三次样条函数c语言代码 三次样条插值函数c语言

三次样条插值用c语言具体怎么做

void SPL(int n, double *x, double *y, int ni, double *xi, double *yi)； 是你所要。

已知 n 个点 x,y; x 必须已按顺序排好。要插值 ni 点，横坐标 xi[], 输出 yi[]。

程序里用double 型，保证计算精度。

SPL调用现成的程序。

现成的程序很多。端点处理方法不同，结果会有不同。想同matlab比较，你需 尝试 调用 spline（）函数 时，令 end1 为 1, 设 slope1 的值，令 end2 为 1 设 slope2 的值。

相关问答

Q1: 三次样条插值 C++程序

#includeiostream.h

#includeiomanip.h

#includemath.h

void main()

{

float a[37],b[37];

cout" ""度数"" ""sin(x)值"" ""一阶导值"" ""二阶导值"endl;

for(int i=0;i37;i++)

coutsetw(11)setprecision(3)

10*i

setw(11)setprecision(3)

sin(i*31.4/180)

setw(11)setprecision(3)

cos(i*31.4/180)

setw(11)setprecision(3)

-sin(i*31.4/180)

endl;

cout"一个周期内的积分值：0"endl;

}

Q2: 求助：求三次样条插值函数的C++程序

#includeiostream

#includeiomanip

using

namespace

std;

const

int

MAX

=

50;

float

x[MAX],

y[MAX],

h[MAX];

float

c[MAX],

a[MAX],

fxym[MAX];

float

f(int

x1,

int

x2,

int

x3){

float

a

=

(y[x3]

-

y[x2])

/

(x[x3]

-

x[x2]);

float

b

=

(y[x2]

-

y[x1])

/

(x[x2]

-

x[x1]);

return

(a

-

b)/(x[x3]

-

x[x1]);

}

//求差分

void

cal_m(int

n){

//用追赶法求解出弯矩向量M……

float

B[MAX];

B[0]

=

c[0]

/

2;

for(int

i

=

1;

i

n;

i++)

B[i]

=

c[i]

/

(2

-

a[i]*B[i-1]);

fxym[0]

=

fxym[0]

/

2;

for(i

=

1;

i

=

n;

i++)

fxym[i]

=

(fxym[i]

-

a[i]*fxym[i-1])

/

(2

-

a[i]*B[i-1]);

for(i

=

n-1;

i

=

0;

i--)

fxym[i]

=

fxym[i]

-

B[i]*fxym[i+1];

}

void

printout(int

n);

int

main(){

int

n,i;

char

ch;

do{

cout"Please

put

in

the

number

of

the

dots:";

cinn;

for(i

=

0;

i

=

n;

i++){

cout"Please

put

in

X"i':';

cinx[i];

//coutendl;

cout"Please

put

in

Y"i':';

ciny[i];

//coutendl;

}

for(i

=

0;

i

n;

i++)

//求

步长

h[i]

=

x[i+1]

-

x[i];

cout"Please

输入边界条件\n

1:

已知两端的一阶导数\n

2:两端的二阶导数已知\n

默认:自然边界条件\n";

int

t;

float

f0,

f1;

cint;

switch(t){

case

1:cout"Please

put

in

Y0\'

Y"n"\'\n";

cinf0f1;

c[0]

=

1;

a[n]

=

1;

fxym[0]

=

6*((y[1]

-

y[0])

/

(x[1]

-

x[0])

-

f0)

/

h[0];

fxym[n]

=

6*(f1

-

(y[n]

-

y[n-1])

/

(x[n]

-

x[n-1]))

/

h[n-1];

break;

case

2:cout"Please

put

in

Y0\"

Y"n"\"\n";

cinf0f1;

c[0]

=

a[n]

=

0;

fxym[0]

=

2*f0;

fxym[n]

=

2*f1;

break;

default:cout"不可用\n";//待定

};//switch

for(i

=

1;

i

n;

i++)

fxym[i]

=

6

*

f(i-1,

i,

i+1);

for(i

=

1;

i

n;

i++){

a[i]

=

h[i-1]

/

(h[i]

+

h[i-1]);

c[i]

=

1

-

a[i];

}

a[n]

=

h[n-1]

/

(h[n-1]

+

h[n]);

cal_m(n);

cout"\n输出三次样条插值函数：\n";

printout(n);

cout"Do

you

to

have

anther

try

?

y/n

:";

cinch;

}while(ch

==

'y'

||

ch

==

'Y');

return

0;

}

void

printout(int

n){

coutsetprecision(6);

for(int

i

=

0;

i

n;

i++){

couti+1":

["x[i]"

,

"x[i+1]"]\n""\t";

/*

coutfxym[i]/(6*h[i])"

*

("x[i+1]"

-

x)^3

+

""

*

(x

-

"x[i]")^3

+

"

(y[i]

-

fxym[i]*h[i]*h[i]/6)/h[i]"

*

("x[i+1]"

-

x)

+

"

(y[i+1]

-

fxym[i+1]*h[i]*h[i]/6)/h[i]"(x

-

"x[i]")\n";

coutendl;*/

float

t

=

fxym[i]/(6*h[i]);

if(t

0)coutt"*("x[i+1]"

-

x)^3";

else

cout-t"*(x

-

"x[i+1]")^3";

t

=

fxym[i+1]/(6*h[i]);

if(t

0)cout"

+

"t"*(x

-

"x[i]")^3";

else

cout"

-

"-t"*(x

-

"x[i]")^3";

cout"\n\t";

t

=

(y[i]

-

fxym[i]*h[i]*h[i]/6)/h[i];

if(t

0)cout"+

"t"*("x[i+1]"

-

x)";

else

cout"-

"-t"*("x[i+1]"

-

x)";

t

=

(y[i+1]

-

fxym[i+1]*h[i]*h[i]/6)/h[i];

if(t

0)cout"

+

"t"*(x

-

"x[i]")";

else

cout"

-

"-t"*(x

-

"x[i]")";

coutendlendl;

}

coutendl;

}

Q3: 谁来帮帮我啊:运用三次样条插值函数法对一条已知的折线进行圆滑（编程实现）。

matlab算么？

function output = spline(x,y,xx)

%SPLINE Cubic spline data interpolation.

% PP = SPLINE(X,Y) provides the piecewise polynomial form of the

% cubic spline interpolant to the data values Y at the data sites X,

% for use with the evaluator PPVAL and the spline utility UNMKPP.

% X must be a vector.

% If Y is a vector, then Y(j) is taken as the value to be matched at X(j),

% hence Y must be of the same length as X -- see below for an exception

% to this.

% If Y is a matrix or ND array, then Y(:,...,:,j) is taken as the value to

% be matched at X(j), hence the last dimension of Y must equal length(X) --

% see below for an exception to this.

%

% YY = SPLINE(X,Y,XX) is the same as YY = PPVAL(SPLINE(X,Y),XX), thus

% providing, in YY, the values of the interpolant at XX. For information

% regarding the size of YY see PPVAL.

%

% Ordinarily, the not-a-knot end conditions are used. However, if Y contains

% two more values than X has entries, then the first and last value in Y are

% used as the endslopes for the cubic spline. If Y is a vector, this

% means:

% f(X) = Y(2:end-1), Df(min(X))=Y(1), Df(max(X))=Y(end).

% If Y is a matrix or N-D array with SIZE(Y,N) equal to LENGTH(X)+2, then

% f(X(j)) matches the value Y(:,...,:,j+1) for j=1:LENGTH(X), then

% Df(min(X)) matches Y(:,:,...:,1) and Df(max(X)) matches Y(:,:,...:,end).

%

% Example:

% This generates a sine-like spline curve and samples it over a finer mesh:

% x = 0:10; y = sin(x);

% xx = 0:.25:10;

% yy = spline(x,y,xx);

% plot(x,y,'o',xx,yy)

%

% Example:

% This illustrates the use of clamped or complete spline interpolation where

% end slopes are prescribed. In this example, zero slopes at the ends of an

% interpolant to the values of a certain distribution are enforced:

% x = -4:4; y = [0 .15 1.12 2.36 2.36 1.46 .49 .06 0];

% cs = spline(x,[0 y 0]);

% xx = linspace(-4,4,101);

% plot(x,y,'o',xx,ppval(cs,xx),'-');

%

% Class support for inputs x, y, xx:

% float: double, single

%

% See also INTERP1, PPVAL, UNMKPP, MKPP, SPLINES (The Spline Toolbox).

% Carl de Boor 7-2-86

% Copyright 1984-2004 The MathWorks, Inc.

% $Revision: 5.18.4.3 $ $Date: 2004/03/02 21:48:06 $

output=[];

% Check that data are acceptable and, if not, try to adjust them appropriately

[x,y,sizey,endslopes] = chckxy(x,y);

n = length(x); yd = prod(sizey);

% Generate the cubic spline interpolant in ppform

dd = ones(yd,1); dx = diff(x); divdif = diff(y,[],2)./dx(dd,:);

if n==2

if isempty(endslopes) % the interpolant is a straight line

pp=mkpp(x,[divdif y(:,1)],sizey);

else % the interpolant is the cubic Hermite polynomial

pp = pwch(x,y,endslopes,dx,divdif); pp.dim = sizey;

end

elseif n==3isempty(endslopes) % the interpolant is a parabola

y(:,2:3)=divdif;

y(:,3)=diff(divdif')'/(x(3)-x(1));

y(:,2)=y(:,2)-y(:,3)*dx(1);

pp = mkpp(x([1,3]),y(:,[3 2 1]),sizey);

else % set up the sparse, tridiagonal, linear system b = ?*c for the slopes

b=zeros(yd,n);

b(:,2:n-1)=3*(dx(dd,2:n-1).*divdif(:,1:n-2)+dx(dd,1:n-2).*divdif(:,2:n-1));

if isempty(endslopes)

x31=x(3)-x(1);xn=x(n)-x(n-2);

b(:,1)=((dx(1)+2*x31)*dx(2)*divdif(:,1)+dx(1)^2*divdif(:,2))/x31;

b(:,n)=...

(dx(n-1)^2*divdif(:,n-2)+(2*xn+dx(n-1))*dx(n-2)*divdif(:,n-1))/xn;

else

x31 = 0; xn = 0; b(:,[1 n]) = dx(dd,[2 n-2]).*endslopes;

end

dxt = dx(:);

c = spdiags([ [x31;dxt(1:n-2);0] ...

[dxt(2);2*[dxt(2:n-1)+dxt(1:n-2)];dxt(n-2)] ...

[0;dxt(2:n-1);xn] ],[-1 0 1],n,n);

% sparse linear equation solution for the slopes

mmdflag = spparms('autommd');

spparms('autommd',0);

s=b/c;

spparms('autommd',mmdflag);

% construct piecewise cubic Hermite interpolant

% to values and computed slopes

pp = pwch(x,y,s,dx,divdif); pp.dim = sizey;

end

if nargin==2, output = pp; else output = ppval(pp,xx); end

Q4: 急求二维矩阵三次样条插值的程序,要C或C++语言。望有注释！谢谢！ 邮箱lsmann9@hotmail.com

/*********************下面程序是C语言程序（标准C）******************/

/* 计算给定M0,Mn值的三次样条插值多项式 */

/*给定离散点(1.1,0.4),(1.2,0.8),(1.4,1.65),(1.5,1.8),M0=Mn=0,*/

/*用M关系式构造三次样条插值多项式S(x),计算S(1.25)。 */

/*************************************************************/

#include stdio.h

#define Max_N 20

main()

{int i,k,n;

double h[Max_N+1],b[Max_N+1],c[Max_N+1],d[Max_N+1],M[Max_N+1];

double u[Max_N+1],v[Max_N+1],yy[Max_N+1],x[Max_N+1],y[Max_N+1];

double xx,p,q,S;

printf("\nPlease input n value:"); /*输入插值点数n*/

do

{ scanf("%d",n);

if(nMax_N)

printf("\nplease re-input n value:");

}

while(nMax_N||n=0);

printf("Input x[i],i=0,...%d:\n",n-1);

for(i=0;in;i++) scanf("%lf",x[i]);

printf("Input y[i],i=0,...%d:\n",n-1);

for(i=0;in;i++) scanf("%lf",y[i]);

printf("\nInput the M0,Mn value:");

scanf("%lf%lf",M[0],M[n]);

printf("\nInput the x value:"); /*输入计算三次样条插值函数的x值*/

scanf("%lf",xx);

if((xxx[n-1])||(xxx[0]))

{printf("Please input a number between %f and %f.\n",x[0],x[n-1]);

return;

}

/*计算M关系式中各参数的值*/

h[0]=x[1]-x[0];

for(i=1;in;i++)

{h[i]=x[i+1]-x[i];

b[i]=h[i]/(h[i]+h[i-1]);

c[i]=1-b[i];

d[i]=6*((y[i+1]-y[i])/h[i]-(y[i]-y[i-1])/h[i-1])/(h[i]+h[i-1]);

}

/*用追赶法计算Mi,i=1,...,n-1*/

d[1]-=c[1]*M[0];

d[n-1]-=b[n-1]*M[n];

b[n-1]=0; c[1]=0; v[0]=0;

for(i=1;in;i++)

{u[i]=2-c[i]*v[i-1];

v[i]=b[i]/u[i];

yy[i]=(d[i]-c[i]*y[i-1])/u[i];

}

for(i=1;in;i++)

{M[n-i]=yy[n-i]-v[n-i]*M[n-i+1];

}

/*计算三次样条插值函数在x处的值*/

k=0;

while(xx=x[k]) k++;

k=k-1;

p=x[k+1]-xx;

q=xx-x[k];

S=(p*p*p*M[k]+q*q*q*M[k+1])/(6*h[k])+(p*y[k]+q*y[k+1])/h[k]-h[k]*(p*M[k]+q*M[k+1])/6;

printf("S(%f)=%f\n",xx,S); /*输出*/

getch();

}

/*----------------------------------- End of file ------------------------------------*/

/*程序输入输出：

Please input n value:4

Input x[i],i=0,...3:

1.1 1.2 1.4 1.5

Input y[i],i=0,...3:

0.4 0.8 1.65 1.8

Input the M0,Mn value: 0 0

Input the x value:1.25

S(1.250000)=1.033171

*/

Q5: 用vc6.0在mfc中调用opengl如何画三次B样条曲线，求操作步骤和程序代码。谢谢！

#include stdlib.h

#include GL/glut.h

#pragma comment(lib,"glut32.lib")

//

#if 0

// the points of the curve - these are the same as the bezier curve

// points demonstrated in the bezier curve example.

float Points[4][3] = {

{ 10,10,0 },

{ 5,10,2 },

{ -5,0,0 },

{-10,5,-2}

};

#define NUM_POINTS 4

// The following sets of 4 indices are the curves that need to

// be drawn to create a clamped cubic b-spline. In total there

// are 5 curve segments to draw.

//

// 0 0 0 1

// 0 0 1 2

// 0 1 2 3

// 1 2 3 3

// 2 3 3 3

//

// Remember this when trying to understand knot vectors!!

//

#else

float Points[9][3] = {

{ 10,5,0 },

{ 5,10,0 },

{ -5,15,0 },

{ -10,-5,0 },

{ 4,-4,0 },

{ 10,5,0 },

{ 5,10,0 },

{ -5,15,0 },

{ -10,-5,0 }

};

#define NUM_POINTS 9

//若绘制过首尾控制点三次样条函数c语言代码的曲线

// 0 0 0 1

// 0 0 1 2

// 0 1 2 3

// 1 2 3 4

// 2 3 4 5

// 3 4 5 6

// 4 5 6 6

// 5 6 6 6

//

// Remember this when trying to understand knot vectors!!

//

//若绘制首尾相接的平滑曲线 三次样条函数c语言代码，即为当前绘制

// 0 1 2 3

// 1 2 3 4

// 2 3 4 5

// 3 4 5 6

#endif

// the level of detail for the curve

unsigned int LOD=20;

#define NUM_SEGMENTS (NUM_POINTS-3)

//

float* GetPoint(int i)

{

// return 1st point

if (i0)

{

return Points[0];

}

if (iNUM_POINTS)

{

return Points[i];

}

// return last point

return Points[NUM_POINTS-1];

}

//------------------------------------------------------------ OnKeyPress()

void myIdle(void)

{

glutPostRedisplay();

}

//------------------------------------------------------------ OnDraw()

void OnDraw()

{

// clear the screen depth buffer

glClear(GL_COLOR_BUFFER_BIT);

// clear the previous transform

glLoadIdentity();

// set the camera position

// gluLookAt( 1,10,30, // eye pos

// 0,0,0, // aim point

// 0,1,0); // up direction

// glColor3f(0.5,0.2,0);

glPointSize(3);

//

// // draw curve hull

glColor3f(0.3,0,0.5);

glBegin(GL_LINE_STRIP);

for(int i=0;i!=NUM_POINTS;++i)

{

glVertex3fv( Points[i] );

}

glEnd();

glColor3f(0,1,0);

// begin drawing our curve

glBegin(GL_LINE_STRIP);

for(int start_cv=0,j=0;jNUM_SEGMENTS;j++,start_cv++)

{

// for each section of curve, draw LOD number of divisions

for(int i=0;i!=LOD;++i)

{

// use the parametric time value 0 to 1 for this curve

// segment.

float t = (float)i/LOD;

// the t value inverted

float it = 1.0f-t;

// calculate blending functions for cubic bspline

float b0 = it*it*it/6.0f;

float b1 = (3*t*t*t - 6*t*t +4)/6.0f;

float b2 = (-3*t*t*t +3*t*t + 3*t + 1)/6.0f;

float b3 = t*t*t/6.0f;

// calculate the x,y and z of the curve point

float x = b0 * GetPoint( start_cv + 0 )[0] +

b1 * GetPoint( start_cv + 1 )[0] +

b2 * GetPoint( start_cv + 2 )[0] +

b3 * GetPoint( start_cv + 3 )[0] ;

float y = b0 * GetPoint( start_cv + 0 )[1] +

b1 * GetPoint( start_cv + 1 )[1] +

b2 * GetPoint( start_cv + 2 )[1] +

b3 * GetPoint( start_cv + 3 )[1] ;

float z = b0 * GetPoint( start_cv + 0 )[2] +

b1 * GetPoint( start_cv + 1 )[2] +

b2 * GetPoint( start_cv + 2 )[2] +

b3 * GetPoint( start_cv + 3 )[2] ;

// specify the point

glVertex2f( x,y );

}

}

// we need to specify the last point on the curve

//glVertex3fv( Points[NUM_POINTS-1] );

glEnd();

// draw CV's

glBegin(GL_POINTS);

for(int i=0;i!=NUM_POINTS;++i)

{

glVertex3fv( Points[i] );

}

glEnd();

// currently we've been drawing to the back buffer, we need

// to swap the back buffer with the front one to make the image visible

glutSwapBuffers();

}

//------------------------------------------------------------ OnInit()

void OnInit()

{

//glClearColor(1,1,1,0);

}

//------------------------------------------------------------ OnExit()

void OnExit()

{

}

//------------------------------------------------------------ OnReshape()

void OnReshape(int w, int h)

{

// prevents division by zero when minimising window

if (h==0)

{

h=1;

}

// set the drawable region of the window

glViewport(0,0,w,h);

// set up the projection matrix

glMatrixMode(GL_PROJECTION);

glLoadIdentity();

// just use a perspective projection

//gluPerspective(45,(float)w/h,0.1,100);

if(w=h)

{

glOrtho(-20.0,20.0,-20.0*(GLfloat)h/(GLfloat)w,20.0*(GLfloat)h/(GLfloat)w,0.0,100.0);

}

else

{

glOrtho(-20.0,20.0,-20.0*(GLfloat)h/(GLfloat)w,20.0*(GLfloat)h/(GLfloat)w,0.0,100.0);

}

// go back to modelview matrix so we can move the objects about

glMatrixMode(GL_MODELVIEW);

glLoadIdentity();

}

//------------------------------------------------------------ main()

int main(int argc,char** argv)

{

// initialise glut

glutInit(argc,argv);

// request a depth buffer, RGBA display mode, and we want double buffering

glutInitDisplayMode(GLUT_RGBA|GLUT_DOUBLE);

// set the initial window size

glutInitWindowSize(640,480);

// create the window

glutCreateWindow("Clamped B-Spline Curve");

// run our custom initialisation

OnInit();

// set the function to use to draw our scene

glutDisplayFunc(OnDraw);

a href="" target="_blank"涂料加盟/a

// set the function to handle changes in screen size

glutReshapeFunc(OnReshape);

glutIdleFunc(myIdle);

// set the function to be called when we exit

atexit(OnExit);

// this function runs a while loop to keep the program running.

glutMainLoop();

return 0;

}

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