Measure: A Polytope Analysis Tool

## Overview

Measure is a program for interactively examining the geometrical properties of polyhedra that are being viewed with Geomview. Using Measure, a user can determine the area of facets, the length of edges, the coordinates of a vertex (or point), and the distance between points.

## Instructions

Measure determines the geometrical properties of objects within Geomview, and as such, a coordinate system must be defined. The default is to measure properties in "Object" coordinates; to measure properties in "World" coordinates, push the Global button.

• Facet properties :
Select a facet of interest; its bounding vertices are indicated, and the area and normal are displayed by Measure.
• Edge Properties :
Select an edge, and measure displays its length and direction.
• Vertex Properties :
Select a vertex, and measure displays its (xyz) coordinates.
• Distance between Points :
Select a reference point by clicking the Set button; this makes the currently active point magenta. Hereafter, the distance from the reference point to the current "picked" point will be displayed, as will the angle between the vector of the referenced object and the vector of the currently picked object. A new reference point can be selected by clicking on Set again.

### Selection of Objects

The basic operation of the program involves simply selecting an object (vertex, edge, facet) by right-clicking with the mouse. The object selected is indicated in Geomview by placing indicator boxes on the polytope; information about this object is then displayed in the Measure window.

NOTE: Selection of objects in some versions of Geomview is more precise than in others. Occasionally, selection of one vertex, for example, will yield another.

 Facet: Selection of a facet results in a yellow box being placed at the Picked Point and cyan boxes being placed on the vertices of that facet. Edge: Selection of an edge results in a yellow box at the picked point and cyan boxed at the vertices that bound the edge. Vertex: Selection of a vertex yields only a cyan box at that vertex

## Information Display:

The information displayed in the Measure window is a function of the objects that have been selected. Selection of a facet, edge, or vertex causes the corresponding box to become bright blue. The following information is displayed in Measure:

• Facet: The area and normal of the selected facet
• Edge: The length and direction of the selected facet
• Vertex: The coordinates (xyz) of the selected vertex
Some information is displayed regardless of what object has been selected. The Picked Point is the point that was selected by right-clicking the mouse. Reference is a feature that allows distance and angle between two points to be computed. One point is set as the reference point, and thereafter, the distance is displayed from the Reference point to the Picked Point.
• Picked Point: The coordinates (xyz) of the selected point. The slider enables resizing of all points (smallest to largest point size, left to right).
• Reference: Clicking the Set button makes the currently selected point the reference (indicated by a magenta box). After selecting a reference, the distance to the picked point will be displayed to the right of Set, and the angle between the last picked feature's vector and the current one will be shown. For faces, the defining vector is a normal, for edges a tangent, and for corners, the vector from the origin.

Measure is a module for use with Geomview . As such, it is useless unless Geomview is installed. Measure is provided in binary distribution. If unavailable for your specific platform, download the Measure source code and compile. UNIX commands begin with a '%' or are in italics.

• Binary distribution
2. Extract archive:
% uncompress measure32_sgi.Z
3. Install Measure as a Geomview module

• Installation from Source

Download the Xforms library in binary format for the platform of interest from the Xforms web site. Uncompress and extract the Xforms archive and follow the instructions in README.txt for installation.

Measure requires an OOGL library for compilation that can be obtained by compiling Geomview from source. It doesn't matter whether Geomview compiles cleanly, as long as liboogl.a is created. In addition, Measure requires some Geomview header files that are not available without installing from source. Hence, installation of measure depends on whether the version of Geomview at your site was compiled from source (Case I) or obtained from the binary distribution (Case II).

#### Case I (Geomview compiled from source)

1. Locate Geomview Installation directory (gv_dir)

2. Locate relevant Geomview header (*.h) files:
(Default = gv_dir/Geomview/include)

3. Locate liboogl.a:
(Default gv_dir/lib)

4. Make directory for measure source:
% mkdir meas_dirname
% cd meas_dirnam

6. Extract the source archive:
% zcat measure_1.1_src.tar.Z | tar xvf -

7. Modify Makefile variables GVINCLDIR and GVLIBDIR.
Note: On Linux systems, you must do the final link using g++, since the geomview archive requires some c++ symbols.

8. Compile Codes:
% make measure

9. Install Measure as a Module to Geomview

#### Case II (Geomview installed from binary distribution)

1. Create Geomview root directory:
% mkdir gv_root

3. Extract Geomview distribution into gv_root:
% zcat geomview-1.8.1.tar.gz | tar xvf -

4. Compile Geomview:
% cd Geomview
% make

6. Extract the source archive:
% zcat measure_1.1_src.tar.Z | tar xvf -

7. Modify Makefile to reflect at least:
GVINCLDIR = -I/full_path_name/gv_root/Geomview/include
GVLIBDIR = -L/full_path_name/gv_root/Geomview/lib/mach_name
Note: On Linux systems, you must do the final link using g++, since the geomview archive requires some c++ symbols.

8. Compile Codes:
% make measure

9. Install Measure as a Module to Geomview

## Credits

Measure was written by:
Andrew Roosen
Ceramics Division / Center for Theoretical and Computational Materials Science
National Institute of Standards and Technology

Documentation by:
Ryan McCormack
Ceramics Division / Center for Theoretical and Computational Materials Science
National Institute of Standards and Technology

Center for Theoretical and Computational Materials Science, NIST