WEBVTT

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>> In this lecture
we're going to talk

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about pictorial sketching.

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In a pictorial sketch we
try to show several faces

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of an object all at
once and unlike, say,

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a multiview, you see the front
view only focuses on the front.

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So this is like the reverse

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of the previous topic
of multi views.

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Previously you were given
an isometric pictorial

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and were generating multi views.

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This time most of the problems
will involve giving us the multi

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views and creating a pictorial
sketch from these views.

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There's 3 basic types of
pictorial sketches, axonometric,

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oblique, and perspective.

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This figure here illustrates the
differences among those types

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of pictorials.

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The first one here
is the muti view.

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This is an illustration

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of the front view wherein
the observer is at infinity

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and as a result the
lines of projection,

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line of sight are
parallel to each other.

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This figure here
is an illustration

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of an axonometric wherein the
observer is still at infinity;

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however, we orient the object
so that we see several faces

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of the object and
just like multi view,

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the projection lines
are perpendicular

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to the projection plane.

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In an oblique perspective, the
observer is still at infinity;

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however, the projection lines
are projected at an angle.

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It's not normal or perpendicular

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to the picture plane,
it's oblique.

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Here's the perspective
projection.

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In the perspective projection
the observer is actually

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at the finite distance
from the object,

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which means that the lines
corresponding to the line

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of sight are not
parallel to each other,

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they're actually converging.

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Let's focus on the
axonometric projection.

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It comes from the word axon,
which means axis, okay?

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In axonometric we try to show
the 3 axes simultaneous, okay?

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And it's obtained by rotating
the object on an axis relative

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to the projection plane so that
we simultaneously see several

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faces of the object.

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And there's 3 types of
axonomic projections,

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we have the isometric,
dimetric, and trimetric.

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Iso means the same
because the 3 angles,

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angles between the 3 axes, x,
y, z are equal to each other.

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For dimetric 2 out
of the 3 are equal,

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for the trimetric the 3 are
different from each other.

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Here's an illustration of
how a basic cube would appear

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in a trimetric.

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See this angle is here
between the axes x, y,

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z. They are not equal
to each other.

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In the dimetric, 2 out
of the 3 are equal.

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Here a and c are equal.

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And, of course, in
isometric all the 3 angles

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in between the axes are
equal to each other.

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So angles a, b, and c are
all equal to 120 degrees.

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So we're going to focus
on the isometric drawing

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because obviously
it's the easiest

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because the angles are
equal and most commonly used

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in engineering, as I said,

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the axes make 120
degrees from each other.

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Iso means the same, okay,
metric means measure

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and generally, isometric
drawings scales

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and measurements along the 3
axes are the same, along x,

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along y, along z
so we try to focus

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on transferring measurements
and distances along those axes.

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So, distances along the other
directions not parallel to x

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or y or z are not true

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and consequently angles
cannot be drawn and measured

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because they are also distorted.

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So the best way to create
isometric drawing is

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to locate points by
measuring coordinates,

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that is the position of any
point relative along the x,

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along y, along z and then
going on to the next point

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and connecting points
that have been located.

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There's different types
of isometric projection.

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We have 80% isometric; we will be using

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almost always full-scale
isometric drawing

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because it's easier,
no scaling involved.

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So in creating an isometric
drawing it's best to start

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with a rectangular prism or cube

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that represents the overall
dimensions of the objects;

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however, for more complicated
figures it might be useful

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to label points in given
views and use projection lines

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to determine corresponding
positions of those points

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in the other given views.

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Plot positions are points,
one by one, using coordinates

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that are measured along x, y,

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z and then a few plot
consecutive points,

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you just keep connecting
the lines

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that are connecting
these points.

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So I usually use this
technique for objects

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that are really complicated
and it's not easy

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to visualize right away
the 3-dimensional drawing.

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As a general rule, unless
absolutely necessary,

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and I will give you an
example of that later,

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we do not show hidden lines
in an isometric drawing.

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Okay, here's an illustration
of the step-by-step creation

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of an isometric sketch, okay?

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Step 1 is you create your
axis 30 degrees, 30 degrees,

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and vertical with
dimensions, depth dimensions

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and height dimensions.

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You lay out the overall
dimensions

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and then create here your
basic rectangular box

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and then start trimming away
details of the object; measure

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out these locations
here and then trim

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over on this part, and goes down here

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and then measure the notch
here, measure these locations

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and then trim away until you
get the 3D picture.

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This technique is
especially useful if it's easy

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to visualize what the object
looks like in 3-D sketch.

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Here's an illustration of a
case wherein it's absolutely

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necessary to draw
the hidden lines.

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As a general rule,
as I said earlier,

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we don't show hidden
lines unless it's

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absolutely necessary.

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In this case it's
absolutely necessary

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because without the hidden
lines here there's no way for us

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to show or to know that there
is a wedge supporting this

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horizontal part connected
to this vertical part.

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An illustration of how you would
create a circle as it appears

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in isometric view, a circle
becomes an ellipse. The

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orientation as shown here, okay,
and as you can see it's tangent,

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these are the points
of tangency, okay,

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right in the mid point of
each of the edges of the cube.

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These are correct
representations

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of the ellipse.

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These are wrong, okay?

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One thing is the points
of tangency are not

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on the mid point of the edges.

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So in terms of illustrating
how you would create that,

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here's a face, okay,
of a square.

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You locate the center
of the ellipse

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by connecting the diagonals
and then locate the points

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of tangency by locating the
mid points of the edges.

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Okay, so A, B, C, and D
are the points of tangency

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and the way you do
it is you make sure

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that your ellipse is tangent
to the edges of those 4 points

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and it says here this
would be the minor axis

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of the left ellipse, meaning
that's the short dimension

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of the ellipse and this
will be the major diameter.

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So we create tangent
here, tangent here.

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Here's an example.

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We are given the front view here
and the right side view here.

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There's a hidden line
here and we're asked

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to create isometric pictorial.

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So what I've done is I've
created an isometric box so,

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this doesn't look accurate

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but these angles here should be
equal to 30 degrees on the left

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and also 30 degrees
on the right.

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Once we have your
rectangular prism based

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on the overall dimensions,
width here and height here

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and the depth on the right side
view, okay, I'm going to draw

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on each of the faces,
the right side view

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and the given front
view as shown.

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So the right side view looks

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like I see a solid
here, okay?

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Whereas on the front view it
looks like I see, so if I look

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at the correspondence of
details in the front view

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and the right side view,

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it looks like this horizontal
part here is corresponding

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to the lower part of
this hidden incline line,

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which means that
it's this part here,

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is that incline plane there,
and the upper part of that plane

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over here is therefore
this part here.

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So this part here or this
smaller rectangle is actually

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slightly towards, it's
actually towards the back.

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So that means that only
the u-shaped feature,

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so I measure this distance
here, measure the distance

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on the other side also, like so,
and then measure the height here

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like so and then I'm going
to start creating what I see

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in the face of the
frontal plane.

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I'm just doing this by, it's
hard to do it on a tablet PC.

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So there's my u-shape
that's in the front, okay?

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And I know that this plane
here is not in the same plane

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as the u because they are
separated by a solid line

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and also I've already
concluded earlier

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that this smaller rectangle
actually corresponds

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to this incline plane here.

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What that means is
that somewhere here,

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all the way to the
back here, okay,

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there's maybe my
incline plane, okay,

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like that, something like that.

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So hopefully even if
my drawing is not accurate

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because it's hard to draw
accurately on computer.

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So hopefully you understand.

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Okay, here's another
example here.

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The object is a little
more complicated.

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I will not show you the solution
here, instead I want you to look

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at tutorial of lab 6, there's
actually part of lab 6.

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For this particular case
the object is a little more

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complicated and as you can
see here, what I suggest

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that you do is instead
of going straight

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through to visualizing
how it looks in 3-D space,

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work on the object plane
by plane, point by point

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as illustrated by the numbered
points on the plane here.

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But, just watch the
tutorial for lab 6.

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Oblique sketches, okay, the
second group of tutorials, okay,

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is based on a system wherein
with a perpendicular pair

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of axes and 1 receding line.

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So you have perpendicular
axis like this,

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the front is actually showing
the correct size and shape

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and the third axis is receding.

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The frontal projection
plane is rectangular

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and there is receding lines for
the depth dimension are parallel

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to each other and can
be anything between zero

00:12:27.566 --> 00:12:32.406 A:middle
and 90 degrees although 30
degrees is the most commonly

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used angle.

00:12:33.936 --> 00:12:37.306 A:middle
Distances on the
frontal planes as well

00:12:37.306 --> 00:12:41.756 A:middle
as the angles are
correct or true, okay?

00:12:42.956 --> 00:12:45.836 A:middle
Along the receding
lines distances may

00:12:45.836 --> 00:12:47.816 A:middle
or may not be true
depending on the type

00:12:47.816 --> 00:12:49.726 A:middle
of oblique that you have.

00:12:49.816 --> 00:12:53.356 A:middle
We have something called a
cavalier wherein measurements

00:12:53.356 --> 00:12:55.296 A:middle
along the third axis,
the receding axis,

00:12:55.296 --> 00:12:57.156 A:middle
are to scale or full size.

00:12:57.326 --> 00:13:01.216 A:middle
We have cabinet wherein it's
half size along the receding

00:13:01.216 --> 00:13:04.296 A:middle
axis and we have
general one that's

00:13:04.296 --> 00:13:06.786 A:middle
between half size and full size.

00:13:07.366 --> 00:13:08.576 A:middle
And here's an illustration

00:13:08.576 --> 00:13:11.256 A:middle
on those 3 types of
oblique tutorials.

00:13:11.346 --> 00:13:13.396 A:middle
We have the cavalier, okay,

00:13:14.206 --> 00:13:18.376 A:middle
that's full scale along
the receding axis, okay?

00:13:18.806 --> 00:13:23.606 A:middle
Take note that if you measure
this edge here and this edge

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and this length here they're
actually equal to each other.

00:13:27.736 --> 00:13:32.546 A:middle
Although, as you can
see, it doesn't appear

00:13:32.546 --> 00:13:38.046 A:middle
to be visually accurate because
the receding lines were supposed

00:13:38.046 --> 00:13:40.336 A:middle
to be along an incline
and therefore should be foreshortened

00:13:40.336 --> 00:13:47.126 A:middle
so it appears that this is not
a cube but it has the dimension

00:13:47.126 --> 00:13:50.276 A:middle
that it's longer along
the depth direction, okay?

00:13:50.276 --> 00:13:53.296 A:middle
And that's why sometimes you
might want to use the cabinet,

00:13:54.316 --> 00:13:56.356 A:middle
okay, which seems to be
a little more accurate.

00:13:56.446 --> 00:13:59.976 A:middle
It looks more of a
cube even though, okay,

00:13:59.976 --> 00:14:04.126 A:middle
if you take a ruler and measure
the distance along the receding

00:14:04.486 --> 00:14:07.496 A:middle
axis it's actually just
half of the distances

00:14:08.026 --> 00:14:09.986 A:middle
in the front view, okay?

00:14:10.126 --> 00:14:11.776 A:middle
And that's the cabinet
and, of course,

00:14:11.776 --> 00:14:17.216 A:middle
a general oblique is one
that's between being half sized

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and full sized in the
receding direction.

00:14:23.426 --> 00:14:27.686 A:middle
Now, the last type of pictorial
is the perspective sketch.

00:14:28.526 --> 00:14:32.766 A:middle
Just like oblique it has
receding lines, okay,

00:14:32.766 --> 00:14:34.766 A:middle
but the receding lines
are like the oblique,

00:14:35.946 --> 00:14:37.586 A:middle
they're not parallel anymore.

00:14:37.616 --> 00:14:40.346 A:middle
They actually converge
to a vanishing point,

00:14:40.386 --> 00:14:41.706 A:middle
which is a point in the horizon.

00:14:42.516 --> 00:14:46.756 A:middle
The reason why this is useful
is it's actually more visually

00:14:47.036 --> 00:14:49.756 A:middle
accurate in that
objects that are farther

00:14:49.756 --> 00:14:52.906 A:middle
from the observer
appear to be smaller,

00:14:53.026 --> 00:14:57.266 A:middle
so this is popular among
architects and artists

00:14:57.986 --> 00:15:01.476 A:middle
because they represent,
they're closer to reality.

00:15:02.346 --> 00:15:04.546 A:middle
It's not as popular
for engineering

00:15:04.546 --> 00:15:07.496 A:middle
because even though it's
visually accurate it's more

00:15:07.496 --> 00:15:10.836 A:middle
difficult to get
quantitative measurements

00:15:10.836 --> 00:15:11.866 A:middle
of distances and angles.

00:15:12.406 --> 00:15:15.256 A:middle
There's 2 types, we have
the 2-point perspective,

00:15:16.106 --> 00:15:19.176 A:middle
which has 2 vanishing
points and, as we will see,

00:15:19.356 --> 00:15:22.336 A:middle
looks somewhat similar to
an isometric pictorial.

00:15:23.026 --> 00:15:25.186 A:middle
The second type is the
1-point perspective,

00:15:25.686 --> 00:15:30.216 A:middle
which only has 1 vanishing
point and it looks kind

00:15:30.216 --> 00:15:31.866 A:middle
of similar to an oblique sketch.

00:15:32.176 --> 00:15:35.926 A:middle
Just to illustrate
this roughly, okay,

00:15:35.926 --> 00:15:38.036 A:middle
here is a 2-point perspective.

00:15:38.876 --> 00:15:43.546 A:middle
We have the front
edge of our box, okay,

00:15:43.946 --> 00:15:45.966 A:middle
and we have 2 vanishing points.

00:15:47.116 --> 00:15:49.626 A:middle
Let's say vanishing points
are always on the horizon.

00:15:49.756 --> 00:15:51.306 A:middle
Vanishing point number
1 is there,

00:15:51.776 --> 00:15:56.276 A:middle
vanishing point number 2 is
here and then, as we said,

00:15:57.126 --> 00:15:59.956 A:middle
we attach receding lines and
the receding lines actually

00:16:00.646 --> 00:16:04.436 A:middle
intersect or converge
in the vanishing points.

00:16:04.436 --> 00:16:06.566 A:middle
So this is vanishing
point number 1,

00:16:07.486 --> 00:16:09.026 A:middle
vanishing point number 2,

00:16:09.026 --> 00:16:12.646 A:middle
the reason why it's called
2-point perspective is

00:16:12.696 --> 00:16:15.836 A:middle
because it has 2
vanishing points, okay?

00:16:15.836 --> 00:16:23.096 A:middle
And based on that we can now
construct our basic rectangular

00:16:23.156 --> 00:16:27.626 A:middle
prism by connecting this
vanishing point there again,

00:16:28.456 --> 00:16:34.236 A:middle
connecting this vanishing
point there, and this edge,

00:16:34.736 --> 00:16:36.956 A:middle
this vertex there, okay?

00:16:37.326 --> 00:16:42.456 A:middle
So, as you can see, here is
the approximate appearance

00:16:43.766 --> 00:16:49.856 A:middle
of the rectangular box in
the 2-point perspective.

00:16:49.856 --> 00:16:53.626 A:middle
It looks like, as I said, it
kind of looks like isometric

00:16:54.006 --> 00:16:57.396 A:middle
in that these 2 axes are
actually angled there

00:16:58.176 --> 00:16:59.716 A:middle
but they're not 30
degrees, okay?

00:16:59.986 --> 00:17:02.086 A:middle
However, it's not
quite isometric

00:17:02.086 --> 00:17:06.806 A:middle
because these distances
are, the edges are shown

00:17:07.256 --> 00:17:09.236 A:middle
in the representation
as equal to each other.

00:17:10.686 --> 00:17:16.236 A:middle
On the other hand, the 1-point
perspective is very similar

00:17:19.806 --> 00:17:23.926 A:middle
to an oblique wherein
you have the front view

00:17:23.926 --> 00:17:26.756 A:middle
so the front view is showing
the perfect true size

00:17:26.756 --> 00:17:29.526 A:middle
and shape and we only
have 1 vanishing point.

00:17:30.526 --> 00:17:33.876 A:middle
Here is our single
vanishing point here and then

00:17:33.876 --> 00:17:40.136 A:middle
from that we can create our
receding lines that intersect

00:17:41.056 --> 00:17:42.906 A:middle
or converge in the
vanishing point

00:17:43.396 --> 00:17:50.896 A:middle
and then we can deconstruct
our basic rectangular prism

00:17:54.046 --> 00:17:57.496 A:middle
as the angular prism
for 1-point perspective.

00:17:58.216 --> 00:18:01.996 A:middle
Again, it looks like oblique
because the front is the same,

00:18:01.996 --> 00:18:05.916 A:middle
however the receding lines are
not parallel but converging

00:18:05.966 --> 00:18:09.156 A:middle
into a single vanishing point.

00:18:09.156 --> 00:18:12.656 A:middle
I think that's all I have
to say about this topic.

00:18:13.276 --> 00:18:16.736 A:middle
What I suggest you do now
is to understand this more

00:18:16.736 --> 00:18:21.386 A:middle
and for more examples look at
the tutorials for the labs.