X3D CAD/TransposeNurbsAxes

The web page [[1]] demonstrates a disagreement among current X3D browsers that implement the NURBS Component as to how they interpret the standard to place the parametric axes (generally labelled the u-v axes) on the created and rendered 2D surface.

<?xml version="1.0" encoding="ISO-8859-1"?>
<!-- 
Transposes the u-v parametric coordinate axes on a NurbsPatchSurface or NurbsTrimmedSurface


For NurbsPatchSurface nodes and TrimmedNurbsSurface node the parameters which 
come in u-v pairs (ex uKnot, vKnot) have their values swapped

The attributes NurbsPatchSurface/@weight and NurbsPatchSurface/Coordinate/@point
are, in the input x3d data, lists of numbers which are the weight,control_points arrays listed in column-major order.
In the transformed data these lists are the same arrays flattened in row-major order.

For the nodes ContourPolyline2D/@controlPoint and NurbsCurve2D//@controlPoint: these attributes are
lists of u-v coordinates of points in parametric coordinates. In the transformed attributes, each
element of this list is transformed u,v ==> v,u
The ordering of the list is unchanged.


Copyright 2012 Vincent Marchetti

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

-->
<xsl:stylesheet version="1.0" 
                xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
                xmlns:exsl="http://exslt.org/common"
                xmlns:str="http://exslt.org/strings"
                extension-element-prefixes="exsl"
                xmlns:ksh="http://kshell.com/ns/x3d">

<xsl:output method="xml" encoding="utf-8"/>


<xsl:template match="@*|node()">
    <xsl:copy>
        <xsl:apply-templates select="@*|node()"/>
    </xsl:copy>
</xsl:template>




<xsl:template match="NurbsPatchSurface/@uKnot|NurbsTrimmedSurface/@uKnot">
<xsl:if test="../@vKnot">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@vKnot"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@vKnot|NurbsTrimmedSurface/@vKnot">
<xsl:if test="../@uKnot">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@uKnot"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@uDimension|NurbsTrimmedSurface/@uDimension">
<xsl:if test="../@vDimension">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@vDimension"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@vDimension|NurbsTrimmedSurface/@vDimension">
<xsl:if test="../@uDimension">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@uDimension"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@uTessellation|NurbsTrimmedSurface/@uTessellation">
<xsl:if test="../@vTessellation">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@vTessellation"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@vTessellation|NurbsTrimmedSurface/@vTessellation">
<xsl:if test="../@uTessellation">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@uTessellation"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@uClosed|NurbsTrimmedSurface/@uClosed">
<xsl:if test="../@vClosed">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@vClosed"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@vClosed|NurbsTrimmedSurface/@vClosed">
<xsl:if test="../@uClosed">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@uClosed"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@uOrder|NurbsTrimmedSurface/@uOrder">
<xsl:if test="../@vOrder">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@vOrder"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>

<xsl:template match="NurbsPatchSurface/@vOrder|NurbsTrimmedSurface/@vOrder">
<xsl:if test="../@uOrder">
    <xsl:attribute name="{name()}">
    <xsl:value-of select="../@uOrder"/>
    </xsl:attribute>
</xsl:if>
</xsl:template>



<xsl:template match="NurbsPatchSurface/@weight|NurbsTrimmedSurface/@weight">
<xsl:attribute name="{name()}">
    <xsl:variable name="transposed_weights">  
    <xsl:call-template name="ksh:transpose">
        <xsl:with-param name="NC" select="number(../@vDimension)"/>
        <xsl:with-param name="NR" select="number(../@uDimension)"/>
        <xsl:with-param name="elements" select="str:split(normalize-space(.))"/>
    </xsl:call-template>
    </xsl:variable>
    
    <xsl:for-each select="exsl:node-set($transposed_weights)/token">
        <xsl:value-of select="."/>
        <xsl:if test="last()>position()"><xsl:text> </xsl:text></xsl:if>
    </xsl:for-each>

</xsl:attribute>
</xsl:template>

<xsl:template match="NurbsPatchSurface/Coordinate/@point|NurbsTrimmedSurface/Coordinate/@point">
<xsl:attribute name="{name()}">
    <xsl:variable name="transposed_point">
    <xsl:call-template name="ksh:transpose">
        <xsl:with-param name="NC" select="number(../../@vDimension)"/>
        <xsl:with-param name="NR" select="number(../../@uDimension)"/>
        <xsl:with-param name="elements" select="str:split(.,',')"/>
    </xsl:call-template>
    </xsl:variable>
    
    <xsl:for-each select="exsl:node-set($transposed_point)/token">
        <xsl:value-of select="."/>
        <xsl:if test="last() > position()"><xsl:text>, </xsl:text></xsl:if>
    </xsl:for-each>
</xsl:attribute>
</xsl:template>


<!-- 
Templates for taking an array of nodes , NR rows and NC columns, output in
column-major order, and preparing a node set of those nodes listed in
row-major order
 -->
<xsl:template name="ksh:transpose">
    <xsl:param name="IR" select="1"/>
    <xsl:param name="NR"/>
    <xsl:param name="NC"/>
    <xsl:param name="elements"/>
    
    <!-- call the template which will list (in row major order
    the IR'th row -->
    <xsl:call-template name="ksh:transpose-row-out">
        <xsl:with-param name="IR" select="$IR"/>
        <xsl:with-param name="NC" select="$NC"/>
        <xsl:with-param name="NR" select="$NR"/>
        <xsl:with-param name="elements" select="$elements"/>
    </xsl:call-template>

    <!-- the recursion: call this template starting at the next row -->
    <xsl:if test="$NR > $IR">
        <xsl:call-template name="ksh:transpose">
            <xsl:with-param name="IR" select="$IR + 1"/>
            <xsl:with-param name="NC" select="$NC"/>
            <xsl:with-param name="NR" select="$NR"/>
            <xsl:with-param name="elements" select="$elements"/>
        </xsl:call-template>
    </xsl:if>
</xsl:template>
  
<xsl:template name="ksh:transpose-row-out">
    <xsl:param name="IC" select="1"/>
    <xsl:param name="IR"/>
    <xsl:param name="NR"/>
    <xsl:param name="NC"/>
    <xsl:param name="elements"/>
    
    <!-- send out the IC'th column of the IR'th row, using the 
    indexing appropriate for column major indexing of the underlying list -->
    <xsl:param name="index" select="($IC -1)*$NR + $IR"/>
    <xsl:copy-of select="$elements[$index]"/>
    
    <!-- and the recursion, send out the rest of the columns of this row,
    starting at IC+1 -->
    <xsl:if test="$NC > $IC">
        <xsl:call-template name="ksh:transpose-row-out">
            <xsl:with-param name="IC" select="$IC + 1"/>
            <xsl:with-param name="IR" select="$IR"/>
            <xsl:with-param name="NC" select="$NC"/>
            <xsl:with-param name="NR" select="$NR"/>
            <xsl:with-param name="elements" select="$elements"/>
        </xsl:call-template>
    </xsl:if>
</xsl:template>



</xsl:stylesheet>