module Geometry.LHS (
    isLHS,
    isRHS,
) where

import Geometry.Data

{- | Test whether a point is stricly on the LHS of a line.
 Returns False if the line is of zero length.
-}
isLHS ::
    -- | First line point.
    Point2 ->
    -- | Second line point.
    Point2 ->
    -- | Point not on line.
    Point2 ->
    Bool
{-# INLINE isLHS #-}
isLHS (V2 x y) (V2 x' y') (V2 x'' y'')
    | (x, y) == (x', y') = False
    | otherwise = a1 * b2 - a2 * b1 > 0
  where
    a1 = x' - x
    a2 = y' - y
    b1 = x'' - x
    b2 = y'' - y

{- | Test whether a point is on the RHS of a line.
 Returns False if the line is of zero length.
-}
isRHS ::
    -- | First line point.
    Point2 ->
    -- | Second line point.
    Point2 ->
    -- | Point not on line.
    Point2 ->
    Bool
{-# INLINE isRHS #-}
isRHS
    (V2 x y)
    (V2 x' y')
    (V2 x'' y'')
        | (x, y) == (x', y') = False
        | otherwise = a1 * b2 - a2 * b1 < 0
      where
        a1 = x' - x
        a2 = y' - y
        b1 = x'' - x
        b2 = y'' - y