Conics intersection

Version 1.5.0.0 (6.54 KB) by
Given the homogeneous matrices of two conics it recovers the (up to) four intersection points
Updated 30 Aug 2015

The homogeneous representation of a conic is a matrix
m = [A C D; C B E; D E F] that represents the equation
A x^2 + B y^2 + 2C xy + 2D x + 2Ey + F = 0
Given two matrix E1 and E2 representing two conics, the code will detect all their intersections.

For instance:
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%a circle centered in the origin
E1 = [1 0 0; 0 1 0; 0 0 -3]

%an ellipse centered in the origin
E2 = [1 0 0; 0 3 0; 0 0 -6]

%get the four homogeneous intersections
P = intersectConics(E1, E2)

%plot the normalized points
plot(P(1,:) ./ P(3,:) , P(2,:) ./ P(3,:), 'ro');

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and a detailed example describing the method: http://math.stackexchange.com/questions/316849/intersection-of-conics-using-matrix-representation

A C++ open souce implementation is also present at https://bitbucket.org/pierluigi/conicsintersection

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If this code was useful, please consider a donation:
Bitcoin: 3BUD7cEnbpp15hZXbPZpdgnH11FAV1kvfi

Cite As

Pierluigi Taddei (2024). Conics intersection (https://www.mathworks.com/matlabcentral/fileexchange/28318-conics-intersection), MATLAB Central File Exchange. Retrieved .

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Created with R2008a
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Version Published Release Notes
1.5.0.0

summary update

1.4.0.0