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An instance of data type Ray_d is a ray in d-dimensional Euclidean space. It starts in a point called the source of r and it goes to infinity.
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the linear algebra layer.
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introduces some ray in
d-dimensional space.
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introduces a ray
through p and q and starting at p.
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introduces
a ray starting in p with direction dir.
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introduces a ray through
s.source() and s.target() and starting at
s.source().
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| returns the dimension of the ambient space. | ||
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| returns the source point of r. | ||
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returns a point on
r. point(0) is the source. point(i), with i>0, is
different from the source.
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| returns the direction of r. | ||
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| returns the supporting line of r. | ||
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| returns the ray with direction opposite to r and starting in source. | ||
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returns t(r).
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returns
r+v, i.e., r translated by vector v.
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A point is on r,
iff it is equal to the source of r, or if it is in the interior
of r.
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returns true if the unoriented supporting lines of r1 and
r2 are parallel and false otherwise.
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Rays are implemented by a pair of points as an item type. All operations like creation, initialization, tests, direction calculation, input and output on a ray r take time O(r.dimension()). dimension(), coordinate and point access, and identity test take constant time. The space requirement is O(r.dimension()).