gloss-1.8.0.1: 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)
```