机械图纸汽车:谁会实现贝塞尔曲线

/* 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
*/

#include <math.h>

/* function to calculate the factorial */

float factrl(int n)
{
static int ntop=6;
static float 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) printf("\nNegative factorial in routine FACTRL\n");
if (n > 32) printf("\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 floating point number */
}

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

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

/* function to calculate the Bernstein basis */

float Basis(int n,int i,float t)
{
float basis;
float ti; /* this is t^i */
float 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 */

bezier(npts,b,cpts,p)

int cpts;
int npts;

float b[];
float p[];

{
int i;
int j;
int i1;
int icount;
int jcount;
int n;

float step;
float t;

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

/* calculate the points on the Bezier curve */

icount = 0;
t = 0;
step = 1.0/((float)(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;
}
}