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An instance s of the data type Segment_d is a directed straight line segment in d-dimensional Euclidean space connecting two points p and q. p is called the source point and q is called the target point of s, both points are called endpoints of s. A segment whose endpoints are equal is called degenerate.
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the linear algebra layer.
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introduces a variable s
of type Segment_d<Kernel>.
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introduces a
variable s of type Segment_d<Kernel> which is initialized to
the segment (p,q).
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introduces a
variable s of type Segment_d<Kernel> which is initialized to
the segment (p,p+v).
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| returns the dimension of the ambient space. | ||
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| returns the source point of segment s. | ||
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| returns the target point of segment s. | ||
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returns source or target of
s: vertex(0) returns the source, vertex(1) returns
the target. The parameter i is taken modulo 2, which gives easy
access to the other vertex.
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| returns vertex(i). | ||
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| returns vertex(i). | ||
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| returns the lexicographically smaller vertex. | ||
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| returns the lexicographically larger vertex. | ||
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| returns the segment (target(),source()). | ||
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returns the direction from
source to target.
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| returns the vector from source to target. | ||
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| returns the square of the length of s. | ||
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returns true if p lies
on s and false otherwise.
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returns the supporting line
of s.
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returns t(s).
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returns
s+v, i.e., s translated by vector v.
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| returns true if s is degenerate i.e. s.source()=s.target(). | ||
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Test for equality as unoriented
segments.
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return true if one of the segments is degenerate or if the
unoriented supporting lines are parallel.
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if s1 and s2
touch in a common end point, this point is assigned to common
and the result is true, otherwise the result is false. If
s1==s2 then one of the endpoints is returned.
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Segments are implemented by a pair of points as an item type. All operations like creation, initialization, tests, the calculation of the direction and source - target vector, input and output on a segment s take time O(s.dimension()). dimension(), coordinate and end point access, and identity test take constant time. The operations for intersection calculation also take time O(s.dimension()). The space requirement is O(s.dimension()).