:þ֧жάֵ(Radial Basis Function)

ʽ:
InterpolationRBF2D(x0,y0,f0,x,y,n,a,k,t)
InterpolationRBF2D(x0,y0,f0,x,y,n,a,k)
InterpolationRBF2D(x0,y0,f0,x,y,n,a)
InterpolationRBF2D(x0,y0,f0,x,y,n)
InterpolationRBF2D(x0,y0,f0,x,y)

x0:洢ɢx
y0:洢ɢy,˲x0άһ
f0:洢ɢ(x,y)¶Ӧĺֵ,,˲x0y0άһ
x:洢Ҫֵx
y:洢Ҫֵy,˲xάһ
n:ѡȡֵ֪,ĬΪ4
a:뾶̬Ʊ(>=1),ĬΪ16
k:һ1*2ľ,Ԫطֱʾx0y0Բֵf0Ȩϵ,ĬϾһ,ȡ1ע,ȨϵС0.
t:֧(ֵ110)ӦɲοԭĬΪ5


˵:
ɹxyͬάĲֵֵ,ɳԸӦƽȲ,ʹú{SmoothGrid<\SmoothGrid>}Խмӹ

ԭ:

1xвֵʱ,ҳxٽnx0,ñ㷨뾶r

2þ

3(tӦֵ)
(1)t=1-10[1]
t=1,  f(r)=1-r
t=2,  f(r)=(1-r)^3*(3*r+1)
t=3,  f(r)=(1-r)^5*(8*r^2+5*r+1)
t=4,  f(r)=(1-r)^2
t=5,  f(r)=(1-r)^4*(4*r+1)
t=6,  f(r)=(1-r)^6*(35*r^2+18*r+3)
t=7,  f(r)=(1-r)^8*(32*r^3+25*r^2+8*r+1)
t=8,  f(r)=(1-r)^3
t=9,  f(r)=(1-r)^5*(5*r+1)
t=10, f(r)=(1-r)^7*(16*r^2+7*r+1)

(2)t=11-19[2]
t=11, f(r)=(1-r)^2*(2+r)
t=12, f(r)=(1-r)^3*(1+3*r+r^2)
t=13, f(r)=(1-r)^3*(8+9*r+3*r^2)
t=14, f(r)=(1-r)^4*(4+16*r+12*r^2+3*r^3)
t=15, f(r)=(1-r)^5*(1+5*r+9*r^2+5*r^3+r^4)
t=16, f(r)=(1-r)^4*(16+29*r+20*r^2+5*r^3)
t=17, f(r)=(1-r)^5*(8+40*r+48*r^2+25*r^3+5*r^4)
t=18, f(r)=(1-r)^6*(6+36*r+82*r^2+72*r^3+30*r^4+5*r^5)
t=19, f(r)=(1-r)^7*(5+35*r+101*r^2+147*r^3+101*r^4+35*r^5+5*r^6)

ο:
/*
[1] Wendland H.Piecewise polynomial,positive definite and compactly supported radial functions of minimal degree[J]. Advances in computational Mathematics,1995,4(1):389-396. 

[2] Wu Z. Compactly supported positive definite radial functions[J]. Advances in Computational Mathematics, 1995, 4(1): 283-292.
*/

:

//Сľ{ά<http://emuch.net/bbs/viewthread.php?tid=5999724&fpage=1>}Ϊ,data,λسִиɿ


x=data(,1);//data1
y=data(,2);
z=data(,3);
a=max(x);
b=min(x);
x0=MeshGrid2(b,a,50);//x
a=max(y);
b=min(y);
y0=MeshGrid2(b,a,50);//y
y0=y0';//עҪתһ
z0=InterpolationRBF2D(x,y,z,x0,y0);//ñ
cloud(x0,y0,z0)//Իͼ鿴Ч
{<http://img2.ph.126.net/BszLgWAey2XLqMujFX_cNg==/1059753287333311586.png>}
