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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Graphics-Gloss-Geometry-Line.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">gloss-1.7.8.3: Painless 2D vector graphics, animations and simulations.</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>Safe-Inferred</td></tr></table><p class="caption">Graphics.Gloss.Geometry.Line</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Closest points
</a></li><li><a href="#g:2">Line-Line intersection
</a></li><li><a href="#g:3">Seg-Line intersection
</a></li><li><a href="#g:4">Seg-Seg intersection
</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Geometric functions concerning lines and segments.
</p><p>A <code>Line</code> is taken to be infinite in length, while a <code>Seg</code> is finite length
line segment represented by its two endpoints.
</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><a href="#v:segClearsBox">segClearsBox</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:closestPointOnLine">closestPointOnLine</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li><li class="src short"><a href="#v:closestPointOnLineParam">closestPointOnLineParam</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></li><li class="src short"><a href="#v:intersectLineLine">intersectLineLine</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li><li class="src short"><a href="#v:intersectSegLine">intersectSegLine</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li><li class="src short"><a href="#v:intersectSegHorzLine">intersectSegHorzLine</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li><li class="src short"><a href="#v:intersectSegVertLine">intersectSegVertLine</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li><li class="src short"><a href="#v:intersectSegSeg">intersectSegSeg</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li><li class="src short"><a href="#v:intersectSegHorzSeg">intersectSegHorzSeg</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li><li class="src short"><a href="#v:intersectSegVertSeg">intersectSegVertSeg</a> :: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><a name="v:segClearsBox" class="def">segClearsBox</a><a href="src/Graphics-Gloss-Geometry-Line.html#segClearsBox" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P1 First point of segment.
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P2 Second point of segment.
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P3 Lower left point of box.
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P4 Upper right point of box.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Check if line segment (P1-P2) clears a box (P3-P4) by being well outside it.
</p></div></div><h1 id="g:1">Closest points
</h1><div class="top"><p class="src"><a name="v:closestPointOnLine" class="def">closestPointOnLine</a><a href="src/Graphics-Gloss-Geometry-Line.html#closestPointOnLine" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P1</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P2</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P3</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>the point on the line P1-P2 that is closest to <code>P3</code>
</p></td></tr></table></div><div class="doc"><p>Given an infinite line which intersects <code>P1</code> and <code>P1</code>,
return the point on that line that is closest to <code>P3</code>
</p></div></div><div class="top"><p class="src"><a name="v:closestPointOnLineParam" class="def">closestPointOnLineParam</a><a href="src/Graphics-Gloss-Geometry-Line.html#closestPointOnLineParam" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P1</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P2</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P3</code>
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Given an infinite line which intersects P1 and P2,
let P4 be the point on the line that is closest to P3.
</p><p>Return an indication of where on the line P4 is relative to P1 and P2.
</p><pre>
if P4 == P1 then 0
if P4 == P2 then 1
if P4 is halfway between P1 and P2 then 0.5
</pre><pre>
|
P1
|
P4 +---- P3
|
P2
|
</pre></div></div><h1 id="g:2">Line-Line intersection
</h1><div class="top"><p class="src"><a name="v:intersectLineLine" class="def">intersectLineLine</a><a href="src/Graphics-Gloss-Geometry-Line.html#intersectLineLine" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P1</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P2</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P3</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P4</code>
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>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.
</p><pre>
\ /
P1 P4
\ /
+
/ \
P3 P2
/ \
</pre></div></div><h1 id="g:3">Seg-Line intersection
</h1><div class="top"><p class="src"><a name="v:intersectSegLine" class="def">intersectSegLine</a><a href="src/Graphics-Gloss-Geometry-Line.html#intersectSegLine" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P1</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P2</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P3</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P4</code>
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Get the point where a segment <code>P1-P2</code> crosses an infinite line <code>P3-P4</code>,
if any.
</p></div></div><div class="top"><p class="src"><a name="v:intersectSegHorzLine" class="def">intersectSegHorzLine</a><a href="src/Graphics-Gloss-Geometry-Line.html#intersectSegHorzLine" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P1 First point of segment.
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P2 Second point of segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>y value of line.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Get the point where a segment crosses a horizontal line, if any.
</p><pre>
+ P1
/
-------+---------
/ y0
P2 +
</pre></div></div><div class="top"><p class="src"><a name="v:intersectSegVertLine" class="def">intersectSegVertLine</a><a href="src/Graphics-Gloss-Geometry-Line.html#intersectSegVertLine" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P1 First point of segment.
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P2 Second point of segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>x value of line.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Get the point where a segment crosses a vertical line, if any.
</p><pre>
|
| + P1
| /
+
/ |
P2 + |
| x0
</pre></div></div><h1 id="g:4">Seg-Seg intersection
</h1><div class="top"><p class="src"><a name="v:intersectSegSeg" class="def">intersectSegSeg</a><a href="src/Graphics-Gloss-Geometry-Line.html#intersectSegSeg" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P1</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P2</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P3</code>
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p><code>P4</code>
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Get the point where a segment <code>P1-P2</code> crosses another segement <code>P3-P4</code>,
if any.
</p></div></div><div class="top"><p class="src"><a name="v:intersectSegHorzSeg" class="def">intersectSegHorzSeg</a><a href="src/Graphics-Gloss-Geometry-Line.html#intersectSegHorzSeg" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P1 First point of segment.
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P2 Second point of segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>(y3) y value of horizontal segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>(xa) Leftmost x value of horizontal segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>(xb) Rightmost x value of horizontal segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>(x3, y3) Intersection point, if any.
</p></td></tr></table></div><div class="doc"><p>Check if an arbitrary segment intersects a horizontal segment.
</p><pre>
+ P2
/
(xa, y3) +---+----+ (xb, y3)
/
P1 +
</pre></div></div><div class="top"><p class="src"><a name="v:intersectSegVertSeg" class="def">intersectSegVertSeg</a><a href="src/Graphics-Gloss-Geometry-Line.html#intersectSegVertSeg" class="link">Source</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P1 First point of segment.
</p></td></tr><tr><td class="src">-> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>P2 Second point of segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>(x3) x value of vertical segment
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>(ya) Lowest y value of vertical segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></td><td class="doc"><p>(yb) Highest y value of vertical segment.
</p></td></tr><tr><td class="src">-> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Graphics-Gloss-Data-Point.html#t:Point">Point</a></td><td class="doc"><p>(x3, y3) Intersection point, if any.
</p></td></tr></table></div><div class="doc"><p>Check if an arbitrary segment intersects a vertical segment.
</p><pre>
(x3, yb) +
| + P1
| /
+
/ |
P2 + |
+ (x3, ya)
</pre></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.13.2</p></div></body></html>
|