      std::vector<int> x;
  
      nplusc = npts + k;
  
      x.resize( nplusc+1 );
      nbasis.resize( npts+1 );
  
  /*  zero and redimension the knot vector and the basis array */
  
      for(i = 0; i <= npts; i++){
          nbasis[i] = 0.;
      }
  
      for(i = 0; i <= nplusc; i++){
          x[i] = 0;
      }
  
  /* generate the uniform open knot vector */
  
      knot(npts,k,&(x[0]));
  
  /*
    printf("The knot vector is ");
    for (i = 1; i <= nplusc; i++){
    printf(" %d ", x[i]);
    }
    printf("\n");
  */
  
      icount = 0;
  
  /*    calculate the points on the rational B-spline curve */
  
      t = 0;
      step = ((double)x[nplusc])/((double)(p1-1));
  
      for (i1 = 1; i1<= p1; i1++){
  
          if ((double)x[nplusc] - t < 5e-6){
              t = (double)x[nplusc];
          }
  
          /* generate the basis function for this value of t */
          rbasis(k,t,npts,&(x[0]),h,&(nbasis[0])); 
          for (j = 1; j <= 3; j++){      /* generate a point on the curve */
              jcount = j;
              p[icount+j] = 0.;
  
              for (i = 1; i <= npts; i++){ /* Do local matrix multiplication */
                  temp = nbasis[i]*b[jcount];
                  p[icount + j] = p[icount + j] + temp;
  /*
    printf("jcount,nbasis,b,nbasis*b,p = %d %f %f %f %f\n",jcount,nbasis[i],b[jcount],temp,p[icount+j]);
  */
                  jcount = jcount + 3;
              }
          }
  /*
    printf("icount, p %d %f %f %f \n",icount,p[icount+1],p[icount+2],p[icount+3]);
  */
      	icount = icount + 3;
          t = t + step;
      }
  }
  
  /************************************************************************/
  /*                              rbsplinu()                              */
  /************************************************************************/
  
  /*  Subroutine to generate a rational B-spline curve using an uniform periodic knot vector
  
  	C code for An Introduction to NURBS
  	by David F. Rogers. Copyright (C) 2000 David F. Rogers,
  	All rights reserved.
  	
  	Name: rbsplinu.c
  	Language: C
  	Subroutines called: knotu.c, rbasis.c, fmtmul.c
  	Book reference: Chapter 4, Alg. p. 298
  
      b[]         = array containing the defining polygon vertices
                    b[1] contains the x-component of the vertex
                    b[2] contains the y-component of the vertex
                    b[3] contains the z-component of the vertex
  	h[]			= array containing the homogeneous weighting factors 
      k           = order of the B-spline basis function
      nbasis      = array containing the basis functions for a single value of t
      nplusc      = number of knot values
      npts        = number of defining polygon vertices
      p[,]        = array containing the curve points
                    p[1] contains the x-component of the point
                    p[2] contains the y-component of the point
                    p[3] contains the z-component of the point
      p1          = number of points to be calculated on the curve
      t           = parameter value 0 <= t <= npts - k + 1
      x[]         = array containing the knot vector
  */
  
  void rbsplinu(int npts,int k,int p1,double b[],double h[], double p[])
  
  {
      int i,j,icount,jcount;
      int i1;
      int nplusc;
  
      double step;
      double t;
      double temp;
      std::vector<double> nbasis;
      std::vector<int> x;
  
      nplusc = npts + k;
  
      x.resize( nplusc+1);
      nbasis.resize(npts+1);
  
  /*  zero and redimension the knot vector and the basis array */
  
      for(i = 0; i <= npts; i++){
          nbasis[i] = 0.;
      }
  
      for(i = 0; i <= nplusc; i++){
          x[i] = 0;
      }
  
  /* generate the uniform periodic knot vector */
  
      knotu(npts,k,&(x[0]));
  
  /*
    printf("The knot vector is ");
    for (i = 1; i <= nplusc; i++){
    printf(" %d ", x[i]);
    }
    printf("\n");
  
    printf("The usable parameter range is ");
    for (i = k; i <= npts+1; i++){
    printf(" %d ", x[i]);
    }
    printf("\n");
  */
  
      icount = 0;
  
  /*    calculate the points on the rational B-spline curve */
  
      t = k-1;
      step = ((double)((npts)-(k-1)))/((double)(p1-1));
  
      for (i1 = 1; i1<= p1; i1++){
  
          if ((double)x[nplusc] - t < 5e-6){
              t = (double)x[nplusc];
          }
  
          rbasis(k,t,npts,&(x[0]),h,&(nbasis[0]));      /* generate the basis function for this value of t */
  /*
    printf("t = %f \n",t);
    printf("nbasis = ");
    for (i = 1; i <= npts; i++){
    printf("%f  ",nbasis[i]);
    }
    printf("\n");
  */
          for (j = 1; j <= 3; j++){      /* generate a point on the curve */
              jcount = j;
              p[icount+j] = 0.;
  
              for (i = 1; i <= npts; i++){ /* Do local matrix multiplication */
                  temp = nbasis[i]*b[jcount];
                  p[icount + j] = p[icount + j] + temp;
  /*
    printf("jcount,nbasis,b,nbasis*b,p = %d %f %f %f %f\n",jcount,nbasis[i],b[jcount],temp,p[icount+j]);
  */
                  jcount = jcount + 3;
              }
          }
  /*
    printf("icount, p %d %f %f %f \n",icount,p[icount+1],p[icount+2],p[icount+3]);
  */
          icount = icount + 3;
          t = t + step;
      }
  }
  