Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	GHC2021

HGeometry.Plane.LowerEnvelope.Clipped

Description

A Representation of the Lower envelope of planes inside a given triangle. This means now all regions are actually bounded.

Synopsis

type ClippedMinimizationDiagram plane = ClippedMinimizationDiagram' (NumType plane) plane
data ClippedMinimizationDiagram' r plane
_ClippedMinimizationDiagramMap :: NumType plane ~ r => Iso' (ClippedMinimizationDiagram plane) (NEMap plane (ClippedMDCell r plane))
type ClippedMDCell r plane = ClippedMDCell' r (MDVertex r plane)
newtype ClippedMDCell' r vertex = ClippedMDCell (PossiblyDegenerateSimplePolygon (OriginalOrExtra vertex (Point 2 r)) (ClippedBoundedRegion r vertex (Point 2 r)))
lowerEnvelopeIn :: (Plane_ plane r, Ord plane, Ord r, Fractional r, Point_ corner 2 r, Foldable1 set, Show r, Show corner, Show plane) => Triangle corner -> set plane -> ClippedMinimizationDiagram plane

Documentation

type ClippedMinimizationDiagram plane = ClippedMinimizationDiagram' (NumType plane) plane Source #

The representing (the minimization diagram) of the lower envelope of a set of planes, clipped to some bounding triangle.

A ClippedMinimizationDiagram is essentially just a non-empty Map mapping planes to cells.

data ClippedMinimizationDiagram' r plane Source #

Implementatino of the ClippedMinimizationDiagram type; r is the numeric type of the planes

Instances

Instances details

CFunctor (ClippedMinimizationDiagram' r) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type Methods cmap :: (Dom (ClippedMinimizationDiagram' r) a, Dom (ClippedMinimizationDiagram' r) b) => (a -> b) -> ClippedMinimizationDiagram' r a -> ClippedMinimizationDiagram' r b Source # (<$:) :: (Dom (ClippedMinimizationDiagram' r) a, Dom (ClippedMinimizationDiagram' r) b) => a -> ClippedMinimizationDiagram' r b -> ClippedMinimizationDiagram' r a Source #
Constrained (ClippedMinimizationDiagram' r) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type
(Show r, Num r, Show plane) => Show (ClippedMinimizationDiagram' r plane) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type Methods showsPrec :: Int -> ClippedMinimizationDiagram' r plane -> ShowS # show :: ClippedMinimizationDiagram' r plane -> String # showList :: [ClippedMinimizationDiagram' r plane] -> ShowS #
type Dom (ClippedMinimizationDiagram' r) plane Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type type Dom (ClippedMinimizationDiagram' r) plane = Ord plane
type Dimension (ClippedMinimizationDiagram' r plane) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type type Dimension (ClippedMinimizationDiagram' r plane) = 2
type NumType (ClippedMinimizationDiagram' r plane) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type type NumType (ClippedMinimizationDiagram' r plane) = r

_ClippedMinimizationDiagramMap :: NumType plane ~ r => Iso' (ClippedMinimizationDiagram plane) (NEMap plane (ClippedMDCell r plane)) Source #

Get access to the underlying NonEmpty Map

type ClippedMDCell r plane = ClippedMDCell' r (MDVertex r plane) Source #

Cells in the Minimization diagram (i.e. the projected lower envelope of planes) parameterized by the numeric type and the planes

newtype ClippedMDCell' r vertex Source #

Helper type for representing cells in a minimzation diagram. These cells are possibly degenerate convex polygons, whose vertices are either of type vertex or of type 'Point 2 r'.

Constructors

ClippedMDCell (PossiblyDegenerateSimplePolygon (OriginalOrExtra vertex (Point 2 r)) (ClippedBoundedRegion r vertex (Point 2 r)))

Instances

Instances details

Functor (ClippedMDCell' r) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type Methods fmap :: (a -> b) -> ClippedMDCell' r a -> ClippedMDCell' r b # (<$) :: a -> ClippedMDCell' r b -> ClippedMDCell' r a #
(Show vertex, Point_ vertex 2 r, Show r) => Show (ClippedMDCell' r vertex) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type Methods showsPrec :: Int -> ClippedMDCell' r vertex -> ShowS # show :: ClippedMDCell' r vertex -> String # showList :: [ClippedMDCell' r vertex] -> ShowS #
(Eq vertex, Eq r) => Eq (ClippedMDCell' r vertex) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type Methods (==) :: ClippedMDCell' r vertex -> ClippedMDCell' r vertex -> Bool # (/=) :: ClippedMDCell' r vertex -> ClippedMDCell' r vertex -> Bool #
type Dimension (ClippedMDCell' r vertex) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type type Dimension (ClippedMDCell' r vertex) = 2
type NumType (ClippedMDCell' r vertex) Source #
Instance details Defined in HGeometry.Plane.LowerEnvelope.Clipped.Type type NumType (ClippedMDCell' r vertex) = r

lowerEnvelopeIn :: (Plane_ plane r, Ord plane, Ord r, Fractional r, Point_ corner 2 r, Foldable1 set, Show r, Show corner, Show plane) => Triangle corner -> set plane -> ClippedMinimizationDiagram plane Source #

Compute the lower envelope of planes inside a given triangle.

$O(n^4)$ (as it currently uses the brute force algorithm).