view release on metacpan or  search on metacpan

lib/Math/Geometry/IntersectionArea.pm  view on Meta::CPAN

    #    /       \
    #    |   x---|-x
    #

    # The two points where the segment intersects the circle are found
    # solving the following cuadratic equation:
    #
    #   norm(a + alfa * ab) = d
    #
    #
    # The coeficientes c2, c1, c0 are deduced from the formula
    # above such that:
    #
    #   c2 * alfa**2 + 2 * c1 * alfa + c0 = 0
    #
    # And then the clasical formula for quadratic equation solved is
    # used:
    #
    #   alfa0 = 1/c2 + (-$c1 + sqrt($c1*$c1 - 4 * $c0 * $c2))
    #   alfa1 = 1/c2 + (-$c1 - sqrt($c1*$c1 - 4 * $c0 * $c2))

    my $ab = $b - $a;
    my $c2 = $ab->norm2 or return 0; # a and b are the same point
    my $c1 = $a * $ab;
    my $c0 = $a->norm2 - $r2;
    my $discriminant = $c1 * $c1 - $c0 * $c2;