Diagrams.Points

Points in space. For more tools for working with points and vectors, see Data.AffineSpace and Diagrams.Coordinates.

Points

data Point v :: * -> *

Point is a newtype wrapper around vectors used to represent points, so we don't get them mixed up. The distinction between vectors and points is important: translations affect points, but leave vectors unchanged. Points are instances of the AffineSpace class from Data.AffineSpace.

Instances

Functor Point

HasR P2

HasR P3

HasZ P3

HasY P2

HasY P3

HasX P2

HasX P3

HasTheta P2

HasTheta P3

HasPhi P3

Cylindrical P3

Spherical P3

Eq v => Eq (Point v)

Data v => Data (Point v)

Ord v => Ord (Point v)

Read v => Read (Point v)

Show v => Show (Point v)

(OrderedField (Scalar v), InnerSpace v) => Enveloped (Point v)

(Ord (Scalar v), VectorSpace v) => Traced (Point v)

The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope).

HasLinearMap v => Transformable (Point v)

VectorSpace v => HasOrigin (Point v)

AdditiveGroup v => AffineSpace (Point v)

Coordinates v => Coordinates (Point v)

(InnerSpace v, OrderedField (Scalar v)) => TrailLike [Point v]

A list of points is trail-like; this instance simply computes the vertices of the trail, using trailVertices.

Deformable (Point v)

Typeable (* -> *) Point

type V (Point v) = v

type Diff (Point v) = v

type FinalCoord (Point v) = FinalCoord v

type PrevDim (Point v) = PrevDim v

type Decomposition (Point v) = Decomposition v

origin :: AdditiveGroup v => Point v

The origin of the vector space v.

(*.) :: VectorSpace v => Scalar v -> Point v -> Point v

Scale a point by a scalar.

Point-related utilities

centroid :: (VectorSpace v, Fractional (Scalar v)) => [Point v] -> Point v

The centroid of a set of n points is their sum divided by n.

pointDiagram :: (Fractional (Scalar v), InnerSpace v) => Point v -> QDiagram b v m

Create a "point diagram", which has no content, no trace, an empty query, and a point envelope.