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2. It is
defined by the set of points with
Cartesian
coordinates (x,y)
that satisfy the equation
l : ax + by + c = 0
The line splits 2 in a positive and a negative
side. A point p with
Cartesian
coordinates
(px, py) is on the positive side of l, iff
a px + b py +c > 0, it is
on the negative side of l, iff
a px + b py +c < 0.
The positive side is to the left of l.
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introduces a line l with the line equation in
Cartesian
coordinates ax +by +c = 0.
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introduces a line l passing through the points p and q.
Line l is directed from p to q.
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introduces a line l passing through point p with
direction d.
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introduces a line l passing through point p and
oriented by v.
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introduces a line l supporting the segment s,
oriented from source to target.
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introduces a line l supporting the ray r,
with same orientation.
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| Test for equality: two lines are equal, iff they have a non empty intersection and the same direction. | ||
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| Test for inequality. | ||
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| returns the first coefficient of l. | ||
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| returns the second coefficient of l. | ||
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| returns the third coefficient of l. | ||
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| returns an arbitrary point on l. It holds point(i) == point(j), iff i==j. Furthermore, l is directed from point(i) to point(j), for all i < j. | ||
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| returns the orthogonal projection of p onto l. | ||||
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returns the x-coordinate of the point at l with
given y-coordinate.
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returns the y-coordinate of the point at l with
given x-coordinate.
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| line l is degenerate, if the coefficients a and b of the line equation are zero. |
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| returns ON_ORIENTED_BOUNDARY, ON_NEGATIVE_SIDE, or the constant ON_POSITIVE_SIDE, depending on the position of p relative to the oriented line l. | ||
For convenience we provide the following Boolean functions:
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| returns a vector having the direction of l. |
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| returns the direction of l. |
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| returns the line with opposite direction. |
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| returns the line perpendicular to l and passing through p, where the direction is the direction of l rotated counterclockwise by 90 degrees. | ||
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| returns the line obtained by applying t on a point on l and the direction of l. | ||
2. Their
dimension and the fact that they are
Cartesian
is expressed by
the suffix _2 and the representation type Cartesian.
Point_2< Cartesian<double> > p(1.0,1.0), q(4.0,7.0);
To define a line l we write:
Line_2< Cartesian<double> > l(p,q);