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1. Write a MATLAB script that computes the surface area of a function

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Answer #1

Note : There is no MATLAB function which calculates surface area of the surface directly over any plane.However,it can be

calculated by splitting the rectangular or square grids into triangular pieces and adding them together.

Solution : If the coordinates of the vertices of triangle in three-dimensional space are given by Vi=(Xi,Yi,Zi), then area can be calculated by ;

Area(A) = 1/2* |(v2-v1) $\times$ (v3-v1)|

Similarly,

SURFACE AREA OF f(x,y) :

[x,y] = peaks;

[m,n] = zeros(z);

area = 0;

for i = 1:m-1

for j = 1:n-1

v0 = [x(i,j) y(i,j) ];

v1 = [x(i,j+1) y(i,j+1) ];

v2 = [x(i+1,j) y(i+1,j)];

v3 = [x(i+1,j+1) y(i+1,j+1)];

a = v1 - v0;

b = v2 - v0;

c = v3 - v0;

A = 1/2*(norm(cross(a, c)) + norm(cross(b, c)));

area = area + A;

end

end

fprintf('\n Total area is: %f\n\n', area);

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Answer 1

Note : There is no MATLAB function which calculates surface area of the surface directly over any plane.However,it can be

calculated by splitting the rectangular or square grids into triangular pieces and adding them together.

Solution : If the coordinates of the vertices of triangle in three-dimensional space are given by Vi=(Xi,Yi,Zi), then area can be calculated by ;

Area(A) = 1/2* |(v2-v1) $\times$ (v3-v1)|

Similarly,

SURFACE AREA OF f(x,y) :

[x,y] = peaks;

[m,n] = zeros(z);

area = 0;

for i = 1:m-1

for j = 1:n-1

v0 = [x(i,j) y(i,j) ];

v1 = [x(i,j+1) y(i,j+1) ];

v2 = [x(i+1,j) y(i+1,j)];

v3 = [x(i+1,j+1) y(i+1,j+1)];

a = v1 - v0;

b = v2 - v0;

c = v3 - v0;

A = 1/2*(norm(cross(a, c)) + norm(cross(b, c)));

area = area + A;

end

end

fprintf('\n Total area is: %f\n\n', area);