I'm having difficulty plotting the Reuleaux triangle, i.e. the three arcs of circumference that connect the vertices of the equilateral triangle plotted in red are missing.

function plotReuleauxTriangle(r, d)

% Plotta un triangolo di Reuleaux con i vertici specificati

% Definisci i vertici del triangolo

A = [-2.59808*r, 3*r/2 - d];

B = [2.59808*r, 3*r/2 - d];

C = [0, -d-3*r];

% Calcola i centri dei cerchi che compongono il triangolo

centerAB = [(A(1)+B(1))/2, (A(2)+B(2))/2];

centerBC = [(B(1)+C(1))/2, (B(2)+C(2))/2];

centerCA = [(C(1)+A(1))/2, (C(2)+A(2))/2];

% Calcola il raggio dei cerchi che compongono il triangolo

radius = norm(A-B)/2;

% Plotta i cerchi

t = linspace(0, 2*pi, 100);

xCircleAB = centerAB(1) + radius*cos(t);

yCircleAB = centerAB(2) + radius*sin(t);

xCircleBC = centerBC(1) + radius*cos(t);

yCircleBC = centerBC(2) + radius*sin(t);

xCircleCA = centerCA(1) + radius*cos(t);

yCircleCA = centerCA(2) + radius*sin(t);

hold on

plot(xCircleAB, yCircleAB, 'b')

plot(xCircleBC, yCircleBC, 'b')

plot(xCircleCA, yCircleCA, 'b')

% Plotta il triangolo equilatero

plot([A(1), B(1), C(1), A(1)], [A(2), B(2), C(2), A(2)], 'r')

axis equal

title('Triangolo equilatero')

xlabel('x')

ylabel('y')

end

I'm having difficulty plotting the Reuleaux triangle, i.e. the three arcs of circumference that connect the vertices of the equilateral triangle plotted in red are missing.

Answer 1

[Himanshu]

Hello Alessandro,

As per my understanding, you are trying to plot a Reuleaux triangle. To plot a Reuleaux triangle, you have to set the centres of the circles to be the vertices of the equilateral triangle, and the radius of each circle is equal to the side length of the triangle.

Refer to the below code:

function plotReuleauxTriangle(r, d)
    % Define the vertices of the triangle
    A = [-2.59808*r, 3*r/2 - d];
    B = [2.59808*r, 3*r/2 - d];
    C = [0, -d-3*r];
    % Define the centers of the circles that compose the triangle
    centerA = A;
    centerB = B;
    centerC = C;
    % Calculate the radius of the circles that compose the triangle
    radius = norm(A-B);
    % Plot the circles
    t = linspace(0, 2*pi, 100);
    xCircleA = centerA(1) + radius*cos(t);
    yCircleA = centerA(2) + radius*sin(t);
    xCircleB = centerB(1) + radius*cos(t);
    yCircleB = centerB(2) + radius*sin(t);
    xCircleC = centerC(1) + radius*cos(t);
    yCircleC = centerC(2) + radius*sin(t);
    hold on
    plot(xCircleA, yCircleA, 'b')
    plot(xCircleB, yCircleB, 'b')
    plot(xCircleC, yCircleC, 'b')
    % Plot the equilateral triangle
    plot([A(1), B(1), C(1), A(1)], [A(2), B(2), C(2), A(2)], 'r')
    axis equal
    title('Reuleaux Triangle')
    xlabel('x')
    ylabel('y')
end

I hope this helps.