Question

Please I need help with MATLAB .. PLease help me . Thankyou

Write Matlab code to plot a 2D sinc function over a 2D cartesian grid where x ranges from 100 to 355 and y ranges from 0 to 255 and the sinc is centered at somewhere not midway in the grid. First plot the grid, and then plot the function on the grid (both as grayscale and as a surface plot). Comment the code well, generate the figures and show your code in your report along with the figures. Please it should be a a MATLAB base-script.

The base script is the script that when executed, calls the functions written for each part of the assignment in sequence and produces all the figures in the assignment (named Figure_Question1_1.png, Figure_Question1_2.png etc.). Program MATLAB to also save the images as jpg/png files directly from MATLAB print(gcf,'-dpng',[savefilename '.png']); into a subfolder. Please make sure that the input figures are read in with reference to the location of the base script automatically and these inputs can be hardcoded in the base-script but not inside functions that you write. The particular functions you write should be generic and able to accept any inputs, so they can be called repeatedly from the base-script and passed the necessary information/images.

Answer 1

meshgrid

2-D and 3-D grids

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Syntax

[X,Y] = meshgrid(x,y)

[X,Y] = meshgrid(x)

[X,Y,Z] = meshgrid(x,y,z)

[X,Y,Z] = meshgrid(x)

Description

example

[X,Y] = meshgrid(x,y) returns 2-D grid coordinates based on the coordinates contained in vectors x and y. X is a matrix where each row is a copy of x, and Y is a matrix where each column is a copy of y. The grid represented by the coordinates X and Y has length(y) rows and length(x) columns.

example

[X,Y] = meshgrid(x) is the same as [X,Y] = meshgrid(x,x), returning square grid coordinates with grid size length(x)-by-length(x).

example

[X,Y,Z] = meshgrid(x,y,z) returns 3-D grid coordinates defined by the vectors x, y, and z. The grid represented by X, Y, and Z has size length(y)-by-length(x)-by-length(z).

example

[X,Y,Z] = meshgrid(x) is the same as [X,Y,Z] = meshgrid(x,x,x), returning 3-D grid coordinates with grid size length(x)-by-length(x)-by-length(x).

Examples

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2-D Grid

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Create 2-D grid coordinates with x-coordinates defined by the vector x and y-coordinates defined by the vector y.

x = 1:3;
y = 1:5;
[X,Y] = meshgrid(x,y)

X = 5×3

     1     2     3
     1     2     3
     1     2     3
     1     2     3
     1     2     3

Y = 5×3

     1     1     1
     2     2     2
     3     3     3
     4     4     4
     5     5     5

Evaluate the expression x2+y2 over the 2-D grid.

X.^2 + Y.^2

ans = 5×3

     2     5    10
     5     8    13
    10    13    18
    17    20    25
    26    29    34

Plot Surface

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Create a 2-D grid with uniformly spaced x-coordinates and y-coordinates in the interval [-2,2].

x = -2:0.25:2;
y = x;
[X,Y] = meshgrid(x);

Evaluate and plot the function f(x,y)=xe−x2−y2 over the 2-D grid.

F = X.*exp(-X.^2-Y.^2);
surf(X,Y,F)

Starting in R2016b, it is not always necessary to create the grid before operating over it. For example, computing the expression xe−x2−y2 implicitly expands the vectors x and y. For more information on implicit expansion, see Array vs. Matrix Operations.

surf(x,y,x.*exp(-x.^2-(y').^2))

3-D Grid

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View MATLAB Command

Create 3-D grid coordinates from x-, y-, and z-coordinates defined in the interval [0,6], and evaluate the expression x2+y2+z2.

x = 0:2:6;
y = 0:1:6;
z = 0:3:6;
[X,Y,Z] = meshgrid(x,y,z);
F = X.^2 + Y.^2 + Z.^2;

Determine the size of the grid. The three coordinate vectors have different lengths, forming a rectangular box of grid points.

gridsize = size(F)

gridsize = 1×3

     7     4     3

Use the single-input syntax to generate a uniformly spaced 3-D grid based on the coordinates defined in x. The new grid forms a cube of grid points.

[X,Y,Z] = meshgrid(x);
G = X.^2 + Y.^2 + Z.^2;
gridsize = size(G)

gridsize = 1×3

     4     4     4

Input Arguments

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x — x-coordinates of points
vector

x-coordinates of points, specified as a vector.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

y — y-coordinates of points
vector

y-coordinates of points, specified as a vector.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

z — z-coordinates of points
vector

z-coordinates of points, specified as a vector.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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X — x-coordinates over grid
2-D or 3-D array

x-coordinates over a grid, returned as a 2-D (two inputs) or 3-D array (three inputs).

Y — y-coordinates over grid
2-D or 3-D array

y-coordinates over a grid, returned as a 2-D (two inputs) or 3-D array (three inputs).

Z — z-coordinates over grid
3-D array

z-coordinates over a grid, returned as a 3-D array