how to plot functions of theta and phi..for example {cos(phi).^3 * sin(theta)+sin(phi)} in spherical coordinates.

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yashaswi 2011-9-13

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评论： Walter Roberson 2023-5-28

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Mohamed Abdul-Al 2021-2-26

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How to wirte a matlab code to plot the 3D image of the helix using these parameters and equations that define the axes in 3D:

p=0.199; Pitch distance
a=0.02999500; Radius of the helis wire
b=0.191; Radius of the helix
n = 5, is the number of turns.
δ = atan(p/(2*pi*b));
x’ = b + a cos(Ө)
y’ = -a sin(Ө) sin(δ)
x = x’ sin(ф)+y’ cos(ф);
y =-x’ cos(ф)+y’ sin(ф);
z = p*ф/(2*pi)+a*sin(Ө)*cos(δ);

Walter Roberson 2023-5-28

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@Mohamed Abdul-Al

syms theta phi

Q = @(v) sym(v);

Pi = sym(pi);

p = Q(0.199) %Pitch distance

p =

a = Q(2999500)/Q(10)^8 %Radius of the helis wire

a =

b = Q(0.191) %Radius of the helix

b =

n = 5; % is the number of turns.

delta = atan(p/(2*Pi*b))

delta =

x_prime = b + a * cos(theta)

x_prime =

y_prime = -a * sin(theta) * sin(delta)

y_prime =

x = x_prime * sin(phi) + y_prime * cos(phi)

x =

y = -x_prime * cos(phi) + y_prime * sin(phi)

y =

z = p * phi/(2*pi) + a * sin(theta)*cos(delta)

z =

fsurf(x, y, z, [0, 2*pi, 0, 2*pi]*n)

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Answer 1

Teja Muppirala 2011-9-13

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First create a grid using spherical coordinates, and then convert the result into Cartesian coordinates.

[theta,phi] = meshgrid(linspace(-pi,pi,41),linspace(-pi/2,pi/2,41));
R = cos(phi).^3 .* sin(theta)+sin(phi);
[X,Y,Z] = sph2cart(theta,phi,R);
surf(X,Y,Z)
alpha 0.5
axis vis3d