tutorialacis tutorial 3 understanding and traversing acis topology (part i) - docr18.mht

acis说明文档

The surface of a sphere, a torus, or a block are examples of =
2-dimensional=20
manifolds. (In this context the "surface" of an object refers to its =
exterior=20
boundary, not a specific geometric entity.) Each point on the boundary =
of a=20
manifold solid divides the modeling space into two regions, the region =
inside=20
the solid and the region outside the solid. If at any point on the =
boundary the=20
modeling space is not divided into two regions, then the object is =
non-manifold=20
at that point. </P>
<DIV class=3D"thumb tright">
<DIV class=3Dthumbinner style=3D"WIDTH: 302px"><A class=3Dimage=20
title=3D"Three non-manifold objects"=20
href=3D"http://doc.spatial.com/r18/index.php/Image:Tutorial3_Nonmanifold.=
jpg"><IMG=20
class=3Dthumbimage height=3D510 alt=3D"Three non-manifold objects"=20
src=3D"http://doc.spatial.com/r18/images/thumb/a/a7/Tutorial3_Nonmanifold=
.jpg/300px-Tutorial3_Nonmanifold.jpg"=20
width=3D300 border=3D0></A>=20
<DIV class=3Dthumbcaption>
<DIV class=3Dmagnify style=3D"FLOAT: right"><A class=3Dinternal =
title=3DEnlarge=20
href=3D"http://doc.spatial.com/r18/index.php/Image:Tutorial3_Nonmanifold.=
jpg"><IMG=20
height=3D11 alt=3D"" src=3D"" width=3D15></A></DIV>Three non-manifold=20
objects</DIV></DIV></DIV>
<P>A non-manifold point is depicted in the top image in the figure to =
the right.=20
At the non-manifold vertex there are two "inside" regions. One can go in =
one of=20
two directions and go "into" the object. Looking at this from a =
different=20
perspective, there are two manifold boundary surfaces that meet at the=20
non-manifold point. These are the "separation surfaces" we referred to =
above.=20
</P>
<P>A non-2-manifold region can be larger than a single point. The region =
can=20
extend along a curve. For example, two blocks may share an edge. This is =

depicted in the middle image in the figure to the right. Along the edge =
the=20
boundary of the object is non-2-manifold. Space is not divided into an =
"inside"=20
and "outside" region at any given point along the edge. At any point =
along the=20
edge there are two directions one can travel to go into the object. =
Similarly,=20
the non-2-manifold region can extend along a surface. For example, =
imagine a=20
block with an internal face. Space is not divided into an "inside" and =
"outside"=20
region at any given point along the internal face. At any point along =
the=20
internal face there are two directions one can travel to go into the =
object.=20
</P>
<P>Can a face have a non-manifold region on its interior? Yes. The =
bottom image=20
in the figure to the right depicts a planar face with two circular holes =
aligned=20
such that they just touch each other. The face is non-manifold at the =
point=20
where the two circular holes touch. At this point there are two =
directions into=20
the interior of the face. (We will discuss the specific topology of this =
case in=20
Part II of this Tutorial.) </P>
<P>Being manifold should not be confused with orientable. There are =
objects that=20
are manifold that are not orientable; for instance a Mbius Strip or a =
Klein=20
bottle. (If a surface is orientable that means that directions are =
consistent=20
across the surface. If one defines a direction, for instance clockwise, =
at a=20
given point A, and one travels along a path to point B, thereby =
establishing a=20
consistent clockwise direction at point B. The surface is orientable if =
for all=20
paths on the surface between A and B the direction of clockwise is =
consistent.)=20
Being manifold should also not be confused with being realizable. While =
it true=20
that non-manifold objects are not realizable, there are lots of objects =
that are=20
not realizable that are manifold. </P>
<P>In Part II of this tutorial, <A=20
title=3D"Tutorial:ACIS Tutorial 3: Understanding and traversing ACIS =
topology (Part II)"=20
href=3D"http://doc.spatial.com/r18/index.php/Tutorial:ACIS_Tutorial_3:_Un=
derstanding_and_traversing_ACIS_topology_(Part_II)">Tutorial=20
3: Understanding and traversing ACIS topology (Part II)</A>, we shall =
present=20
additional details about the topological structures of solids, sheets, =
and=20
wires. </P><!-- Tidy found serious XHTML errors --><!-- =0A=
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