P
- Point implementation typepublic interface Hyperplane<P extends Point<P>>
n
is
a subspace of dimension n - 1
. (A hyperplane in Euclidean 3D space,
for example, is a 2 dimensional plane.)
Hyperplanes partition their surrounding space into 3 distinct sets: (1) points
lying on one side of the hyperplane, (2) points lying on the opposite side, and
(3) points lying on the hyperplane itself. One side of the hyperplane is labeled
as the plus side and the other as the minus side. The
offset
of a point in relation to a hyperplane is the distance
from the point to the hyperplane combined with the sign of the side that the point
lies on: points lying on the plus side of the hyperplane have a positive offsets,
those on the minus side have a negative offset, and those lying directly on the
hyperplane have an offset of zero.
HyperplaneLocation
,
HyperplaneSubset
Modifier and Type | Method and Description |
---|---|
HyperplaneLocation |
classify(P point)
Classify a point with respect to this hyperplane.
|
boolean |
contains(P point)
Return true if the given point lies on the hyperplane.
|
double |
offset(P point)
Get the offset (oriented distance) of a point with respect
to this instance.
|
P |
project(P point)
Project a point onto this instance.
|
Hyperplane<P> |
reverse()
Return a hyperplane that has the opposite orientation as this instance.
|
boolean |
similarOrientation(Hyperplane<P> other)
Return true if this instance has a similar orientation to the given hyperplane,
meaning that they point in generally the same direction.
|
HyperplaneConvexSubset<P> |
span()
Return a
HyperplaneConvexSubset spanning this entire hyperplane. |
Hyperplane<P> |
transform(Transform<P> transform)
Transform this instance using the given
Transform . |
double offset(P point)
point
- the point to compute the offset forHyperplaneLocation classify(P point)
point
- the point to classifyboolean contains(P point)
point
- the point to testP project(P point)
point
- the point to projectHyperplane<P> reverse()
Hyperplane<P> transform(Transform<P> transform)
Transform
.transform
- object to transform this instance withboolean similarOrientation(Hyperplane<P> other)
other
- the hyperplane to compare withHyperplaneConvexSubset<P> span()
HyperplaneConvexSubset
spanning this entire hyperplane. The returned
subset contains all points lying in this hyperplane and no more.HyperplaneConvexSubset
containing all points lying in this hyperplaneCopyright © 2016–2021 The Apache Software Foundation. All rights reserved.