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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 3.2 Final//FR"><!-- Converted with LaTeX2HTML 95.1 (Fri Jan 20 1995) --><!-- by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><!-- Modified Simulog 03/97 --><HTML><HEAD><TITLE>2.3 Three-dimensional meshes TRNOXX</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="2.3 Three-dimensional meshes TRNOXX"><meta name="keywords" value="Guide6"><meta name="resource-type" value="document"><meta name="distribution" value="global"></HEAD><BODY BGCOLOR="#FFFFFF"><P> <IMG SRC="../icons/smallmod.gif" WIDTH=211 HEIGHT=50 ALIGN=BOTTOM ALT="Modulef"><A NAME=tex2html917 HREF="node36.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html923 HREF="node34.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html925 HREF="node38.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html927 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide6-18/node37.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide6-14/node37.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide6-10/node37.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html926 HREF="node38.html">2.4 Three-dimensional meshes REFEXX</A><B>Up: </B> <A NAME=tex2html924 HREF="node34.html">2 Visualization of meshes</A><B> Prev: </B> <A NAME=tex2html918 HREF="node36.html">2.2 Two-dimensional meshes TRNOXX</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION04330000000000000000>2.3 Three-dimensional meshes TRNOXX</A></H1> <A NAME=3d> </A><P><P><P><H2><A NAME=SECTION04331000000000000000>2.3.1 Aims and utilization limitations</A></H2><P><P><P>Preprocessor <b> TRNOXX</b> is used to visualize meshes (the 3D case is described here). It is alsoused, for an elasticity problem for which the displacements are known, to visualizethe deformed mesh (the displacements, multiplied by a given factor, are added to the nodes of the initial mesh).<P><DL COMPACT><DT>Note:<DD> The visualization of deformations are only possible in the following cases:<P><UL><LI> the finite elements are of type Lagrange,<LI> the displacements are the NDIM (3 here) first degrees of freedom of each node,<LI> <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img39.gif"> where ND is the number of degrees of freedom per node.</UL><P>For other cases, preprocessor <b> TRC3XX</b>, strictly requiring data structures <b> MAIL</b> and <b> COOR</b>, is used.<P> </DL><P><P><P><H2><A NAME=SECTION04332000000000000000>2.3.2 Utilization of TRNOXX (3D)</A></H2><P><P><P><OL><LI> Activate preprocessor <b> TRNOXX</b>.<P><LI> Choose the output terminal.<P><LI> Input the name of the file containing the mesh.<P><LI> The general menu is displayed (see further down).<P><LI> Type 0 to obtain an automatic plot.<P><LI> To obtain the values of the visualization parameters, type V.<P><LI> Modify these values, if necessary, by choosing the corresponding key and entering the required information.Once the desired state is obtained, type 0 to display the plot.<P><LI> A <i> graphics</i> menu is displayed on the plot to perform modifications, to exit or to return to themenu mentioned above and described in the coming sections.</OL><P><P><P><H2><A NAME=SECTION04333000000000000000>2.3.3 Complete description of TRNOXX (3D)</A></H2><P><P><P>The first part of this description presents the different notions necessary for athorough understanding of the operations performed when visual-ising a three-dimensional mesh.<P><P><P><DL COMPACT><DT>Observation conditions:<DD> <P>The module automatically calculates the extrema corresponding to the mesh under consideration, which are used todefine the corners of the box in which the plot is displayed.<P>The observation conditions of a three-dimensional mesh are defined by:<P><UL><LI> the barycentre of the box defined above, which is the point viewed, <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img45.gif"><LI> the observation point, <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img46.gif">, which is calculated in such a way that the entire object is viewed with aspan <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img47.gif">, an observation angle (or longitude) <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img48.gif"> and an elevation (or latitude) <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img49.gif">. In practice,fixing <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img50.gif">, <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img51.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img52.gif"> degrees, the distance <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img53.gif"> is calculated such that theobject is viewed in full.</UL><P><P><A NAME=1625> </A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img54.gif"><BR><STRONG>Figure 2.6:</STRONG> <i> Observation mode</i><A NAME=1621iObservationmodei1621> </A><BR><P><P><P><P>Note that the observation angle and point are such that the extrema are taken <em> vis-a-vis</em> this pointwhich, <em> a priori</em>, defines extrema which are different to those of the initial box, as shown in figure<A HREF="#figextrema">2.7</A> which is reduced to the 2D case for an improved readability (the natural extrema <b>M</b> and <b>m</b>are replaced by the couples <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img55.gif"> or <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img56.gif"> depending on the choice of <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img57.gif"> or <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img58.gif">).<P><P><A NAME=1635> </A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img59.gif"><BR><STRONG>Figure 2.7:</STRONG> <i> Extrema function of the observer</i><A NAME=1631iExtremafunctionoftheobserveri1631> </A><BR><P><P>Automatic mode corresponds to the above specified choices for the values of <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img48.gif">, <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img49.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img47.gif">. Inmanual mode, the user specifies:<UL><LI> the observation angle, the elevation and the span (<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img60.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img47.gif">), or<LI> the points <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img45.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img46.gif"> (in Cartesian coordinates).</UL><P>The type of observation mode and the corresponding parameters are displayed in the menu (key 15 and 16, orkey 15, 17 and 18). Once the plot is displayed, the two sets of parameters are indicated and the user can easilychange from one observation mode to another.<P><P><P><DT>Visibility:<DD> <P>In dimension 3, the readability of a plot depends very much on the manner in which is plotted. There are, <em> a priori</em> several types of plots:<P><UL><LI> a <em> solid line</em> plot of the edges and elements,<LI> plots taking into account the visibility of items in the mesh which includesalgorithms of the <em> hidden</em> parts.</UL><P>The notion of visibility is interpreted differently depending to the capabilities of the computer terminalused. For a terminal without selective deletion, an edge is called visible if the normal of the face to which itbelongs is directed towards the observation point <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img46.gif">. This simple algorithm presents some imperfections. For more advanced terminals, it is replaced by aa "painter" type algorithm :the faces are sorted and then plotted by starting by those furthest off, so that only those faces that are not hiddenby the closer up faces are visible on the plot.<P><P><P><DT>Choice of items to display:<DD> <P>A three-dimensional mesh can be displayed by plotting:<P><UL><LI> all the elements in solid line mode, shrunken or not,<LI> the outer surface only by plotting its faces, generated by displaying:<UL><LI> all the edges with or without elimination (by default) of edges belonging to two adjacent and coplanar faces.Two faces are called coplanar if their normals are identical w.r.t. a coefficient (by default 0.00001, value modified via key 53 (see below)).<LI> all the visible edges with or without this elimination.<LI> all the hidden edges with or without this elimination.</UL></UL><P>The faces can be colored-in, or not.<P> </DL><P>The general menu of TRGEOM (module called in this case) is given below.<P> <PRE> ------------------------------------------------------------ | 10 | PLOT TYPE | MESH ONLY ------------------------------------------------------------ | 11 | DEVICE NUMBER | 1 ------------------------------------------------------------ | 20 | MESH TO PLOT | c3.nopoi ------------------------------------------------------------ | 15 | OBSERVATION MODE | LONGITUDE / OX LATITUDE APERTURE ------------------------------------------------------------ | 16 | LONGIT. LATIT. APERTURE | 30.00000 30.00000 10.00000 ------------------------------------------------------------ | 31 | QUESTIONS ABOUT THIS MESH | NO ------------------------------------------------------------ | 30 | PLOT SIZE | AUTO ------------------------------------------------------------ | 40 | CHARACTER TYPE | HARD ------------------------------------------------------------ | 50 | ITEMS TO BE PLOTTED | EDGES OF OUTER SURFACE (ALL) ------------------------------------------------------------ | 51 | COPLANAR EDGES | ELIMINATED ------------------------------------------------------------ | 53 | COPLANARITY CRITERION | 0.1000000E-04 ------------------------------------------------------------⌨️ 快捷键说明
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