MATLAB: Find intersection point of two lines inside a circle

inside a circleintersection pointtwo lines

I have to find and check the intersection point of two lines with additional conditions that the lines intersect inside a circle. Can anybody help? Thank you

Best Answer

Just set the two line equations equal to each other to get the (x,y) of the intersection.

m1*x + b1 = m2*x + b2;

then solve for x, and plug that x back in either equation to get the y. It's trivial 10th grade stuff so I'm sure a smart engineer like you will be able to solve it in seconds. I don't want to insult you by doing it for you. Of course the m's and b's must be given to you so you know the equations of the lines.

Then compute the distance of that from the center to see if it's closer than the radius

if sqrt((x-xCenter)^2 + (y-yCenter)^2) <= radius
    % Intersection is inside the circle.
else
    % Intersection is not inside the circle.
end

Related Solutions

MATLAB: How to discover intersecting circles

Try this:

% Create sample data.
numCircles = 10;
xy = rand(numCircles, 2);
radii = 0.1 * rand(numCircles, 1) + 0.1;
viscircles(xy, radii);
% Label them so we know what circle is what.
for k = 1 : numCircles
	text(xy(k, 1), xy(k, 2), num2str(k));
end
axis square;
% See if any intersect
for k = 1 : numCircles
	% Compute the distance between centers.
	distances = sqrt((xy(k, 1) - xy(:, 1)).^2 + (xy(k, 2) - xy(:, 2)) .^2);
	sumOfRadii = radii(k) + radii(:);
	intersectingIndexes = distances < sumOfRadii;
	% Don't compare circle to itself.  Of course that one intersects!
	intersectingIndexes(k) = false;
	% Convert to linear indexes
	intersectingIndexes = find(intersectingIndexes);
	for k2 = 1 : length(intersectingIndexes)
		fprintf('Circle %d intersects with circle #%d.\n', k, intersectingIndexes(k2));
	end
end

You see

Circle 1 intersects with circle #2.

Circle 1 intersects with circle #5.

Circle 1 intersects with circle #7.

Circle 2 intersects with circle #1.

Circle 2 intersects with circle #5.

Circle 3 intersects with circle #7.

Circle 3 intersects with circle #9.

Circle 5 intersects with circle #1.

Circle 5 intersects with circle #2.

Circle 6 intersects with circle #10.

Circle 7 intersects with circle #1.

Circle 7 intersects with circle #3.

Circle 8 intersects with circle #9.

Circle 9 intersects with circle #3.

Circle 9 intersects with circle #8.

Circle 10 intersects with circle #6.

and it's trivial to find out if one circle is completely contained within another. See if you can do it.

MATLAB: How to draw a circle in a log-log plot

Use the FAQ to draw a circle, then exponentiate:

http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F

xCenter = 12;
yCenter = 10;
theta = 0 : 0.01 : 2*pi;
radius = 5;
x = radius * cos(theta) + xCenter;
y = radius * sin(theta) + yCenter;
xe = exp(x);
ye = exp(y);
loglog(xe, ye, 'LineWidth', 2);
axis square;
grid on;
hold on;
% Draw second circle
radius = 3;
x = radius * cos(theta) + xCenter;
y = radius * sin(theta) + yCenter;
xe = exp(x);
ye = exp(y);
loglog(xe, ye, 'LineWidth', 2);

Best Answer

Related Solutions

MATLAB: How to discover intersecting circles

MATLAB: How to draw a circle in a log-log plot

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