bezier.cpp

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// missing_desc
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// SUMO, Simulation of Urban MObility; see http://sumo.sourceforge.net/
// Copyright 2001-2010 DLR (http://www.dlr.de/) and contributors
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//
//   This program is free software; you can redistribute it and/or modify
//   it under the terms of the GNU General Public License as published by
//   the Free Software Foundation; either version 2 of the License, or
//   (at your option) any later version.
//
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/* Subroutine to generate a Bezier curve.
    Copyright (c) 2000 David F. Rogers. All rights reserved.

    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
    Basis      = function to calculate the Bernstein basis value (see MECG Eq 5-65)
    cpts       = number of points to be calculated on the curve
    Fractrl    = function to calculate the factorial of a number
    j[]        = array containing the basis functions for a single value of t
    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
    t          = parameter value 0 <= t <= 1
*/

// ===========================================================================
// included modules
// ===========================================================================
#ifdef _MSC_VER
#include <windows_config.h>
#else
#include <config.h>
#endif

#include <math.h>
#include <iostream>

#ifdef CHECK_MEMORY_LEAKS
#include <foreign/nvwa/debug_new.h>
#endif // CHECK_MEMORY_LEAKS

/* function to calculate the factorial */

SUMOReal factrl(int n) {
    static int ntop=6;
    static SUMOReal a[33]= {
        1.0,1.0,2.0,6.0,24.0,120.0,720.0
    }
    ; /* fill in the first few values */
    int j1;

    if (n < 0) {
        throw 1;
    } //cout << "\nNegative factorial in routine FACTRL\n" ;
    if (n > 32) {
        throw 1;
    } //cout << "\nFactorial value too large in routine FACTRL\n";

    while (ntop < n) { /* use the precalulated value for n = 0....6 */
        j1 = ntop++;
        a[n]=a[j1]*ntop;
    }
    return a[n]; /* returns the value n! as a SUMORealing point number */
}

/* function to calculate the factorial function for Bernstein basis */

SUMOReal Ni(int n,int i) {
    SUMOReal ni;
    ni = factrl(n)/(factrl(i)*factrl(n-i));
    return ni;
}

/* function to calculate the Bernstein basis */

SUMOReal Basis(int n,int i,SUMOReal t) {
    SUMOReal basis;
    SUMOReal ti; /* this is t^i */
    SUMOReal tni; /* this is (1 - t)^i */

    /* handle the special cases to avoid domain problem with pow */

    if (t==0. && i == 0) ti=1.0;
    else ti = pow(t,i);
    if (n==i && t==1.) tni=1.0;
    else tni = pow((1-t),(n-i));
    basis = Ni(n,i)*ti*tni; /* calculate Bernstein basis function */
    return basis;
}

/* Bezier curve subroutine */
void
bezier(int npts, SUMOReal b[], int cpts, SUMOReal p[]) {
    int i;
    int j;
    int i1;
    int icount;
    int jcount;

    SUMOReal step;
    SUMOReal t;

    SUMOReal factrl(int);
    SUMOReal Ni(int,int);
    SUMOReal Basis(int,int,SUMOReal);

    /*    calculate the points on the Bezier curve */

    icount = 0;
    t = 0;
    step = (SUMOReal) 1.0/(cpts -1);

    for (i1 = 1; i1<=cpts; i1++) { /* main loop */

        if ((1.0 - t) < 5e-6) t = 1.0;

        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 x,y,z components */
                p[icount + j] = p[icount + j] + Basis(npts-1,i-1,t)*b[jcount];
                jcount = jcount + 3;
            }
        }

        icount = icount + 3;
        t = t + step;
    }
}



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