# Converting Iso Ortho

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So today we're going to talk about
a few different strategies that are available to you for converting
from a isometric pictorial to an orthographic projection.
And the outline is we're first gonna talk about
using the infinite perspective properties of the
orthographic drawings to be able to create
an orthographic projection from an
isometric pictorial. We are then going to
look at the glass box approach and track some points around
and some surfaces around. And
before we get into these, I just want to say that it's not necessarily that
one of these is better than any of the others.
They can be useful in different circumstances.
I actually use all of them when converting, depending
on what type of objects that I'm dealing with.
So they can work better for different people,
they can work better for different objects,
No one is significantly better than any other.
So we're going to first
look at the infinite perspective property
of the orthographic projection. So when I am creating
an orthographic projection, what I am
doing is imagining that I am this little guy here
and I am standing
really, really, really far back from my object.
Now why am I standing really far back? Well
if I am this little eye here and
I am looking at a tree,
and I am up fairly close to the tree,
my lines of sight are going
to do something like this, so
you see them at an angle and this is where you get the perspective you see
in real life. The further back I stand,
The shallower and
shallower these perspective lines
get. So that as I'm
infinitely far back,
they are effectively parallel to one another.
So that's why its called an infinite perspective. Its as if
I was standing infinitely far away so that my perspective
lines are virtually horizontal and perpendicular
to the object that I'm looking at.
So I'm this little guy, I'm standing really far away
and I am looking at
this front surface. And all I'm going to do is
draw what I see. So I see
a few different edges here. I see
the front surface here. So I draw that
in down here. I
see this surface here.
And I draw that in here.
And then I
see the circle so I draw that in as well.
When it gets down to it
there are three major
reasons that I will be drawing a line on a drawing.
And the first one is
that I am seeing the edge of a plane. So here
I have this plane up top and
I'm seeing its edge right here. So that's
where this line comes from.
I have this plane over here and I'm seeing its
edge over here. So that's kinda where this line comes
from. So the lines that I'm drawing
are the side view, basically, or the edge
view of a plane. Another reason
I could be drawing a line is if I have the intersection of two surfaces.
So if I have something that looks kind of
like this. So I have this kind of
triangular prism.
And I am for some reason drawing it from this perspective,
which doesn't make a whole lot of sense but let's just say I am.
I'm drawing it from this perspective. So then
the view that I would be seeing
would look something like this.
And
Let's change ink colors...
So now if I look at it, this line here
is represented here.
And what that is, actually, is
the intersection of this surface
with this surface. So
our first type of line was the side view of the
surface. Our second type of line was
the intersection of two surfaces.
There's a third type of line that we may draw that may not be
quite as obvious. And that is,
basically, the limiting element of a
curved surface. So if instead of a
triangular prism, I had a
circular prism. And
now I am looking at it again
from this perspective. What I would
draw
is essentially a rectangle.
Now where this top line and this bottom line
comes from is
the limiting element of this
cylinder. So I have
the top line here.
I have this bottom line here.
The very, very extreme
part of the cylinder is what I'm seeing
in these two lines. So these are the
three different types of lines I'm really encountering.
I'm encountering the edge view of a surface.
Like there. I'm encountering
the intersection of two surfaces,
like I am here. Or I am
encountering the extremes of a cylinder, which is what I have
here.
So I draw these lines based on my infinite perspective.
And for a lot of shapes, they're simple enough that I can do that by
imagining myself standing here,
imagining myself standing here, and imagining myself
standing there.
Another way to think about something very similar
is this glass box approach.
So here I have a glass box and I put an object inside
of it. And what I want to do is project
the things that I see from a
certain view of that object onto that glass box.
So lets look at that. So here
if I'm standing at the front surface of this glass box
looking in, I project forward
the points and the vertices that I can see. And now I
get this view you see now on the front face.
Top face: I get something similar,
and the side view I get something similar.
So then what I do is I unfold
my glass box. And now what I end up with is
something that looks somewhat like this. So this looks very similar
to the infinite perspective view.
You don't draw perspective lines, you don't worry about perspective. You
just project in a certain direction
the points and vertices that you see.
You project it onto the front face, the top face, and the right side face in this case.
It could also be a left-side face, that's just not what I did here.
So this is the glass box approach.
And you can see that in this kind of video that I have
playing here; so you have a front face,
that's being projected, a top and a right-side
face, which become the front view, the top view, and the right-side view.
This
drawing has a bit more detail in it. You can see
on this drawing that we've included centerlines
and hidden lines. You didn't need that on the object
that we looked at a few slides ago.
Okay, now we are going to talk about point tracking.
So we've talked about the infinite perspective, we've
looked at the glass box, now we're going to look at point tracking.
So what I do with point tracking is I basically
assign a coordinate system to my object.
So we all know that
if you have a coordinate system and I
create an x-axis
and I create a y-axis
then by the right-hand rule
this would be my z-axis.
So this is what we're going to be using for
this object.
So if I look at my object
over here in
the orthographic views
I can figure out which axis is in which direction. So this part
I have a y-axis going
this way, and I have an
x-axis going this way and
down here I have a z-axis.
And
an x-axis, and
here I have a z-axis
and a y-axis.
So you can see that roughly
z is the height axis, x is the
width axis, and y is the depth axis.
So now, what I'm going to want to do is
figure out the coordinates of each of these.
So I have x, I have y,
and I have z.
And I have, for instance, lets say
points A, B,
C and D.
And I would end up doing this for more than just these
because I have lots of different points on this object.
But we're just going to look at a few of them for an example.
So we're gonna say that the A
point is at our origin.
Now what I want you to do is I want you to pause
the video and I want you to figure out
the coordinates of B, C, and D.
And then once you figure them out, play it again
and we'll go over what the answers are.
Okay so
now that you've figured out what you think
the coordinates are for B, C, and D, let's check ourselves.
So B in the x direction
is 1...2...3...
away from
the origin. So I have three
And then I'm gonna have to look
at a different view than the front view
to figure out the y-axis, so lets do the z direction next.
So in the z direction
I am 1...2...3...
4...5 units in the z direction.
And then if I hop
over to the right-side view I
am 1...2...3...
4...5 units in the y direction.
Similarly, I can
figure out that C is 4, 1, 2
and D is 7, 1, 0.
So I've figured out
the coordinates for all these different points.
Now what I would do is I would go
ahead and plot them on
my isometric grid here. So I would
figure out what my axes were, put them on the isometric
grid and plot them.
So here, I've done that here. So let's remind
ourselves.
So now I can check and make sure that I've actually
drawn this correctly. So let's look at
this... So this is
my x direction, this is my y direction,
and this is my z direction and right here
is my origin. So this would be
my point A. And A is at 0, 0, 0.
Now lets plot out where point B would be.
Point B would be 1...
2...3 units
in the x direction. 1...
2...3...4...
5 units in the y direction.
And 1...2...3...4...
5 units in the z direction.
So this is point B and I can see that
down here, it looks like I've actually drawn the right
point. I can look at the C
and D points as well.
C ends up being right here.
And D ends up being right
there. And so
what I would do is I would either
draw the isometric based on
what I'm visualizing from the three
orthographic views or I would actually start plotting these
points out one by one, figure out where B is and
plot it, figure out where this point is and plot it,
figure out where this point is and plot it. And
then basically connect the dots together. And that's how I could
go back and forth between the orthographic and isometric.
Now we're going to track
surfaces instead of tracking points. Before we do this
we need to know the three types of surfaces we tend to encounter
when we are drawing
objects. So our three types of surfaces are
principal surfaces, inclined surfaces, and oblique surfaces.
So here's a principal surface. And what makes a principal
surface a principal surface is that you see it as its
true size and shape in one view
and you see it as a line in
two other views. You see its edge, which shows up as a
line. So here
I have
the shape showing up as a rectangle in the top view,
as a line in the front
view and as a line in the right-side view.
So with a principal surface, I can look at any of
these views to get the dimensions of this shape.
So if I look—I can look at
the top view to get the distance
between 4 and 3, or I can look
at the front view to get the distance between 4 and 3.
I can look at the top view to get the
distance between 2 and 3 or I can look at the
right-side view to get the distance between 2 and 3.
So this is a principal surface. An
inclined surface shows up as the characteristic
shape in two views and then as a line
in the third view. So here I have
the inclined surface showing up as a rectangle in
the top view and in the right
side view. It doesn't have to be a rectangle,
that's just what it was this time. It could be a circle, it could be a
triangle, it could be anything. In this case
its a rectangle. And then I
also have it showing up as a line in
the front view.
So here if I want to get true dimensions, if I want to get the
distance between 2 and 3, I could do that in the top view,
or in the right-side view.
And that would be the same deal for the distance between
4 and 1. If I wanna get the distance
between 4 and 3
or 1 and 2
I can't do that in the top view or the right-side view
because its on an incline. So if I wanna get
the linear distance between 4 and 3
I need to do that here in
the front view.
Our third type of surface is an oblique surface.
And here it shows up as its
characteristic shape in all three views.
So here its a triangle, it could be something else,
but it shows up as a triangle in all three views.
I never see just the edge, that's how I know I have an oblique
surface. If I wanna get true distances
between 1 and 2, I would be up here in the top view.
Between 1 and 3, I'd be here in the front view.
And between 2 and 3, I'd be here in this right-side
view. None of these other distances are the true
distances between the points. They are all
shortened because of the way that I'm looking at them.
So now that I know my three different types of surfaces
I can use them to solve a problem and figure out
something about a drawing.
So here I have an orthographic drawing and I want to
draw the isometric and I want to figure out what line
I'm missing. I'm missing something. I'm missing a line and I want to
figure out what line it is that I'm missing.
So what I'm going to do is
look at each of these surfaces,
draw them in my isometric and use them
to figure out what information is missing and what line I need to add.
So here I've blocked out my
object. It is roughly
a 9 x 5 x 5 rectangular
prism. And I'm going to within that
blocked out rectangular prism, draw my
different surfaces. So I have a principal surface
here because it shows up as its true shape in one
view and as an edge view in two other views.
Here I have a surface
that shows up as a rectangle twice and as a line the third time,
meaning its an inclined surface. I have
another principal surface. Here I have an oblique surface
because I see it as a triangle in all three views.
I have a few more principal surfaces.
And now I find out where I'm
missing my information. So I'm missing my
information here where I see two rectangles.
Now it looks to me like it probably isn't going to be an
oblique surface. It would be very difficult to fit an
oblique surface into this cavity.
So because I'm seeing two rectangles
its a pretty safe assumption that I'm dealing with an inclined
surface. So if I draw in my inclined
surface, I can draw in my associated
line down here on my side view
and now I have figured out
my missing information by tracking surfaces.
So here's my finished example.
One thing I want you to do is to convince yourself that
this surface here needs to be an inclined surface
and that it can't just be a notch.
If you can't figure out how to convince yourself that it couldn't just be
a notch back into the object
then ask your instructor about it
because its an important thing to be able to understand.
There's actually one other shape this technically could be.
It technically could've been
some sort of curved surface and it would've shown up similarly.
So in summary, we've looked at using
infinite perspective and the glass box approach to just look at
an object and be able to draw it. We've looked at point
tracking and we've looked at surface tracking.
And any of these different strategies could be useful at
different times. You don't have to use all of them,
but they are very useful.