Can Antenna Toolbox used to design 3d antenna geometries?
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Need to design a 3d fractal antenna which would be 3d printed on the inside of a curved surface (a hemisphepre) with a dielectric layer.
Conceptual code below:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1363888/image.jpeg)
function koch4onhemisphere % using R2023a 30-day trial with antenna toolbox
clear all
close all
tic
% Parameters
order = 4;
radius = 1;
% Generate a Koch fractal with length equal to the hemisphere's circumference
circumference = 2 * pi * radius;
points = [0, 0; circumference, 0];
fractal_points = generateKochPoints(points, order);
% Normalize the length of the Koch fractal to fit [0, 2*pi]
fractal_points(:,1) = fractal_points(:,1) / circumference * 2 * pi;
% Map the Koch fractal points onto the surface of the hemisphere
mapped_points = zeros(size(fractal_points, 1), 3);
for i = 1:size(fractal_points, 1)
theta = fractal_points(i, 1);
phi = pi / 2 * fractal_points(i, 2) / max(fractal_points(:, 2));
[x, y, z] = sph2cart(theta, phi, radius);
mapped_points(i, :) = [x, y, z];
end
% Plot the hemisphere and the mapped Koch fractal points
[X, Y, Z] = sphere(100);
X = X * radius;
Y = Y * radius;
Z = Z * radius;
hemisphere = surf(X, Y, Z .* (Z >= 0));
set(hemisphere, 'FaceAlpha', 0.5, 'FaceColor', 'cyan', 'EdgeColor', 'none');
hold on;
plot3(mapped_points(:,1), mapped_points(:,2), mapped_points(:,3), 'r', 'LineWidth', 2);
axis equal;
xlabel('X');
ylabel('Y');
zlabel('Z');
grid on;
title(['Koch Fractal Order ', num2str(order), ' Mapped to Hemisphere']);
hold off;
%
save koch4onhemisphere
toc
end
function new_points = generateKochPoints(points, order)
if order == 0
new_points = points;
else
new_points = [];
for i = 1:size(points,1)-1
pt1 = points(i,:);
pt2 = points(i+1,:);
% Divide the segment into thirds
seg1 = pt1 + (pt2 - pt1) / 3;
seg3 = pt1 + 2 * (pt2 - pt1) / 3;
% Calculate the peak point
seg1_complex = complex(seg1(1), seg1(2));
seg3_complex = complex(seg3(1), seg3(2));
temp = (seg3_complex - seg1_complex) * exp(1i * pi/3);
peak = seg1 + [real(temp), imag(temp)];
% Recursively generate Koch points
new_points = [new_points;
generateKochPoints([pt1; seg1], order-1);
generateKochPoints([seg1; peak], order-1);
generateKochPoints([peak; seg3], order-1);
generateKochPoints([seg3; pt2], order-1)];
end
end
end
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