| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Data.Geometry.Line.Internal
Contents
- data Line d r = Line {
- _anchorPoint :: !(Point d r)
- _direction :: !(Vector d r)
- direction :: forall d r. Lens' (Line d r) (Vector d r)
- anchorPoint :: forall d r. Lens' (Line d r) (Point d r)
- lineThrough :: (Num r, Arity d) => Point d r -> Point d r -> Line d r
- verticalLine :: Num r => r -> Line 2 r
- horizontalLine :: Num r => r -> Line 2 r
- perpendicularTo :: Num r => Line 2 r -> Line 2 r
- isIdenticalTo :: (Eq r, Arity d) => Line d r -> Line d r -> Bool
- isParallelTo :: (Eq r, Fractional r, Arity d) => Line d r -> Line d r -> Bool
- onLine :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Bool
- sqDistanceTo :: (Fractional r, Arity d) => Point d r -> Line d r -> r
- sqDistanceToArg :: (Fractional r, Arity d) => Point d r -> Line d r -> (r, Point d r)
- class HasSupportingLine t where
- fromLinearFunction :: Num r => r -> r -> Line 2 r
- toLinearFunction :: forall r. (Fractional r, Eq r) => Line 2 r -> Maybe (r, r)
- data SideTest
- onSide :: (Ord r, Num r) => Point 2 r -> Line 2 r -> SideTest
- liesAbove :: (Ord r, Num r) => Point 2 r -> Line 2 r -> Bool
- bisector :: Fractional r => Point 2 r -> Point 2 r -> Line 2 r
d-dimensional Lines
A line is given by an anchor point and a vector indicating the direction.
Constructors
| Line | |
Fields
| |
Instances
Functions on lines
lineThrough :: (Num r, Arity d) => Point d r -> Point d r -> Line d r Source #
A line may be constructed from two points.
verticalLine :: Num r => r -> Line 2 r Source #
horizontalLine :: Num r => r -> Line 2 r Source #
perpendicularTo :: Num r => Line 2 r -> Line 2 r Source #
Given a line l with anchor point p, get the line perpendicular to l that also goes through p.
isIdenticalTo :: (Eq r, Arity d) => Line d r -> Line d r -> Bool Source #
Test if two lines are identical, meaning; if they have exactly the same anchor point and directional vector.
isParallelTo :: (Eq r, Fractional r, Arity d) => Line d r -> Line d r -> Bool Source #
Test if the two lines are parallel.
>>>lineThrough origin (point2 1 0) `isParallelTo` lineThrough (point2 1 1) (point2 2 1)True>>>lineThrough origin (point2 1 0) `isParallelTo` lineThrough (point2 1 1) (point2 2 2)False
onLine :: (Eq r, Fractional r, Arity d) => Point d r -> Line d r -> Bool Source #
Test if point p lies on line l
>>>origin `onLine` lineThrough origin (point2 1 0)True>>>point2 10 10 `onLine` lineThrough origin (point2 2 2)True>>>point2 10 5 `onLine` lineThrough origin (point2 2 2)False
sqDistanceTo :: (Fractional r, Arity d) => Point d r -> Line d r -> r Source #
Squared distance from point p to line l
sqDistanceToArg :: (Fractional r, Arity d) => Point d r -> Line d r -> (r, Point d r) Source #
The squared distance between the point p and the line l, and the point m realizing this distance.
Supporting Lines
class HasSupportingLine t where Source #
Types for which we can compute a supporting line, i.e. a line that contains the thing of type t.
Minimal complete definition
Instances
| HasSupportingLine (Line d r) Source # | |
| HasSupportingLine (HalfLine d r) Source # | |
| (Num r, Arity d) => HasSupportingLine (LineSegment d p r) Source # | |
Convenience functions on Two dimensional lines
fromLinearFunction :: Num r => r -> r -> Line 2 r Source #
Create a line from the linear function ax + b
toLinearFunction :: forall r. (Fractional r, Eq r) => Line 2 r -> Maybe (r, r) Source #
get values a,b s.t. the input line is described by y = ax + b. returns Nothing if the line is vertical
Result of a side test
onSide :: (Ord r, Num r) => Point 2 r -> Line 2 r -> SideTest Source #
Given a point q and a line l, compute to which side of l q lies. For vertical lines the left side of the line is interpeted as below.
>>>point2 10 10 `onSide` (lineThrough origin $ point2 10 5)Above>>>point2 10 10 `onSide` (lineThrough origin $ point2 (-10) 5)Above>>>point2 5 5 `onSide` (verticalLine 10)Below>>>point2 5 5 `onSide` (lineThrough origin $ point2 (-3) (-3))On