WEBVTT

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>> In this lecture, we're going
to talk about auxiliary views.

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Let's start by recalling that
for the principal planes,

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the frontal, horizontal,
and the profile planes,

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when you make those
principal projections,

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you use those principal
projection planes

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and project points
perpendicular to those planes.

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They will give you the principal
orthographic views of front,

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top and right side
views respectively.

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On the other hand, an auxiliary
plane is a plane that is used

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as a projection plane but
it's not parallel to any

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of the front, top or the
right profile planes, OK.

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And as a result of
projection in--

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projecting into this
auxiliary plane,

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we will get what's
called auxiliary views.

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And auxiliary views are used
to show true sizes of planes

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that are either oblique
or inclined.

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Here's an illustration
of an auxiliary view.

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We are given the top, front

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and right side views
of these solid here.

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And take note that plane A,
B, C is an inclined plane

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because it's shown as
foreshortened in the top

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and also foreshortened
in the right side view

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and an edge view
and the front view.

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So, none of these two views
here that show plane A, B, C,

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D as planes, it's the true size.

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If you want to see the true
size of this plane, what we need

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to do is make a line of sight

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from up here along the
direction that's perpendicular

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to the plane.

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So as illustrated here, this
is the direction of line

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of sight exactly
perpendicular to the edge view

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of the inclined plane
in the front,

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you will see the true size
and shape of this plane.

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And that view-- resulting
view is an auxiliary view.

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So you're looking along a
direction that is perpendicular

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to this reference
plane that is parallel

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to the edge view
and the front view.

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Here's an illustration of how

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that develops using
glass box model.

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Recall for the six
principal views.

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We have the glass box.

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We put the object inside
and then we project

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into the surfaces of this
glass box, the features

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of your object, and
then you open the box

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to get view the top
view, front, right,

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as well as the other views.

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For an auxiliary view
on the other hand,

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instead of having a
regular rectangular box,

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one of the faces of our glass
box is intentionally constructed

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parallel to this inclined plane.

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And then what we do is
project the features

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of the object orthographically,
so perpendicular

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to this auxiliary
reference plane, OK.

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That corresponds to
taking a line of sight

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that is perpendicular to the
auxiliary reference plane

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and hence perpendicular
to this inclined plane,

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and then we open it to
give us the auxiliary view.

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So, we're going to start

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in what's called primary
auxiliary views which just

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like the previous example.

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It's one in which the--

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it is projected from a principal
orthographic view using a

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primary auxiliary plane.

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So it could be from the
top-- projected from the top,

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the front, or the
right side view.

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A primary auxiliary reference
plane is perpendicular to one

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of the principal planes but
inclined with the other two.

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So in this case here, this
auxiliary reference plane here

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that is inclined is
perpendicular to the front view,

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to the frontal plane
and inclined relative

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to the other two planes.

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And we can use the
folding-line method

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to construct our auxiliary view.

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Think of auxiliary
planes as planes that fold

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from the principal planes,
just like a glass box model.

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Here it is an illustration.

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So, very similar to the objects

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that we had inside the
glass box here, OK.

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Here's the top, front, right
side view and you can think

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of the auxiliary reference
plane as in this case,

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being folded off of
the frontal plane.

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So in this case, this
auxiliary view is projected off

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of the front view because this
primary auxiliary reference

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plane was perpendicular

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to the frontal plane
before we unfolded the box.

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And the key here is, in
finding locations of this--

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any point in the auxiliary
view, we take measurements

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from the existing view.

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So for instance, here,
this distance here M

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which is a measure of how far
the object is behind the frontal

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plane, is really the
depth of the object

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and that depth is shown
both in the top view

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and the right side view.

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So in locating this edge of the
blue plane, we simply borrow

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or transfer the depth
of the top view

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or over the right side view,

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because this distance M
represents how far this edge

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of the plane is relative to
or behind the frontal plane.

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And that distance behind the
frontal plane is the same

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as seen from the top view, as
seen from the right side view,

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and consequently as seen
from the auxiliary view.

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So there's three types of
a primary auxiliary views.

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Again, primary auxiliary views
are views that are projected off

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of one of the three principal
planes, front, top, and right.

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So the first one is
called the auxiliary view

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and it's projected
from the top view.

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It's called a height auxiliary
view because the dimension

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of height is perpendicular
to the top view.

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And the idea is you take a fold
line right here up on the top,

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and what we see is the heights

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of objects below the top plane
is the same whether you're

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looking it from the front
or you're looking it

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from the right side
view or looking at it

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from the height auxiliary view.

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So what we do is to locate the
details of the points here,

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the bottom of this
here, OK, has a depth--

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has a height of H below
the top horizontal planes.

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So this fold line here separates
the top and the frontal planes,

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the top horizontal plane.

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This fold line here
between the top view

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and the auxiliary view
represents the fold line

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between the top horizontal plane
and the primary reference plane.

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And take note that it's very
useful to label your planes--

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your projection planes.

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It's H on this side.

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It's giving you the
top view here.

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It's F on this side
giving the front view here.

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And one here or auxiliary
reference plane number 1

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to give you the primary
auxiliary view.

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Again, this height here is
the same as this height, OK.

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And then if you want to
look at this part here,

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this height here, it should
be the same as this height.

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Here are the steps for creating
the height auxiliary view.

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So let's say that this inclined
plane here, I've labeled 1, 2,

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3, 4, 1 and 4 over
here, 2 and 3 over here.

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And we're interested in
finding the two sides

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of that inclined plane.

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So what we do is we take a fold
line here or a reference plane

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that is parallel to 1, 2,
3, 4 at its edge view, OK.

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This fold line here corresponds
to H or horizontal top plane

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on this side and first auxiliary
reference plane on this side,

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in the same way that this fold
line here corresponds to H

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above here and F below.

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And since its height auxiliary
view, when trying to locate 0.1,

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0.1 can be anywhere
along this projection.

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So I create a construction
lines from 0.1 perpendicular

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to my reference plane,
construction line from 0.2,

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perpendicular to
the reference plane.

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And then to find the location of
1, we say that the height of 1,

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how far it is below
the horizontal plane.

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Remember, this is
the horizontal plane?

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So this distance here
represents how far below you are

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from the top horizontal
plane before you unfolded the

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glass box.

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It must be the same as this
height here in the front view.

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Same thing along
the projection of 2,

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the height of 2 here is
transferred from the height

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of 2 given in the front view.

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And then project 3
also perpendicular

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to the reference plane
and 4 perpendicular

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to the reference plane.

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Take note that the
projection line--

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construction line for 3
is exactly the same as 2

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because they are exactly
the same location here.

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Projection for 4
is the same as 1.

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And then to find the
location of 3 and 4,

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this height here should
be the same as the height

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of 3 below the horizontal plane.

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We transfer that, same
thing with 4 over here.

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And then that gives you the
two sides of the plane, OK.

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In this example here, we only
are focusing on how a plane,

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1 here, 2, 3, 4, appears in
the auxiliary reference plane.

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Take note that the
other features

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of the 3D object, right?

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You have other objects here, OK,
need to be shown here as well,

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as you will see in our lab.

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And the second type of primary
auxiliary view is the depth

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auxiliary view and it's
projected off of the front view.

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It's called the depth auxiliary
view because the dimension

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of depth is perpendicular
to the front view.

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And we're going to
use the depth of--

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look at locations of points to
construct the auxiliary view.

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And here's an illustration.

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Here's the front view.

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And I want to find the true size
of this inclined plane here,

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so what I do is I take a fold
line off of the front view

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that is parallel to
that inclined plane.

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Take note that this reference
plane is perpendicular

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to the front view.

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In locating points in my
auxiliary reference plane,

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what I do is project points from
the existing front view, OK,

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along construction lines.

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All construction lines need to
be constructed perpendicular

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to the reference plane.

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And just to help
us, it's a good idea

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to always label your
projection planes on both sides.

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So this side here, this is
the fold line between the top

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and the front, and it's F on
this side and H on that side.

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This is the fold line
between the front

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and the right profile plane, F
on this side and P on that side.

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This is the fold line
between the front

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and the first auxiliary view.

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So this is front here and ARP,

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auxiliary reference
plane number 1 here.

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And then to find locations

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of points along the
projection construction lines,

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you borrow the depth of points.

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So depth D for instance here,

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represents how far
this object here is,

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this point in the object is
behind the frontal plane,

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and that distance depth
behind the frontal plane

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of course we knew from before,
is shown both in the top view

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and the right side view.

00:12:18.216 --> 00:12:21.276 A:middle
However, that distance behind
the frontal thing is also the

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same in the primary
auxiliary view.

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So we measure this distance
here, that will be the location

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of this point and that point
is along this projection.

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Take note that when
measuring away from F, OK,

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all the depths are measured
away from the frontal plane.

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Here's an illustration of the
depth auxiliary construction.

00:12:48.156 --> 00:12:50.436 A:middle
Here is the top view and
here is the front view.

00:12:51.126 --> 00:12:53.566 A:middle
And I see the edge view
of the inclined plane.

00:12:53.946 --> 00:12:55.826 A:middle
What I do is I want
to find the two sides

00:12:55.826 --> 00:12:57.716 A:middle
of that inclined plane.

00:12:57.766 --> 00:13:01.396 A:middle
So I take a reference plane that
is parallel to that edge view.

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That reference plane is
F on this side and ARP1,

00:13:05.916 --> 00:13:09.026 A:middle
auxiliary reference plane number
1 on this side, the same way

00:13:09.026 --> 00:13:10.796 A:middle
that this is F here and H here.

00:13:11.606 --> 00:13:17.726 A:middle
Take projection lines from
the points here of the plane,

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perpendicular to
the reference plane.

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Whenever a line of sight
or the projection lines,

00:13:23.376 --> 00:13:25.616 A:middle
construction lines
cause a reference plane,

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they should be perpendicular
to the reference plane.

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So, how do I know how
far the points are?

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So I'm calling this
0.1 here, 0.2 here, OK?

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How do I know the
location of 0.1?

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This is 0.1.

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It's going to be in
anywhere along this--

00:13:46.596 --> 00:13:48.346 A:middle
actually the 0.1 is over here.

00:13:49.306 --> 00:13:50.946 A:middle
So let's start with
this corner here.

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OK. It's along this projection.

00:13:54.256 --> 00:13:55.916 A:middle
How far along that projection?

00:13:56.316 --> 00:13:57.336 A:middle
You measure this depth.

00:13:58.046 --> 00:14:01.796 A:middle
That depth there
defines the depth of 1.

00:14:02.686 --> 00:14:05.806 A:middle
Here's the other point here
corresponding to this, OK.

00:14:06.026 --> 00:14:07.076 A:middle
It's along this line.

00:14:07.076 --> 00:14:11.636 A:middle
And take note that it's also
depth D. So transfer the depths

00:14:11.936 --> 00:14:15.266 A:middle
of points measured away
from this fold line.

00:14:15.336 --> 00:14:19.776 A:middle
It should be the same as depths
measure for this fold line

00:14:20.106 --> 00:14:22.866 A:middle
and laid out along
the corresponding

00:14:23.706 --> 00:14:24.816 A:middle
construction lines.

00:14:25.296 --> 00:14:28.816 A:middle
Do the same thing for
the two points here

00:14:28.816 --> 00:14:30.326 A:middle
that are closer to the front.

00:14:30.906 --> 00:14:34.276 A:middle
This depth here is the
same as the depth here

00:14:35.206 --> 00:14:36.786 A:middle
to give you the true sizes.

00:14:37.086 --> 00:14:38.556 A:middle
This is an error.

00:14:38.656 --> 00:14:41.136 A:middle
This D here should be over here.

00:14:42.006 --> 00:14:45.156 A:middle
Now the third type of
primarily auxiliary view

00:14:45.156 --> 00:14:46.586 A:middle
in the width auxiliary view.

00:14:47.476 --> 00:14:51.196 A:middle
It's the one that's projected
off of the right side view.

00:14:52.336 --> 00:14:56.296 A:middle
Take note that the right
profile plane is perpendicular

00:14:56.296 --> 00:14:58.446 A:middle
to the dimension of width, OK.

00:14:58.666 --> 00:15:00.876 A:middle
Width is a measure
of how far you are

00:15:01.186 --> 00:15:03.406 A:middle
to the left of the right plane.

00:15:04.586 --> 00:15:07.836 A:middle
So use width measurements
of points with respect

00:15:07.836 --> 00:15:12.156 A:middle
to the profile plane as basis
for finding locations of points.

00:15:12.156 --> 00:15:18.906 A:middle
So here, if you take this as
your fold line, it will be front

00:15:18.906 --> 00:15:21.606 A:middle
on this side and P on this side.

00:15:22.526 --> 00:15:24.676 A:middle
You take this fold line here.

00:15:24.676 --> 00:15:28.206 A:middle
It's going to be P on this
side and ARP1 on this side.

00:15:28.516 --> 00:15:32.566 A:middle
So this is P and this is
also P, distances away

00:15:32.566 --> 00:15:36.156 A:middle
from the right plane which
we call width is the same

00:15:36.156 --> 00:15:39.676 A:middle
as the distances here away
from the corresponding P here

00:15:40.096 --> 00:15:43.766 A:middle
when constructing
the auxiliary view.

00:15:44.936 --> 00:15:51.566 A:middle
Secondary auxiliary views,
this will be in lab number 12.

00:15:51.566 --> 00:15:54.536 A:middle
Lab number 11 will be
primary auxiliary views.

00:15:54.666 --> 00:15:57.706 A:middle
And you will understand it
more when we do lab number 11.

00:15:58.136 --> 00:16:01.456 A:middle
Lab number 12 deals with
secondary auxiliary views.

00:16:02.056 --> 00:16:05.776 A:middle
These are projected from
a primary auxiliary view.

00:16:05.776 --> 00:16:09.216 A:middle
So you have an existing
primary auxiliary view

00:16:09.216 --> 00:16:13.216 A:middle
or it could be a depth or height
or a width auxiliary view.

00:16:13.926 --> 00:16:17.836 A:middle
And then you take another
reference plane perpendicular

00:16:17.836 --> 00:16:19.496 A:middle
to that primary auxiliary view.

00:16:19.686 --> 00:16:22.996 A:middle
It gives you a secondary
auxiliary reference plane

00:16:22.996 --> 00:16:27.036 A:middle
that gives you the
secondary auxiliary view.

00:16:27.256 --> 00:16:30.786 A:middle
And these are-- the secondary
auxiliary view are used

00:16:30.876 --> 00:16:32.946 A:middle
to show the true size
of oblique planes.

00:16:33.926 --> 00:16:36.596 A:middle
Primary auxiliary views are used

00:16:37.106 --> 00:16:40.236 A:middle
to find the true size
of inclined planes.

00:16:41.186 --> 00:16:45.826 A:middle
Inclined plane is
inclined only with respect

00:16:45.856 --> 00:16:49.526 A:middle
to two principal planes and
perpendicular to the third.

00:16:50.086 --> 00:16:53.526 A:middle
On the other hand, an oblique
plane is actually rotated

00:16:54.026 --> 00:16:57.906 A:middle
directed to all three
principal planes.

00:16:58.076 --> 00:17:01.506 A:middle
That's why you need two
auxiliary reference planes

00:17:01.596 --> 00:17:05.076 A:middle
to find the true size
of this oblique plane.

00:17:05.076 --> 00:17:07.716 A:middle
Secondary auxiliary
reference plane that is used

00:17:07.796 --> 00:17:11.456 A:middle
to find the secondary
auxiliary view is constructed

00:17:11.576 --> 00:17:13.686 A:middle
perpendicular to
an existing ARP1.

00:17:13.906 --> 00:17:17.416 A:middle
And we use distance from point--

00:17:18.046 --> 00:17:22.866 A:middle
of a point from the ARP1 in the
same secondary auxiliary view

00:17:22.866 --> 00:17:25.366 A:middle
as in the principal
orthographic view.

00:17:25.786 --> 00:17:27.556 A:middle
So let's illustrate this.

00:17:27.866 --> 00:17:29.946 A:middle
And again, you will
understand it more

00:17:30.396 --> 00:17:32.556 A:middle
when you do lab number 12.

00:17:33.136 --> 00:17:36.796 A:middle
We're given the top and the
front view of this 3D object.

00:17:37.396 --> 00:17:41.286 A:middle
This is the top plane or H, you
will see the label in this H

00:17:41.626 --> 00:17:43.206 A:middle
and this is the front, OK.

00:17:43.706 --> 00:17:45.906 A:middle
Let's focus on the plane.

00:17:45.906 --> 00:17:50.686 A:middle
This triangle 1, 2, 3
shown in the top, 1, 2,

00:17:50.686 --> 00:17:53.726 A:middle
3 shown in the front,
and it's inclined.

00:17:54.216 --> 00:17:56.666 A:middle
What we do is-- That's
not inclined.

00:17:56.666 --> 00:17:57.176 A:middle
It's oblique.

00:17:57.526 --> 00:18:03.396 A:middle
OK. I give you this first
auxiliary reference plane.

00:18:04.456 --> 00:18:08.376 A:middle
So this type here, this is
projected off from the front,

00:18:08.836 --> 00:18:13.826 A:middle
which means that this is a
depth auxiliary reference plane.

00:18:14.416 --> 00:18:20.796 A:middle
So what we do is we take a
construction line perpendicular

00:18:20.796 --> 00:18:22.756 A:middle
to the auxiliary
reference plane here.

00:18:23.456 --> 00:18:26.126 A:middle
Take note, the auxiliary
reference plane was actually

00:18:26.126 --> 00:18:28.976 A:middle
constructed perpendicular
to line 1, 3.

00:18:29.686 --> 00:18:34.206 A:middle
So when we project 1, 1 would be
anywhere along this projection.

00:18:34.206 --> 00:18:38.376 A:middle
We project 2, 2 would be
anywhere along this projection.

00:18:38.996 --> 00:18:41.976 A:middle
And when we project
3, OK, the projection

00:18:41.976 --> 00:18:46.686 A:middle
for 3 is exactly the same
as that for 1 because line 1

00:18:46.686 --> 00:18:49.286 A:middle
and 3 here in the
front is perpendicular

00:18:49.286 --> 00:18:50.616 A:middle
to the auxiliary
reference plane.

00:18:51.306 --> 00:18:56.086 A:middle
Now to-- so I labeled
this as ARP1 over here.

00:18:56.736 --> 00:19:00.406 A:middle
And to locate 0.1, I
will use the depth here.

00:19:00.406 --> 00:19:03.586 A:middle
So this distance here from F--

00:19:03.586 --> 00:19:08.026 A:middle
behind F, that's the
depth of 0.1, OK.

00:19:08.026 --> 00:19:12.326 A:middle
Since this is also F, 1
is along this projection.

00:19:12.326 --> 00:19:14.666 A:middle
This distance here
also is the depth of 1.

00:19:15.136 --> 00:19:18.026 A:middle
So this distance of
1 is exactly the same

00:19:18.026 --> 00:19:20.586 A:middle
as the distance of
1 giving you 0.1.

00:19:21.326 --> 00:19:24.606 A:middle
To locate 0.2, 0.2 is
anywhere along this projection

00:19:25.056 --> 00:19:26.936 A:middle
and I measure the depth of 2.

00:19:26.936 --> 00:19:30.396 A:middle
So this distance here from
here to the fold line here

00:19:30.396 --> 00:19:34.766 A:middle
of F is the same as
this distance of 2 here

00:19:34.806 --> 00:19:38.216 A:middle
to the fold line of F.
That's how we located 0.2.

00:19:38.216 --> 00:19:42.536 A:middle
Now 0.3 is exactly in
the same projection

00:19:42.866 --> 00:19:46.246 A:middle
as 1 is also exactly
the same depth as 1.

00:19:46.246 --> 00:19:49.296 A:middle
This distance here is the same
as this distance so that 1

00:19:49.296 --> 00:19:52.926 A:middle
and 3 actually end up
being at the same point,

00:19:53.416 --> 00:19:56.976 A:middle
which means that when you
construct the plane 1, 2, 3,

00:19:57.906 --> 00:20:01.126 A:middle
and the first auxiliary view
is actually an edge view.

00:20:01.906 --> 00:20:06.536 A:middle
So this one here is the
edge view of 1, 2, 3, OK?

00:20:06.636 --> 00:20:10.516 A:middle
Since in this example we're only
focusing on triangle 1, 2, 3,

00:20:10.516 --> 00:20:14.306 A:middle
I'm going to not show
you the construction

00:20:14.306 --> 00:20:17.946 A:middle
of the other points
of this solid object.

00:20:18.416 --> 00:20:23.226 A:middle
So once we have 1, 2, 3 in
the first auxiliary view,

00:20:23.226 --> 00:20:24.816 A:middle
the primary auxiliary view,

00:20:25.426 --> 00:20:28.916 A:middle
we take a secondary
auxiliary reference plane,

00:20:30.056 --> 00:20:33.586 A:middle
this fold line here parallel
to the edge view of 1, 2, 3.

00:20:34.566 --> 00:20:38.636 A:middle
So this fold line here
corresponds on this side ARP1,

00:20:39.396 --> 00:20:43.396 A:middle
this whole thing is the
primary auxiliary view.

00:20:43.396 --> 00:20:46.796 A:middle
So this side of the
fold line here is ARP1,

00:20:46.796 --> 00:20:48.916 A:middle
on this side here would be ARP2.

00:20:49.016 --> 00:20:52.336 A:middle
That will give you
auxiliary view secondary.

00:20:53.636 --> 00:20:57.436 A:middle
Let's try and locate 1, 2 and 3
in the secondary auxiliary view

00:20:57.436 --> 00:21:01.646 A:middle
by projecting 1 and 3 will
be along this projection, OK.

00:21:01.646 --> 00:21:03.326 A:middle
The projection line
is perpendicular

00:21:03.326 --> 00:21:05.756 A:middle
to the reference plane

00:21:05.756 --> 00:21:07.906 A:middle
and 2 will be anywhere
along this projection.

00:21:08.376 --> 00:21:12.086 A:middle
The question now is how do
we find the location of 1

00:21:12.616 --> 00:21:17.186 A:middle
and 3 along this line, and
location of 2 along this line?

00:21:17.706 --> 00:21:20.886 A:middle
What we do is we
borrow distances.

00:21:20.886 --> 00:21:23.906 A:middle
So this distance is here,
this distance is away

00:21:23.906 --> 00:21:27.466 A:middle
from auxiliary 1 and we
already have that here

00:21:27.466 --> 00:21:28.846 A:middle
because this is auxiliary 1.

00:21:29.366 --> 00:21:32.486 A:middle
This whole thing, this current
central view is the first

00:21:32.486 --> 00:21:33.566 A:middle
auxiliary plane.

00:21:34.426 --> 00:21:36.376 A:middle
And distances away
from that plane

00:21:37.126 --> 00:21:40.416 A:middle
in this direction should
be the same as distances

00:21:40.416 --> 00:21:42.676 A:middle
from aux 1 in this plane.

00:21:42.676 --> 00:21:47.626 A:middle
So for instance, in locating
0.1 along this projection,

00:21:48.066 --> 00:21:56.376 A:middle
we notice that 0.1 is this
distance away from ARP1.

00:21:56.376 --> 00:22:00.666 A:middle
So this distance here which
we call X, is the distance

00:22:00.746 --> 00:22:04.976 A:middle
of 0.1 away from ARP1.

00:22:04.976 --> 00:22:11.006 A:middle
So what we do is we borrow
that distance of X-- that's X--

00:22:11.466 --> 00:22:13.886 A:middle
and lay it out along
the projection of 1

00:22:14.346 --> 00:22:16.466 A:middle
to give you location of 1.

00:22:17.656 --> 00:22:20.496 A:middle
Same thing for 2, 2 is
anywhere along this projection,

00:22:20.876 --> 00:22:22.786 A:middle
but how far along this distance?

00:22:22.786 --> 00:22:26.126 A:middle
Well, we notice that
distance of 2

00:22:26.126 --> 00:22:32.166 A:middle
from ARP1 is this
distance Y. OK.

00:22:32.256 --> 00:22:34.806 A:middle
That's how far 2 is from ARP1.

00:22:34.806 --> 00:22:40.666 A:middle
It's the same distance
Y that we construct away

00:22:40.666 --> 00:22:42.476 A:middle
from ARP1 or aux 1.

00:22:43.666 --> 00:22:45.406 A:middle
That will give you 2.

00:22:45.996 --> 00:22:50.186 A:middle
Similarly for 3,
distance of 3 is this

00:22:51.256 --> 00:22:53.596 A:middle
from auxiliary reference.

00:22:53.596 --> 00:22:55.396 A:middle
This is auxiliary reference 1.

00:22:55.396 --> 00:22:56.826 A:middle
The perpendicular distance here

00:22:57.136 --> 00:23:00.276 A:middle
which we call Z should be
the same as the distance

00:23:00.276 --> 00:23:04.736 A:middle
from perpendicular distance
for this corresponding ARP1

00:23:05.296 --> 00:23:10.166 A:middle
and that's Z. So the X here,
distance for 1 is the same

00:23:10.166 --> 00:23:11.356 A:middle
as distance from 1 here.

00:23:12.026 --> 00:23:15.226 A:middle
They're both measured from the
same auxiliary reference A1

00:23:15.226 --> 00:23:17.076 A:middle
and 1 here.

00:23:18.206 --> 00:23:23.866 A:middle
Y here for 2, Y for 2, and
Z here for 3 and Z here

00:23:23.866 --> 00:23:26.506 A:middle
for 3, give you 1, 2, 3.

00:23:27.816 --> 00:23:32.006 A:middle
And you will understand this
when you look at the video

00:23:32.006 --> 00:23:34.726 A:middle
for Lab 12 and also
complete that lab.