minimum distance when a circle is beetween two points

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Zarak kh
Zarak kh on 27 Nov 2019
Answered: darova on 16 Jun 2020
Hello,
I have a question, I have the situation like figure below, a circle and two points A and B. I want to go from point A to point B, I want a code that shows if we have such situations do : first go to A1 (which is the tangent point) then move across the circumference of the circle upto point B1, then go to point B.
How can I show this (Red) path in matlab and calculate the distance?

Answers (3)

Image Analyst
Image Analyst on 27 Nov 2019
Simply get the x and y of the line using simple analytical equations (geometry, algebra) using the known coordinates of the center, point A, point B, and the known radius), then use plot:
plot(x, y, 'r-', 'LineWidth', 5); % Plot thick red curve.
To get the distance, you could just sum x and y segment lengths
distance = sum(sqrt(x(2:end) - x(1:end-1)) .^ 2 + (y(2:end) - y(1:end-1) .^ 2);
if you want MATLAB to do it quantitatively. Of course there is also an analytical equation using the pure mathematical equations of the lines and curve.
  5 Comments
Veronica Spelbrink
Veronica Spelbrink on 30 May 2020
If you're willing to help the function that computes the whole trajectory and the variables to load into the workspace are attached. plot_rollers.m is just a secondary function that plots the line and dashed line circles. You can run the trajectory.m with the inputs like so:
trajectory(circles, shapes, rt, plane_depth);
however the section of the code that I need help with is in the trajectory.m file, from line 76 to 113, which is sort of what I referenced in my first comment, where the curved segments are computed.
UPDATE: I had to change the way I was doing it to choose whether I wanted to draw the curve from point 1 to point 2 clockwise or Anti-clockwise. And now it should work. Since the code above is slightly deprecated as it wasn't functioning correctly, I will leave here the correct solution as an answer once I have it. It might be of help to someone.

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Veronica Spelbrink
Veronica Spelbrink on 31 May 2020
function [X, Y, Z] = arc()
A = [1.66870803851856; 0.500000000000000; 1.22112689094119];
A1 = [0.791819441598963; 0.5; 1.03409208510982]; %your points belonging to the circle ircumference go here
B1 = [0.720451021787587; 0.5; 0.859809300488578];
B = [0.969580132133386;0.500000000000000;0.482295106876854];
r = 0.114; %your circle radius here
center = [0.8156; 0.5; 0.9226]; %your circle center here
winding_direction = 1; %direction in which you want your line to wrap around the circle, clockwise (1) or conter-clockwise (0)
xc = center(1);
yc = center(2);
zc = center(3);
%Separate the X, Y and Z components for easy plotting
P = []; %final path
Points =[A A1 B1 B];
% compute line between A and A1
x_l = linspace(A(1), A1(1), 200);
y_l = linspace(A(2), A1(2), 200);
z_l = linspace(A(3), A1(3), 200);
p_line = [x_l; y_l; z_l];
P = cat(2, P, p_line);
%compute the arc between A1 and B1
if (winding_direction == 1) %clockwise rotation
a = atan2(A1(3) - zc, A1(1) - xc);
b = atan2(B1(3) - zc, B1(1) - xc);
b = mod(b-a, 2*pi)+a; % Ensure that arc moves cw
elseif (winding_direction == 0) %counter-clockwise rotation
a = atan2(A1(3) - zc, A1(1) - xc);
b = atan2(B1(3) - zc, B1(1) - xc);
b = mod(b-a, 2*pi)+a-2*pi; % Ensure that arc moves ccw
end
t = linspace(a, b, 1000);
x_a = xc + r*cos(t);
y_a = repmat(yc, 1, 1000);
z_a = zc + r*sin(t);
p_arc = [x_a; y_a; z_a];
P = cat(2, P, p_arc);
% compute line between B1 and B
x_l = linspace(B1(1), B(1), 200);
y_l = linspace(B1(2), B(2), 200);
z_l = linspace(B1(3), B(3), 200);
p_line = [x_l; y_l; z_l];
P = cat(2, P, p_line)
num_p = size(P, 2);
X = zeros(1, num_p);
Y = zeros(1, num_p);
Z = zeros(1, num_p);
for q = 1:num_p
X(1, q) = P(1, q);
Y(1, q) = P(2, q);
Z(1, q) = P(3, q);
end
plot3(X, Y, Z, 'r-'), grid on, hold on, axis square;
plot3(Points(1,:), Points(2,:), Points(3,:), 'o', 'MarkerFaceColor', 'black');
view(180,0);
hold off
end

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