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Date: Tue, 24 Jun 2008 13:47:34 +0800
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<BODY=20
class=3D"mediawiki ns-0 ltr =
page-Tutorial_ACIS_Tutorial_3_Understanding_and_traversing_ACIS_topology_=
Part_I">
<DIV id=3DglobalWrapper>
<DIV id=3Dcolumn-content>
<DIV id=3Dcontent><A id=3Dtop name=3Dtop></A>
<H1 class=3DfirstHeading>Tutorial:ACIS Tutorial 3: Understanding and =
traversing=20
ACIS topology (Part I)</H1>
<DIV id=3DbodyContent>
<H3 id=3DsiteSub>From DocR18</H3>
<DIV id=3DcontentSub></DIV>
<DIV id=3Djump-to-nav>Jump to: <A=20
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#column-one">navigation<=
/A>,=20
<A=20
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#searchInput">search</A>=
</DIV><!-- start content -->
<P>This tutorial describes the ACIS topological structure and =
demonstrates some=20
common mechanisms for its traversal. This tutorial has been divided into =
four=20
parts: </P>
<UL>
  <LI>In Part I we describe the ACIS topological structure.=20
  <LI>In Part II we present additional details about the topology of =
solids,=20
  sheets, and wires.=20
  <LI>In Part III we present some mechanisms for traversing the =
topology.=20
  <LI>In Part IV we provide a couple C++ examples demonstrating the =
concepts of=20
  presented in Parts I, II, and III. </LI></UL>
<TABLE class=3Dtoc id=3Dtoc summary=3DContents>
  <TBODY>
  <TR>
    <TD>
      <DIV id=3Dtoctitle>
      <H2>Contents</H2></DIV>
      <UL>
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#ACIS_topology"><SPAN=20
        class=3Dtocnumber>1</SPAN> <SPAN class=3Dtoctext>ACIS =
topology</SPAN></A>=20
        <UL>
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Bodies"><SPAN=20
          class=3Dtocnumber>1.1</SPAN> <SPAN =
class=3Dtoctext>Bodies</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Lumps"><SPAN=20
          class=3Dtocnumber>1.2</SPAN> <SPAN =
class=3Dtoctext>Lumps</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Shells"><SPAN=20
          class=3Dtocnumber>1.3</SPAN> <SPAN =
class=3Dtoctext>Shells</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Subshells"><SPAN=20
          class=3Dtocnumber>1.4</SPAN> <SPAN =
class=3Dtoctext>Subshells</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Wires"><SPAN=20
          class=3Dtocnumber>1.5</SPAN> <SPAN =
class=3Dtoctext>Wires</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Faces"><SPAN=20
          class=3Dtocnumber>1.6</SPAN> <SPAN =
class=3Dtoctext>Faces</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Loops"><SPAN=20
          class=3Dtocnumber>1.7</SPAN> <SPAN =
class=3Dtoctext>Loops</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Coedges"><SPAN=20
          class=3Dtocnumber>1.8</SPAN> <SPAN =
class=3Dtoctext>Coedges</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Edges"><SPAN=20
          class=3Dtocnumber>1.9</SPAN> <SPAN =
class=3Dtoctext>Edges</SPAN></A>=20
          <LI class=3Dtoclevel-2><A=20
          =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Vertices"><SPAN=20
          class=3Dtocnumber>1.10</SPAN> <SPAN =
class=3Dtoctext>Vertices</SPAN></A>=20
          </LI></UL>
        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Topology_classes"><SPAN=
=20
        class=3Dtocnumber>2</SPAN> <SPAN class=3Dtoctext>Topology =
classes</SPAN></A>=20

        <LI class=3Dtoclevel-1><A=20
        =
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_I)#Manifold_and_non-manifo=
ld_objects"><SPAN=20
        class=3Dtocnumber>3</SPAN> <SPAN class=3Dtoctext>Manifold and =
non-manifold=20
        objects</SPAN></A> </LI></UL></TD></TR></TBODY></TABLE>
<SCRIPT type=3Dtext/javascript> if (window.showTocToggle) { var =
tocShowText =3D "show"; var tocHideText =3D "hide"; showTocToggle(); } =
</SCRIPT>
<A name=3DACIS_topology></A>
<H2><SPAN class=3Dmw-headline>ACIS topology </SPAN></H2>
<DL>
  <DD><SPAN class=3D"boilerplate seealso"><I>Main article: <A =
class=3Dnew=20
  title=3D"Model Topology"=20
  =
href=3D"http://doc.spatial.com/r18/index.php?title=3DModel_Topology&amp;a=
ction=3Dedit">Model=20
  Topology</A></I></SPAN> </DD></DL>
<P><BR>The basic concept of a boundary representation model is the =
topology=20
describes how elements are bounded and connected; the geometry describes =
the=20
shape of each individual element. A rather thorough description of the =
ACIS=20
topological structure is provided in <A class=3Dnew title=3D"Model =
Topology"=20
href=3D"http://doc.spatial.com/r18/index.php?title=3DModel_Topology&amp;a=
ction=3Dedit">Model=20
Topology</A>. You should familiarize yourself with that description =
before=20
continuing with this tutorial, because this tutorial will assume you =
understand=20
that information. </P>
<P>Topology tells us what is adjacent to what. For example, the topology =
may=20
tell us that an edge, <TT>E_1</TT>, is bounded by vertices <TT>V1</TT> =
and=20
<TT>V_2</TT>. If we also know that another edge, <TT>E_2</TT>, is =
bounded by=20
vertices <TT>V_2</TT> and <TT>V_3</TT>, then we know that edges =
<TT>E1</TT> and=20
<TT>E_2</TT> are adjacent because <TT>V_2</TT> bounds both edges. This =
is=20
depicted in the first diagram below. Similarly if a face, <TT>F_1</TT>, =
is=20
bounded by edges <TT>E_1</TT>, <TT>E_2</TT>, <TT>E_3</TT>, and =
<TT>E_4</TT>, and=20
another face <TT>F_2</TT>, is bounded by edges <TT>E_1</TT>, =
<TT>E_5</TT>,=20
<TT>E_3</TT>, and <TT>E_6</TT>, then we know that faces <TT>F_1</TT> and =

<TT>F_2</TT> are adjacent because both faces are bounded by <TT>E_1</TT> =
and=20
<TT>E_3</TT>. This is depicted in the second diagram below. Much of the=20
adjacency information in the topological data structure is obtained by=20
traversing the data structure. </P>
<CENTER>
<TABLE class=3Dgallery cellSpacing=3D0 cellPadding=3D0>
  <CAPTION>ACIS Topology</CAPTION>
  <TBODY>
  <TR>
    <TD>
      <DIV class=3Dgallerybox style=3D"WIDTH: 375px">
      <DIV class=3Dthumb=20
      style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: =
37px; WIDTH: 330px; PADDING-TOP: 37px">
      <DIV style=3D"MARGIN-LEFT: auto; WIDTH: 300px; MARGIN-RIGHT: =
auto"><A=20
      class=3Dimage title=3D"Tutorial3 Intro1.jpg"=20
      =
href=3D"http://doc.spatial.com/r18/index.php/Image:Tutorial3_Intro1.jpg">=
<IMG=20
      height=3D171 alt=3D""=20
      =
src=3D"http://doc.spatial.com/r18/images/thumb/e/e4/Tutorial3_Intro1.jpg/=
300px-Tutorial3_Intro1.jpg"=20
      width=3D300 border=3D0></A></DIV></DIV>
      <DIV class=3Dgallerytext>
      <P>Two topological structures=20
      <!-- Tidy found serious XHTML errors --></P></DIV></DIV></TD>
    <TD>
      <DIV class=3Dgallerybox style=3D"WIDTH: 375px">
      <DIV class=3Dthumb=20
      style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: =
23px; WIDTH: 330px; PADDING-TOP: 23px">
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