projecting point on plain

Hey everybody, i have to project points on a plain and then link them, so you can see the distance between them. But i have no clue how to solve that problem. My professor ment, that there is a very easy caommand for it, but i could'nt find anything on the internet. Is there somebody who can help me out with this problem? I'm totally new on Matlab.

thanks in advance MadeMo

if true
  % matrix=[6007   8969   96.51
7253   577   100.08
446   7353   101.56
7807   3734   99.98
4256   4681   100.67
606   9631   99.25
5171   4244   100.69
351   3778   105.37
4716   3118   100.09
8542   2541   101.19
2580   2030   101.27
1475   225   102.63
3491   3086   100.23
8053   6564   100.15
9912   4060   102.05
5534   7165   94.86
4636   5979   97.35
4519   2443   98.97
9712   8774   95.31
7124   319   100.46
8406   2296   101.53
4563   8757   96.49
6073   9278   95.99
1876   4615   102.84
6645   9285   95.47
4988   8119   96.42
9510   8479   95.72
1206   7563   101.93
5043   1119   101.04
1623   577   101.89
8284   6259   100.62
6556   2803   103.97
8702   6268   100.18
1578   5826   101.33
6587   9984   94.13
8122   1151   100.37
8741   4196   100.76
429   617   106.28
8811   2249   101.42
5072   5456   97.98
3576   1045   100.81
8539   4781   101.11
8607   3583   99.77
5900   231   101.65
4159   4184   101.12
6489   715   100.95
6987   5192   100.01
6983   8564   97.04
1019   3570   105.68
8548   9140   96.29]

xm=matrix(:,1)
ym=matrix(:,2)
zm=matrix(:,3)

%z(x,y)=u1+u2*x+u3*y+u4*x²+u5*x*y+u6*y²

xquadr=xm.*xm
yquadr=ym.*ym
xy=xm.*ym

A=[ones(size(xm)),xm,ym,xquadr,xy,yquadr]
b=zm
x=A\b

x1=x(1,1)
x2=x(2,1)
x3=x(3,1)
x4=x(4,1)
x5=x(5,1)
x6=x(6,1)

%b)
xpoints=1:100:10000
ypoints=1:100:10000
[meshgridx,meshgridy]=meshgrid(xpoints,ypoints)
meshgridz=x1+x2.*meshgridx+x3.*meshgridy+x4.*meshgridx.*meshgridx+x5.*meshgridx.*meshgridy+x6.*meshgridy.*meshgridy
xlabel ('Kantenlänge a [m]')
ylabel ('Kantenlänge b [m]')
zlabel ('Grundwasserstand [m]')

%c)
mesh(meshgridx,meshgridy,meshgridz)
hold on
scatter3 (xm,ym,zm,'.')
  end

[Rik]

If it is a simple command, maybe quiver3 is something you're looking for?

[KSSV]

@ Madeleine Montagne, note that, you have to terminate all the lines with ;, else unnecessarily it will print the output on the screen.

@Rik Wisselink, what he asked is not about quiver3.

Answer 1

[KSSV]

clc; clear all;

matrix=[6007   8969   96.51
7253   577   100.08
446   7353   101.56
7807   3734   99.98
4256   4681   100.67
606   9631   99.25
5171   4244   100.69
351   3778   105.37
4716   3118   100.09
8542   2541   101.19
2580   2030   101.27
1475   225   102.63
3491   3086   100.23
8053   6564   100.15
9912   4060   102.05
5534   7165   94.86
4636   5979   97.35
4519   2443   98.97
9712   8774   95.31
7124   319   100.46
8406   2296   101.53
4563   8757   96.49
6073   9278   95.99
1876   4615   102.84
6645   9285   95.47
4988   8119   96.42
9510   8479   95.72
1206   7563   101.93
5043   1119   101.04
1623   577   101.89
8284   6259   100.62
6556   2803   103.97
8702   6268   100.18
1578   5826   101.33
6587   9984   94.13
8122   1151   100.37
8741   4196   100.76
429   617   106.28
8811   2249   101.42
5072   5456   97.98
3576   1045   100.81
8539   4781   101.11
8607   3583   99.77
5900   231   101.65
4159   4184   101.12
6489   715   100.95
6987   5192   100.01
6983   8564   97.04
1019   3570   105.68
8548   9140   96.29] ;
xm=matrix(:,1) ;
ym=matrix(:,2) ;
zm=matrix(:,3) ;
%z(x,y)=u1+u2*x+u3*y+u4*x²+u5*x*y+u6*y²
xquadr=xm.*xm ;
yquadr=ym.*ym ;
xy=xm.*ym ;
A=[ones(size(xm)),xm,ym,xquadr,xy,yquadr] ;
b=zm ;
x=A\b ;
x1=x(1,1) ;
x2=x(2,1) ;
x3=x(3,1) ;
x4=x(4,1) ;
x5=x(5,1) ;
x6=x(6,1) ;
%b)
xpoints=1:100:10000 ;
ypoints=1:100:10000 ;
[meshgridx,meshgridy]=meshgrid(xpoints,ypoints) ;
meshgridz=x1+x2.*meshgridx+x3.*meshgridy+x4.*meshgridx.*meshgridx+x5.*meshgridx.*meshgridy+x6.*meshgridy.*meshgridy ;
xlabel ('Kantenlänge a [m]') ;
ylabel ('Kantenlänge b [m]') ;
zlabel ('Grundwasserstand [m]') ;
%c)
mesh(meshgridx,meshgridy,meshgridz) ;
hold on
scatter3 (xm,ym,zm,'.') ;
%%Get nearest neighbor to draw line 
for i = 1:length(xm)
    idx = knnsearch([meshgridx(:) meshgridy(:) meshgridz(:)],[xm(i) ym(i) zm(i)]) ;
    line([xm(i) meshgridx(idx)],[ym(i) meshgridy(idx)],[zm(i) meshgridz(idx)]) ;
end