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因需要研究了一下贝赛尔曲线,并在opencv下实现. 可以修改控制点，连接多条曲线，修改曲线精度。
程序示例如下:
代码下载:
opencv_share@163.com download
代码如下:
//
TrainingTools.cpp : 定义控制台应用程序的入口点。
//
#include
"
stdafx.h
"
#include
<
iostream
>
#include
<
string
.h
>
#include
<
cxcore.h
>
#include
<
cv.h
>
#include
<
highgui.h
>
#include
<
fstream
>
using
namespace
std;
const
int
WW_MAX_MARK_COUNT
=
40
;
//
最大40个控制点
int
mark_count
=
4
;
int
conner_pt_index
=-
1
;
CvPoint3D32f Control_pts[WW_MAX_MARK_COUNT];
IplImage
*
image
=
0
;
//
原始图像
bool
is_showControlLines
=
true
;
//
两个向量相加，p=p+q
 
CvPoint3D32f pointAdd(CvPoint3D32f p, CvPoint3D32f q)
...
{
 p.x += q.x; p.y += q.y; p.z += q.z;
return p;
 }
//
向量和标量相乘p=c*p
CvPoint3D32f pointTimes(
float
c, CvPoint3D32f p)
...
{
p.x *= c; p.y *= c; p.z *= c;
return p;
}
//
计算贝塞尔方程的值
//
变量u的范围在0-1之间
//
P1*t^3 + P2*3*t^2*(1-t) + P3*3*t*(1-t)^2 + P4*(1-t)^3 = Pnew
CvPoint3D32f Bernstein(
float
u, CvPoint3D32f
*
p)
...
{
CvPoint3D32f a, b, c, d, r;
a = pointTimes(pow(u,3), p[0]);
b = pointTimes(3*pow(u,2)*(1-u), p[1]);
c = pointTimes(3*u*pow((1-u),2), p[2]);
d = pointTimes(pow((1-u),3), p[3]);
r = pointAdd(pointAdd(a, b), pointAdd(c, d));
return r;
}
//
画控制线
void
DrawControlLine(CvPoint3D32f
*
p)
...
{
CvPoint pc[4];
for(int i=0;i<4;i++)
  ...{
pc[i].x = (int)p[i].x;
pc[i].y = (int)p[i].y;
 }
cvLine(image,pc[0],pc[1],CV_RGB(0,0,255),1,CV_AA,0);
cvLine(image,pc[2],pc[3],CV_RGB(0,0,255),1,CV_AA,0);
}
//
得到最近Control_pts的index
int
getNearPointIndex(CvPoint mouse_pt)
...
{
CvPoint pt;
for(int i =0; i<mark_count;i++)
...{
pt.x= mouse_pt.x - Control_pts[i].x;
pt.y= mouse_pt.y - Control_pts[i].y;
float distance = sqrt ((float)( pt.x*pt.x + pt.y*pt.y ));
if(distance<10) return i;
}
return -1;
}
void
on_mouse(
int
event
,
int
x,
int
y,
int
flags,
void
*
param )
...
{
if( event == CV_EVENT_LBUTTONDOWN )
...{
CvPoint pt = cvPoint(x,y);
//cout<<x<<","<<y<<endl;
if(conner_pt_index >-1)
conner_pt_index = -1;
else
...{
conner_pt_index = getNearPointIndex(pt);
//添加新的控制点
if(conner_pt_index==-1)
...{
if(mark_count<=(WW_MAX_MARK_COUNT-1))
...{
Control_pts[mark_count].x = pt.x;
Control_pts[mark_count].y = pt.y;
Control_pts[mark_count].z = 0;
mark_count++;
}
}
}
}
else if ( event == CV_EVENT_MOUSEMOVE ) //修改控制点坐标
...{
if(conner_pt_index >-1)
...{
Control_pts[conner_pt_index].x = x;
Control_pts[conner_pt_index].y = y;
}
}
}
;
int
main(
int
argc,
char
*
argv[])
...
{
CvSize image_sz = cvSize( 1000,1000);
image = cvCreateImage(image_sz , 8, 3 );
cvNamedWindow("Win",0);
cvSetMouseCallback( "Win", on_mouse, 0 );
cvResizeWindow("Win",500,500);
cout<<"============== Bezier curve DEMO =============="<<endl;
cout<<" "<<endl;
cout<<"1.use mouse to click control point (red) to select a control point"<<endl;
cout<<"2.use mouse to modify control point"<<endl;
cout<<"3.click mouse on somewhere to add a control point,add three points for add a new curve"<<endl;
cout<<"4.use 'W','S' to add precision or reduce precision."<<endl;
cout<<"5.press 'Z' to show control points."<<endl;
cout<<"===press ESC to exit==="<<endl;
//初始化四个控制点
Control_pts[0].x = 200;
Control_pts[0].y = 200;
Control_pts[0].z = 0;
Control_pts[1].x = 300;
Control_pts[1].y = 500;
Control_pts[1].z = 0;
Control_pts[2].x = 400;
Control_pts[2].y = 560;
Control_pts[2].z = 0;
Control_pts[3].x = 500;
Control_pts[3].y = 100;
Control_pts[3].z = 0;
int divs = 50; //控制精细度
for(;;)
...{
CvPoint pt_now,pt_pre;
cvZero(image);
//绘制控制点
if(is_showControlLines)
...{
for(int i =0;i<mark_count;i++)
...{
CvPoint ptc;
ptc.x = (int) Control_pts[i].x;
ptc.y = (int) Control_pts[i].y;
cvCircle( image, ptc, 4, CV_RGB(255,0,0), 1,CV_AA, 0);
}
}
//绘制Bezier曲线
CvPoint3D32f *pControls = Control_pts;
for(int j=0;j<mark_count-3;j+=3)
...{
for (int i=0;i<=divs;i++)
...{
float u = (float)i/divs;
CvPoint3D32f newPt = Bernstein(u,pControls);
pt_now.x = (int)newPt.x;
pt_now.y = (int)newPt.y;
if(i>0) cvLine(image,pt_now,pt_pre,CV_RGB(230,255,0),2,CV_AA, 0 );
pt_pre = pt_now;
}
//画控制线
if(is_showControlLines)DrawControlLine(pControls);
pControls+=3;
}
cvShowImage("Win",image);
int keyCode = cvWaitKey(20);
if (keyCode==27) break;
if(keyCode=='w'||keyCode=='W') divs+=2;
if(keyCode=='s'||keyCode=='S') divs-=2;
if(keyCode=='z'||keyCode=='Z') is_showControlLines = is_showControlLines^1;
//cout<<"precision : "<<divs<<endl;
}
return 0;
}
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