Geometric functions concerning lines and segments.

A `Line`

is taken to be infinite in length, while a `Seg`

is finite length line segment represented by its two endpoints.

- segClearsBox :: Point -> Point -> Point -> Point -> Bool
- closestPointOnLine :: Point -> Point -> Point -> Point
- closestPointOnLineParam :: Point -> Point -> Point -> Float
- intersectLineLine :: Point -> Point -> Point -> Point -> Maybe Point
- intersectSegLine :: Point -> Point -> Point -> Point -> Maybe Point
- intersectSegHorzLine :: Point -> Point -> Float -> Maybe Point
- intersectSegVertLine :: Point -> Point -> Float -> Maybe Point
- intersectSegSeg :: Point -> Point -> Point -> Point -> Maybe Point
- intersectSegHorzSeg :: Point -> Point -> Float -> Float -> Float -> Maybe Point
- intersectSegVertSeg :: Point -> Point -> Float -> Float -> Float -> Maybe Point

# Documentation

:: Point | P1 First point of segment. |

-> Point | P2 Second point of segment. |

-> Point | P3 Lower left point of box. |

-> Point | P4 Upper right point of box. |

-> Bool |

Check if line segment (P1-P2) clears a box (P3-P4) by being well outside it.

# Closest points

Given an infinite line which intersects `P1`

and `P1`

,
return the point on that line that is closest to `P3`

Given an infinite line which intersects P1 and P2, let P4 be the point on the line that is closest to P3.

Return an indication of where on the line P4 is relative to P1 and P2.

if P4 == P1 then 0 if P4 == P2 then 1 if P4 is halfway between P1 and P2 then 0.5

| P1 | P4 +---- P3 | P2 |

# Line-Line intersection

Given four points specifying two lines, get the point where the two lines cross, if any. Note that the lines extend off to infinity, so the intersection point might not lie between either of the two pairs of points.

\ / P1 P4 \ / + / \ P3 P2 / \

# Seg-Line intersection

Get the point where a segment `P1-P2`

crosses an infinite line `P3-P4`

, if any.

:: Point | P1 First point of segment. |

-> Point | P2 Second point of segment. |

-> Float | y value of line. |

-> Maybe Point |

Get the point where a segment crosses a horizontal line, if any.

+ P1 / -------+--------- / y0 P2 +

:: Point | P1 First point of segment. |

-> Point | P2 Second point of segment. |

-> Float | x value of line. |

-> Maybe Point |

Get the point where a segment crosses a vertical line, if any.

| | + P1 | / + / | P2 + | | x0

# Seg-Seg intersection

Get the point where a segment `P1-P2`

crosses another segement `P3-P4`

, if any.

:: Point | P1 First point of segment. |

-> Point | P2 Second point of segment. |

-> Float | (y3) y value of horizontal segment. |

-> Float | (xa) Leftmost x value of horizontal segment. |

-> Float | (xb) Rightmost x value of horizontal segment. |

-> Maybe Point | (x3, y3) Intersection point, if any. |

Check if an arbitrary segment intersects a horizontal segment.

+ P2 / (xa, y3) +---+----+ (xb, y3) / P1 +

:: Point | P1 First point of segment. |

-> Point | P2 Second point of segment. |

-> Float | (x3) x value of vertical segment |

-> Float | (ya) Lowest y value of vertical segment. |

-> Float | (yb) Highest y value of vertical segment. |

-> Maybe Point | (x3, y3) Intersection point, if any. |

Check if an arbitrary segment intersects a vertical segment.

(x3, yb) + | + P1 | / + / | P2 + | + (x3, ya)