gloss-1.11.1.1: Painless 2D vector graphics, animations and simulations.

Graphics.Gloss.Geometry.Line

Description

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.

Synopsis

# Documentation

Arguments

 :: 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

Arguments

 :: Point P1 -> Point P2 -> Point P3 -> Point the point on the line P1-P2 that is closest to P3

Given an infinite line which intersects P1 and P1, return the point on that line that is closest to P3

Arguments

 :: Point P1 -> Point P2 -> Point P3 -> Float

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

Arguments

 :: Point P1 -> Point P2 -> Point P3 -> Point P4 -> Maybe Point

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 line between either of the two pairs of points.

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


# Seg-Line intersection

Arguments

 :: Point P1 -> Point P2 -> Point P3 -> Point P4 -> Maybe Point

Get the point where a segment P1-P2 crosses an infinite line P3-P4, if any.

Arguments

 :: 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 +


Arguments

 :: 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

Arguments

 :: Point P1 -> Point P2 -> Point P3 -> Point P4 -> Maybe Point

Get the point where a segment P1-P2 crosses another segement P3-P4, if any.

Arguments

 :: 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 +


Arguments

 :: 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)