I'm trying to get code to show the increase of density from the center outward.

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Matthew 2024-2-24

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回答： David Goodmanson 2024-2-26

I'm trying to get a code to show the increase of density from the center outward. The density increase 2kg/m^3 every meter outward from the center. The center is 3kg/M^3. I have working for a cone but don't know how to make it work for a sphere. I need it go from the center outward instead of the cone tip upward. Radius of the sphere is 5 meters. Code for the cone is below:

% Parameters for the cone

cone_height = 5; % in meters

cone_radius = 4; % in meters

% Density parameters

delta_0 = 3; % base density at the tip in kg/m^3

k = 2; % density increase rate in kg/m^3 per meter

% Grid of points

[z, theta] = meshgrid(linspace(0, cone_height, 50), linspace(0, 2*pi, 50));

% Radius at each height

r = (cone_radius / cone_height) * z;

% Polar coordinates to Cartesian coordinates

X = r .* cos(theta);

Y = r .* sin(theta);

% Density at each height

density = delta_0 + k * z;

% Create the figure

figure;

% Color gradient for density

surf(X, Y, z, density, 'FaceAlpha', 0.8);

colormap('jet');

colorbar;

title('Shape 1 Visual');

xlabel('X (m)');

ylabel('Y (m)');

zlabel('Height (m)');

% Adjust view

view(-30, 30);

axis equal;

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Image Analyst 2024-2-24

I'm not sure what it would look like. To have the density vary radially you'd need a volumetric (3-D) image. But then you'd only see the outer shell, which would all be at the same radius and thus the same color. Please mock up a picture of what you need to achieve, and give the "use case" (context).

DGM 2024-2-25

While density may vary throughout a 3D solid, at least in the given example, the underlying relationship is a simple linear function of only one variable. It could be illustrated with a simple line plot, and it would be much easier to accurately read the plot.

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Answer 1

David Goodmanson 2024-2-26

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Hi Matthew,

you could try a cutaway view (which doesn't represent the sphere as a solid)

n = 40;
r0 = 5;
[x y z] = sphere(n);
x1 = r0*x(n/2+1:end,:);
y1 = r0*y(n/2+1:end,:);
z1 = r0*z(n/2+1:end,:);
z2 = 0*z1;
r = sqrt(x1.^2+y1.^2+z1.^2);
rho = (3 + 2*r);
fig(1)
u = .4;
surf(x1,y1,z1,rho,'facealpha',1/2,'edgecolor',[u u u])
hold on
r = sqrt(x1.^2+y1.^2+z2.^2);
rho = (3 + 2*r);
surf(x1,y1,z2,rho,'facealpha',1/2,'edgecolor',[u u u])
hold off
axis equal
view([1 1 -1])
colorbar