Fairmat 2024: base classes to describe computational geometry

base_classes/NXcg_alpha_complex.nxdl.xml

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+<?xml version='1.0' encoding='UTF-8'?>
+<?xml-stylesheet type="text/xsl" href="nxdlformat.xsl"?>
+<!--
+# NeXus - Neutron and X-ray Common Data Format
+#
+# Copyright (C) 2014-2024 NeXus International Advisory Committee (NIAC)
+#
+# This library is free software; you can redistribute it and/or
+# modify it under the terms of the GNU Lesser General Public
+# License as published by the Free Software Foundation; either
+# version 3 of the License, or (at your option) any later version.
+#
+# This library 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
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+#
+# For further information, see http://www.nexusformat.org
+-->
+<!--
+The so-called spectrum or sets of (weighted) alpha shapes includes the convex hull of a point set.-->
+<definition xmlns="http://definition.nexusformat.org/nxdl/3.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" category="base" type="group" name="NXcg_alpha_complex" extends="NXcg_primitive" xsi:schemaLocation="http://definition.nexusformat.org/nxdl/3.1 ../nxdl.xsd">
+    <doc>
+         Computational geometry of alpha complexes (alpha shapes or alpha wrappings) about primitives.
+
+         For details see:
+
+         * https://dx.doi.org/10.1109/TIT.1983.1056714 for 2D,
+         * https://dx.doi.org/10.1145/174462.156635 for 3D,
+         * https://dl.acm.org/doi/10.5555/871114 for weighted, and
+         * https://doc.cgal.org/latest/Alpha_shapes_3 for 3D implementation of alpha shapes, and
+         * https://doc.cgal.org/latest/Manual/packages.html#PkgAlphaWrap3 for 3D alpha wrappings
+
+         in CGAL, the Computational Geometry Algorithms Library respectively.
+         As a starting point, we follow the conventions of the CGAL library.
+
+         In general, an alpha complex is a not necessarily connected or not necessarily pure complex,
+         i.e. singular faces may exist. The number of cells, faces, and edges depends on how a specific
+         alpha complex is filtered for lower-dimensional simplices. The fields is_regularized and
+         regularization can be used to provide details about regularization procedures.
+    </doc>
+    <field name="type">
+        <doc>
+             Type of alpha complex following the terminology used by CGAL for now.
+
+             Alpha_shape means meshes created using one of the alpha_shape algorithm.
+             Alpha_wrapping means meshes created using the alpha_wrapping algorithm.
+        </doc>
+        <enumeration>
+            <item value="convex_hull"/>
+            <item value="alpha_shape"/>
+            <item value="alpha_wrapping"/>
+        </enumeration>
+    </field>
+    <field name="regularization">
+        <doc>
+             Human-readable description about regularization procedures.
+        </doc>
+    </field>
+    <field name="is_regularized" type="NX_BOOLEAN">
+        <doc>
+             Was the alpha complex regularized, i.e. have singular faces been removed, or not.
+        </doc>
+    </field>
+    <field name="alpha" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             The alpha parameter, i.e. the radius of the alpha-sphere that
+             is used when computing the alpha complex.
+        </doc>
+    </field>
+    <field name="offset" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             The offset distance parameter used when computing alpha_wrappings.
+        </doc>
+    </field>
+    <!--check again carefully the CGAL documentation talks about, for 3D, the square of the radius!-->
+    <group name="point_cloudID" type="NXcg_point" nameType="partial">
+        <doc>
+             Point cloud serving as input for the computation of the alpha complex.
+        </doc>
+    </group>
+    <group name="triangle_soupID" type="NXcg_triangle" nameType="partial">
+        <doc>
+             Triangle soup serving as input for the computation of the alpha complex.
+        </doc>
+    </group>
+    <group name="alpha_complexID" type="NXcg_triangle" nameType="partial">
+        <doc>
+             Triangle mesh representing the output of the computation, i.e. the alpha complex.
+        </doc>
+    </group>
+    <group name="tetrahedralizationID" type="NXcg_tetrahedron" nameType="partial">
+        <doc>
+             Tetrahedra representing an interior volume of the alpha complex (if such exists).
+        </doc>
+    </group>
+</definition>

base_classes/NXcg_cylinder.nxdl.xml

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+<?xml version='1.0' encoding='UTF-8'?>
+<?xml-stylesheet type="text/xsl" href="nxdlformat.xsl"?>
+<!--
+# NeXus - Neutron and X-ray Common Data Format
+#
+# Copyright (C) 2014-2024 NeXus International Advisory Committee (NIAC)
+#
+# This library is free software; you can redistribute it and/or
+# modify it under the terms of the GNU Lesser General Public
+# License as published by the Free Software Foundation; either
+# version 3 of the License, or (at your option) any later version.
+#
+# This library 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
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+#
+# For further information, see http://www.nexusformat.org
+-->
+<!--
+redundant as there is NXcsg, NXquadric, NXsolid_geometry with which
+cylinder could be constructed, but NXcylinder is easier to understand-->
+<definition xmlns="http://definition.nexusformat.org/nxdl/3.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" category="base" type="group" name="NXcg_cylinder" extends="NXcg_primitive" xsi:schemaLocation="http://definition.nexusformat.org/nxdl/3.1 ../nxdl.xsd">
+    <symbols>
+        <doc>
+             The symbols used in the schema to specify e.g. dimensions of arrays.
+        </doc>
+        <symbol name="d">
+            <doc>
+                 The dimensionality of the space in which the members are assumed embedded.
+            </doc>
+        </symbol>
+        <symbol name="c">
+            <doc>
+                 The cardinality of the set, i.e. the number of members.
+            </doc>
+        </symbol>
+    </symbols>
+    <doc>
+         Computational geometry description of a set of cylinders or (truncated) cones.
+
+         The radius can either be defined in the radii field or by filling both
+         the upper_cap_radii or lower_cap_radii field. The latter field case can
+         thus be used to represent (truncated) cones.
+    </doc>
+    <field name="height" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             A direction vector which is parallel to the cylinder/cone axis
+             and whose magnitude is the height of the cylinder/cone.
+
+             The upper_cap is defined as the one that is farther away to the origin
+             when inspecting a parallel projection onto the direction vector.
+        </doc>
+        <dimensions rank="2">
+            <dim index="1" value="c"/>
+            <dim index="2" value="d"/>
+        </dimensions>
+    </field>
+    <field name="radius" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             Radius of the cylinder if all have the same radius.
+        </doc>
+    </field>
+    <field name="radii" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             Radii of the cylinder.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+    <field name="upper_cap_radii" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             Radii of the upper circular cap.
+
+             This field, combined with lower_cap_radius can be used to describe
+             (eventually truncated) circular cones.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+    <field name="lower_cap_radii" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             Radii of the upper circular cap.
+
+             This field, combined with upper_cap_radius can be used to describe
+             (eventually truncated) circular cones.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+    <!--properties of the cylinder-->
+    <field name="lateral_surface_area" type="NX_NUMBER" units="NX_AREA">
+        <doc>
+             Lateral surface area of each cylinder.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+    <field name="upper_cap_surface_area" type="NX_NUMBER" units="NX_AREA">
+        <doc>
+             Area of the upper cap of each cylinder.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+    <field name="lower_cap_surface_area" type="NX_NUMBER" units="NX_AREA">
+        <doc>
+             Area of the lower cap of each cylinder.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+    <field name="total_surface_area" type="NX_NUMBER" units="NX_AREA">
+        <doc>
+             Sum of upper and lower cap area and lateral surface area of each cylinder.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+</definition>

base_classes/NXcg_ellipsoid.nxdl.xml

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+<?xml version='1.0' encoding='UTF-8'?>
+<?xml-stylesheet type="text/xsl" href="nxdlformat.xsl"?>
+<!--
+# NeXus - Neutron and X-ray Common Data Format
+#
+# Copyright (C) 2014-2024 NeXus International Advisory Committee (NIAC)
+#
+# This library is free software; you can redistribute it and/or
+# modify it under the terms of the GNU Lesser General Public
+# License as published by the Free Software Foundation; either
+# version 3 of the License, or (at your option) any later version.
+#
+# This library 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
+# Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+#
+# For further information, see http://www.nexusformat.org
+-->
+<!--
+redundant as there is NXcsg, and NXquadric but easier to understand-->
+<definition xmlns="http://definition.nexusformat.org/nxdl/3.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" category="base" type="group" name="NXcg_ellipsoid" extends="NXcg_primitive" xsi:schemaLocation="http://definition.nexusformat.org/nxdl/3.1 ../nxdl.xsd">
+    <symbols>
+        <doc>
+             The symbols used in the schema to specify e.g. dimensions of arrays.
+        </doc>
+        <symbol name="d">
+            <doc>
+                 The dimensionality of the space in which the members are assumed embedded.
+            </doc>
+        </symbol>
+        <symbol name="c">
+            <doc>
+                 The cardinality of the set, i.e. the number of members.
+            </doc>
+        </symbol>
+    </symbols>
+    <doc>
+         Computational geometry description of a set of ellipsoids.
+    </doc>
+    <field name="half_axes_radius" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             Radius of the half axes.
+
+             Use if all ellipsoids in the set have the same half-axes.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="d"/>
+        </dimensions>
+    </field>
+    <field name="half_axes_radii" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             Half-axes radii of each ellipsoid.
+        </doc>
+        <dimensions rank="2">
+            <dim index="1" value="c"/>
+            <dim index="2" value="d"/>
+        </dimensions>
+    </field>
+    <!--convenience dictionary entries when all ellipsoids in the set are spheres.-->
+    <field name="radius" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             In the case that all ellipsoids are spheres.
+        </doc>
+    </field>
+    <field name="radii" type="NX_NUMBER" units="NX_LENGTH">
+        <doc>
+             In the case that all ellipsoids are spheres whose radii differ.
+             For a mixture of spheres use half_axes_radii.
+        </doc>
+        <dimensions rank="1">
+            <dim index="1" value="c"/>
+        </dimensions>
+    </field>
+    <!--properties of ellipsoids-->
+</definition>