Re: XSLT code that implements the Point-in-a-Polygon

jk
Joel Kalvesmaki
Text Alignment Network
http://textalign.net

Hi Folks,

I implemented XSLT code to determine if a point p is inside or outside
a polygon. See below. Admittedly, the tests that I've done thus far
are really simple. See the template rule. I would appreciate it if you
see a bug in the code or see where the code can be improved, you would
let me know please. /Roger

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
    xmlns:xs="http://www.w3.org/2001/XMLSchema"
    xmlns:f="function"
    exclude-result-prefixes="#all"
    version="2.0">

<xsl:output method="text" />

    <!--
        Given a point p, does p reside in the polygon with N edges?
        This program solves the Point-in-a-Polygon problem.
    -->

<!--
The following code implements in XSLT the C code
shown in Solution 1 at this URL:
http://www.eecs.umich.edu/courses/eecs380/HANDOUTS/PROJ2/InsidePoly.html
-->
<xsl:function name="f:iterate-Over-All-Polygons" as="xs:string">
<xsl:param name="polygon" as="xs:string+" />
<xsl:param name="N" as="xs:integer" />
<xsl:param name="p" as="xs:string" />
<xsl:param name="counter" as="xs:integer" />
<xsl:param name="p1" as="xs:string" />
<xsl:param name="i" as="xs:integer" />

        <xsl:variable name="p_x" select="xs:double(tokenize($p, '
')[1])" as="xs:double" />
        <xsl:variable name="p_y" select="xs:double(tokenize($p, '
')[2])" as="xs:double" />

        <xsl:variable name="p1_x" select="xs:double(tokenize($p1, '
')[1])" as="xs:double" />
        <xsl:variable name="p1_y" select="xs:double(tokenize($p1, '
')[2])" as="xs:double" />

<xsl:choose>
<xsl:when test="$i le $N">
<!-- p2 = polygon[i % N] -->
<xsl:variable name="p2" select="$polygon[($i mod $N) +
1]" as="xs:string"/>
<xsl:variable name="p2_x"
select="xs:double(tokenize($p2, ' ')[1])" as="xs:double" />
<xsl:variable name="p2_y"
select="xs:double(tokenize($p2, ' ')[2])" as="xs:double" />
<!-- if (p.y > MIN(p1.y,p2.y)) -->
<xsl:choose>
<xsl:when test="$p_y gt min(($p1_y, $p2_y))">
<!-- if (p.y <= MAX(p1.y,p2.y)) -->
<xsl:choose>
<xsl:when test="$p_y le max(($p1_y, $p2_y))">
<!-- if (p.x <= MAX(p1.x,p2.x)) -->
<xsl:choose>
<xsl:when test="$p_x le
max(($p1_x, $p2_x))">
<!-- if (p1.y != p2.y) -->
<xsl:choose>
<xsl:when test="$p1_y ne $p2_y">
<!-- xinters =
(p.y-p1.y)*(p2.x-p1.x)/(p2.y-p1.y)+p1.x -->
<xsl:variable
name="xinters" select="($p_y - $p1_y)*($p2_x - $p1_x) div ($p2_y -
$p1_y) + $p1_x" as="xs:double" />
<!-- if (p1.x == p2.x
|| p.x <= xinters) -->
<xsl:choose>
<xsl:when
test="$p1_x eq $p2_x or $p_x le $xinters">
<!-- counter++ -->
<!-- p1 = p2 -->
<xsl:sequence
select="f:iterate-Over-All-Polygons($polygon, $N, $p, $counter + 1,
$p2, $i + 1)" />
</xsl:when>
<xsl:otherwise>
<!-- p1 = p2 -->
<xsl:sequence
select="f:iterate-Over-All-Polygons($polygon, $N, $p, $counter, $p2,
$i + 1)" />
</xsl:otherwise>
</xsl:choose>
</xsl:when>
<xsl:otherwise>
<!-- p1 = p2 -->
<xsl:sequence
select="f:iterate-Over-All-Polygons($polygon, $N, $p, $counter, $p2,
$i + 1)" />
</xsl:otherwise>
</xsl:choose>
</xsl:when>
<xsl:otherwise>
<!-- p1 = p2 -->
<xsl:sequence
select="f:iterate-Over-All-Polygons($polygon, $N, $p, $counter, $p2,
$i + 1)" />
</xsl:otherwise>
</xsl:choose>
</xsl:when>
<xsl:otherwise>
<!-- p1 = p2 -->
<xsl:sequence
select="f:iterate-Over-All-Polygons($polygon, $N, $p, $counter, $p2,
$i + 1)" />
</xsl:otherwise>
</xsl:choose>
</xsl:when>
<xsl:otherwise>
<!-- p1 = p2 -->
<xsl:sequence
select="f:iterate-Over-All-Polygons($polygon, $N, $p, $counter, $p2,
$i + 1)" />
</xsl:otherwise>
</xsl:choose>
</xsl:when>
<xsl:otherwise>
<xsl:message>Number of times a horizontal ray
eminating from p to the right intersects the line segments making up
the polygon = <xsl:value-of select="$counter" /></xsl:message>
<!--
if (counter % 2 == 0)
return(OUTSIDE);
else
return(INSIDE)
-->
<xsl:choose>
<xsl:when test="($counter mod 2) eq
0"><xsl:text>OUTSIDE</xsl:text></xsl:when>
<xsl:otherwise><xsl:text>INSIDE</xsl:text></xsl:otherwise>
</xsl:choose>
</xsl:otherwise>
</xsl:choose>

</xsl:function>

    <xsl:function name="f:InsidePolygon" as="xs:string">
        <xsl:param name="polygon" as="xs:string+" />
        <xsl:param name="N" as="xs:integer" />
        <xsl:param name="p" as="xs:string" />  <!-- p1 = polygon[1] -->

        <xsl:variable name="counter" select="0" as="xs:integer" />
        <xsl:variable name="p1" select="$polygon[1]" as="xs:string" />
        <xsl:variable name="i" select="1" as="xs:integer" />

        <xsl:sequence select="f:iterate-Over-All-Polygons($polygon,
$N, $p, $counter, $p1, $i)" />

</xsl:function>

    <xsl:template match="/">
        <xsl:variable name="polygon" as="xs:string+">
            <xsl:sequence select="'0 0'" />
            <xsl:sequence select="'4 0'" />
            <xsl:sequence select="'4 4'" />
            <xsl:sequence select="'0 4'" />
            <xsl:sequence select="'0 0'" />
        </xsl:variable>
        <xsl:variable name="N" select="5" as="xs:integer" />

        <xsl:variable name="p" select="'1 1'" as="xs:string" />
        <xsl:sequence select="f:InsidePolygon($polygon,$N, $p)" />

        <xsl:variable name="p" select="'-1 1'" as="xs:string" />
        <xsl:sequence select="f:InsidePolygon($polygon,$N, $p)" />

        <xsl:variable name="p" select="'0 0'" as="xs:string" />
        <xsl:sequence select="f:InsidePolygon($polygon,$N, $p)" />

        <xsl:variable name="p" select="'0.2 0.5'" as="xs:string" />
        <xsl:sequence select="f:InsidePolygon($polygon,$N, $p)" />

</xsl:template>

</xsl:stylesheet>