均匀B样条的实现(2,3阶)

最新推荐文章于 2024-09-26 11:01:02 发布

AlfredLu

最新推荐文章于 2024-09-26 11:01:02 发布

阅读量2.5k

点赞数

文章标签： input 算法

本文介绍了一种计算B样条曲线的算法，包括二阶和三阶B样条的实现细节。通过控制点和密度参数，该算法能够生成平滑的样条曲线。二阶B样条使用三个控制点，而三阶B样条则使用四个控制点。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

/*
@remark: calculate the bspline in const stage
@input:
density: the density of real point in bspline
ctrlPnts: the control point of this bspline
@ouput:
spline: the b-spline real interpolating points
*/
void bspline (int density, std::vector<POINT*> ctrlPnts, std::vector<POINT*>& spline )
{
int i,j, stage;
double delta, u;
POINT *pPnt;

// init parameter
delta = 1.0/density;
stage = 2;
//stage = 3;

// begin generate
for ( i=0; i<ctrlPnts.size()-2; ++i ){
    // generate spline per section( 3 ctrlPnt & 3 basePolynomial )
    for ( j=0, u=0.0; j<density; ++j, u+=delta ){
      pPnt = new POINT(0.0,0.0);
      for ( k=0; k<=2; ++k ){
    base = bsplineBase2 ( k, u );
//    base = bsplineBase3 ( k, u );            will be replaced when in power 3
        pPnt->x += base * ctrlPnt[i+k].x;
        pPnt->y += base * ctrlPnt[i+k].y;
      }
      spline.push_back ( pPnt );
    }
}
}

/*
@remark: const power of base polynomial
@input:
idx: the index of coefficient of polynomial
u: the parameter of base polynomial
*/
double bsplineBase2( int idx, double u )
{
double rtn = 0;
switch ( idx ){
case 0:
    rtn = (1-u)*(1-u)/2;
    break;
case 1:
    rtn = (1+2*u-2*u*u)/2;
    break;
case 2:
    rtn = u*u/2;
    break;
};

return rtn;
}

/*
@remark: const power of base polynomial
@input:
idx: the index of coefficient of polynomial
u: the parameter of base polynomial
*/
double bsplineBase3( int idx, double u )
{
double rtn = 0;
switch ( idx ){
case 0:
    rtn = (1-u)*(1-u)*(1-u)/6;
    break;
case 1:
    rtn = (3*u*u*u-6*u*u+4)/6;
    break;
case 2:
    rtn = (1+3*u+3*u*u-3*u*u*u)/6;
    break;
case 3:
    rtn = u*u*u/6;
    break;
};

return rtn;
}
二阶的B样条