how to generate a dome shape by using defined points

Hi all,

i am trying to generate a semi ellipsoidal dome shape by using x, y, z values and below is my code. in the code i defined the x,y,z values but i am unable to assign those values to sphere.

any suggestions and thanks in advance

clc
x = [65 55.2125 50.8267 46.7398 42.9232 39.3476 35.9815 32.7882 29.7175 26.6833 23.4690 18.7605];
y = x;
z = [0.0,0.9,2.7,5.2,8.2,11.8,15.8,20.3,25.2,30.7,37.1,47.5]; % max height of dome is 47.5
[x,y,z] = sphere(20);     
x = x(12:end,:);       
y = y(12:end,:);      
z = z(12:end,:);       
r = 65;                % radius of the dome 
surf(r.*x,r.*y,r.*z); 
axis equal; 

Answer 1

[BhaTTa]

To generate a semi-ellipsoidal dome shape using specific x, y, and z values in MATLAB, you'll need to adjust your approach. The sphere function generates a unit sphere, and you're correctly slicing it to get a dome shape, but it seems you want to use predefined x, y, and z values to define an ellipsoidal shape instead.

Given your unique x, y, and z values, it appears you're trying to map these onto a dome shape rather than using the uniform spherical coordinates generated by sphere. To achieve a semi-ellipsoidal dome based on your description, you can use meshgrid to create a grid of x and y values and then calculate the corresponding z values based on the ellipsoidal equation.

However, if your goal is to use the specific z values you've listed with corresponding x and y values to create an ellipsoidal dome, you would typically need a function that represents the dome's shape in terms of z = f(x, y).

If you're looking to create a semi-ellipsoid with predefined dimensions (not necessarily using the x, y, z values you've listed as direct coordinates), you can use the ellipsoid formula:

[ \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1 ]

where a, b, and c are the radii along the x, y, and z axes, respectively. For a dome, you would only plot the upper half of this ellipsoid.

Here's an example code snippet that creates a semi-ellipsoidal dome shape:

clc;
clear;

% Semi-ellipsoid dimensions
a = 65; % semi-major axis in the x-direction
b = 65; % semi-major axis in the y-direction
c = 47.5; % semi-major axis in the z-direction (height of the dome)

% Create a meshgrid for x and y
[x, y] = meshgrid(linspace(-a, a, 50), linspace(-b, b, 50));

% Calculate corresponding z values for the semi-ellipsoid
% Ensure the argument inside the sqrt is non-negative
insideSqrt = 1 - (x.^2/a^2) - (y.^2/b^2);
insideSqrt(insideSqrt < 0) = 0; % Avoid complex numbers by setting negative values to 0
z = c * sqrt(insideSqrt);

% Plot the semi-ellipsoidal dome
surf(x, y, z);
axis equal;
xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');
title('Semi-Ellipsoidal Dome Shape');