MATLAB: Equation from 2D Matrix of data

2d matrixequation

Hi,

I have a 2D matrix representing system supply current, this value depends on two variables x and y x along the row and y along the column of the 2D matrix

How and what function is to be used to generate one equation from the 2D matrix

example:

i( supply current)=f(x,y)

     x---->
y    I1   I2   I3
|    I4   I5   I6
|    I7   I8   I9
v

Best Answer

For most purposes, MATLAB's interp2 will be sufficient.

If you really need an equation, you will have to choose an appropriate form of a function with free parameters (e.g. a polynomial in x and y with unknown coefficients) and use "lsqcurvefit" to fit the parameters to your data.

Best wishes

Torsten.

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MATLAB: How to measure the volume of a cone using surface area of triangles in matlab

Your post is not clear (see our comments). However I guess what you want is approximate the volume of the (cone) object from the point cloud.

% Cone parameters
R = 10;
h = 20;
N = 10000;
% Generate points in cone
dx = (pi*R^2*h/3/N)^(1/3);
rvec = linspace(-R,R,ceil(2*R/dx));
hvec = linspace(0,h,ceil(h/dx));
[X,Y,Z] = ndgrid(rvec,rvec,hvec);
is_in_cone = (X.^2+Y.^2) <= (R/h*(h-Z)).^2;
x = X(is_in_cone);
y = Y(is_in_cone);
z = Z(is_in_cone);
% Method1: Estimate the volume of the 3D object assuming the object is convex
tri = delaunay(x,y,z);
trisurf(tri,x,y,z)
% indices of triangle
i1 = tri(:,1);
i2 = tri(:,2);
i3 = tri(:,3);
i4 = tri(:,4);
% Method1: Volume by summing tetrahedron
v1 = [x(i1)-x(i2) y(i1)-y(i2) z(i1)-z(i2)];
v2 = [x(i1)-x(i3) y(i1)-y(i3) z(i1)-z(i3)];
v3 = [x(i1)-x(i4) y(i1)-y(i4) z(i1)-z(i4)];
A = 1/2*cross(v1,v2,2);                     % surface of a triangle
V = 1/3*dot(A,v3,2);                        % volume of a tetrahedron
format long
V = sum(abs(V))
% Method2: use CONVHULL
[~,V]=convhull(x,y,z)
% Method3: theoretical volume of a cone computed directly from base radius and heigh
V = pi*R^2*h/3

MATLAB: Simplify(~(~(x | y) & ~(y | z)))

Remember these equivalences ( De Morgan's laws ):

 ~(x | y) <==>  ~x & ~y
 ~(x & y) <==>  ~x | ~y

Then

~(~(x | y) & ~(y | z))         ==>
~((~x & ~y) & (~y & ~z))       ==>
~(~x & ~y) | ~(~y & ~z)        ==>
~~x | ~~y | ~~y | ~~z          ==>
x | y | y | z                  ==>
x | y | z

Applying the operations from the outside to the inside is faster:

~(~(x | y) & ~(y | z))         ==>
~~(x | y) | ~~(x | z)          ==>
x | y | y | z

Best Answer

Related Solutions

MATLAB: How to measure the volume of a cone using surface area of triangles in matlab

MATLAB: Simplify(~(~(x | y) & ~(y | z)))

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