some meshgrid and matlab.chart.graphics errors

Hi. i wana draw my function of three variable. this is my code and i got those Errors. what shloud i do?

>> Q=[1 2 3;4 5 6;7 8 9];

>> S=[0;1;2];

>> u1=linspace(-10,10,20);

>> u2=linspace(-10,10,20);

>> u3=linspace(-10,10,20);

>> [U1,U2,U3]=meshgrid(u1,u2,u3);

>> L=1/2*(Q(1,1)*U1.^2+(Q(1,2)+Q(1,3)+Q(2,1)+Q(2,3)+Q(3,1)+Q(3,2))*U1.*U2.*U3+Q(2,2)*U2.^2+Q(3,3)*U3.^2)+S(1)*U1+S(2)*U2+S(3)*U3;

>> meshc(U1,U2,U3,L)

Error using matlab.graphics.chart.primitive.Surface/set

Value must be a vector or 2D array of numeric type

Error in matlab.graphics.chart.internal.ctorHelper (line 8)

set(obj, pvpairs{:});

Error in matlab.graphics.chart.primitive.Surface

Error in mesh (line 143)

hh = matlab.graphics.chart.primitive.Surface('XData',x,'YData',y,'ZData',z,'CData',c,...

Error in meshc (line 58)

hm = mesh(cax, x, y, z, c);

Answer 1

[Steven Lord]

Q=[1 2 3;4 5 6;7 8 9];
S=[0;1;2];
u1=linspace(-10,10,20);
u2=linspace(-10,10,20);
u3=linspace(-10,10,20);
[U1,U2,U3]=meshgrid(u1,u2,u3);
L=1/2*(Q(1,1)*U1.^2+(Q(1,2)+Q(1,3)+Q(2,1)+Q(2,3)+Q(3,1)+Q(3,2))*U1.*U2.*U3+Q(2,2)*U2.^2+Q(3,3)*U3.^2)+S(1)*U1+S(2)*U2+S(3)*U3;
whos U1 U2 U3 L

  Name       Size               Bytes  Class     Attributes

  L         20x20x20            64000  double              
  U1        20x20x20            64000  double              
  U2        20x20x20            64000  double              
  U3        20x20x20            64000  double              

Does meshc accept 3-dimensional arrays as input? [Hint: it does not.] I think you probably want one of the volume visualization functions (https://www.mathworks.com/help/matlab/volume-visualization.html) instead.

[Hamid Reza N.D]

meshc accepts 2-dimensional arrays. and gives me figure. but this time i have these errors how can i find that my meshc accepts 3-dimensional arrays as input?

Answer 2

[Walter Roberson]

You cannot use meshc to draw a function with three independent variables and one dependent variable.

You also cannot use patch or surface for this purpose, at least not directly.

You could do a triangulation and a triangular mesh plot in which the dependent variable was represented by color https://www.mathworks.com/help/matlab/ref/trimesh.html

but with the grid being evenly spaced you are going to have trouble looking "into" the volume.