[xsl] XSLT code that implements the Point-in-a-Polygon problem

["Roger L Costello costello@xxxxxxxxx" <xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx>]

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.h
tml
    -->
    <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>