>> In this lecture we're going to talk
about pictorial sketching.
In a pictorial sketch we try to show several faces
of an object all at once and unlike, say,
a multiview, you see the front view only focuses on the front.
So this is like the reverse
of the previous topic of multi views.
Previously you were given an isometric pictorial
and were generating multi views.
This time most of the problems will involve giving us the multi
views and creating a pictorial sketch from these views.
There's 3 basic types of pictorial sketches, axonometric,
oblique, and perspective.
This figure here illustrates the differences among those types
of pictorials.
The first one here is the muti view.
This is an illustration
of the front view wherein the observer is at infinity
and as a result the lines of projection,
line of sight are parallel to each other.
This figure here is an illustration
of an axonometric wherein the observer is still at infinity;
however, we orient the object so that we see several faces
of the object and just like multi view,
the projection lines are perpendicular
to the projection plane.
In an oblique perspective, the observer is still at infinity;
however, the projection lines are projected at an angle.
It's not normal or perpendicular
to the picture plane, it's oblique.
Here's the perspective projection.
In the perspective projection the observer is actually
at the finite distance from the object,
which means that the lines corresponding to the line
of sight are not parallel to each other,
they're actually converging.
Let's focus on the axonometric projection.
It comes from the word axon, which means axis, okay?
In axonometric we try to show the 3 axes simultaneous, okay?
And it's obtained by rotating the object on an axis relative
to the projection plane so that we simultaneously see several
faces of the object.
And there's 3 types of axonomic projections,
we have the isometric, dimetric, and trimetric.
Iso means the same because the 3 angles,
angles between the 3 axes, x, y, z are equal to each other.
For dimetric 2 out of the 3 are equal,
for the trimetric the 3 are different from each other.
Here's an illustration of how a basic cube would appear
in a trimetric.
See this angle is here between the axes x, y,
z. They are not equal to each other.
In the dimetric, 2 out of the 3 are equal.
Here a and c are equal.
And, of course, in isometric all the 3 angles
in between the axes are equal to each other.
So angles a, b, and c are all equal to 120 degrees.
So we're going to focus on the isometric drawing
because obviously it's the easiest
because the angles are equal and most commonly used
in engineering, as I said,
the axes make 120 degrees from each other.
Iso means the same, okay, metric means measure
and generally, isometric drawings scales
and measurements along the 3 axes are the same, along x,
along y, along z so we try to focus
on transferring measurements and distances along those axes.
So, distances along the other directions not parallel to x
or y or z are not true
and consequently angles cannot be drawn and measured
because they are also distorted.
So the best way to create isometric drawing is
to locate points by measuring coordinates,
that is the position of any point relative along the x,
along y, along z and then going on to the next point
and connecting points that have been located.
There's different types of isometric projection.
We have 80% isometric; we will be using
almost always full-scale isometric drawing
because it's easier, no scaling involved.
So in creating an isometric drawing it's best to start
with a rectangular prism or cube
that represents the overall dimensions of the objects;
however, for more complicated figures it might be useful
to label points in given views and use projection lines
to determine corresponding positions of those points
in the other given views.
Plot positions are points, one by one, using coordinates
that are measured along x, y,
z and then a few plot consecutive points,
you just keep connecting the lines
that are connecting these points.
So I usually use this technique for objects
that are really complicated and it's not easy
to visualize right away the 3-dimensional drawing.
As a general rule, unless absolutely necessary,
and I will give you an example of that later,
we do not show hidden lines in an isometric drawing.
Okay, here's an illustration of the step-by-step creation
of an isometric sketch, okay?
Step 1 is you create your axis 30 degrees, 30 degrees,
and vertical with dimensions, depth dimensions
and height dimensions.
You lay out the overall dimensions
and then create here your basic rectangular box
and then start trimming away details of the object; measure
out these locations here and then trim
over on this part, and goes down here
and then measure the notch here, measure these locations
and then trim away until you get the 3D picture.
This technique is especially useful if it's easy
to visualize what the object looks like in 3-D sketch.
Here's an illustration of a case wherein it's absolutely
necessary to draw the hidden lines.
As a general rule, as I said earlier,
we don't show hidden lines unless it's
absolutely necessary.
In this case it's absolutely necessary
because without the hidden lines here there's no way for us
to show or to know that there is a wedge supporting this
horizontal part connected to this vertical part.
An illustration of how you would create a circle as it appears
in isometric view, a circle becomes an ellipse. The
orientation as shown here, okay, and as you can see it's tangent,
these are the points of tangency, okay,
right in the mid point of each of the edges of the cube.
These are correct representations
of the ellipse.
These are wrong, okay?
One thing is the points of tangency are not
on the mid point of the edges.
So in terms of illustrating how you would create that,
here's a face, okay, of a square.
You locate the center of the ellipse
by connecting the diagonals and then locate the points
of tangency by locating the mid points of the edges.
Okay, so A, B, C, and D are the points of tangency
and the way you do it is you make sure
that your ellipse is tangent to the edges of those 4 points
and it says here this would be the minor axis
of the left ellipse, meaning that's the short dimension
of the ellipse and this will be the major diameter.
So we create tangent here, tangent here.
Here's an example.
We are given the front view here and the right side view here.
There's a hidden line here and we're asked
to create isometric pictorial.
So what I've done is I've created an isometric box so,
this doesn't look accurate
but these angles here should be equal to 30 degrees on the left
and also 30 degrees on the right.
Once we have your rectangular prism based
on the overall dimensions, width here and height here
and the depth on the right side view, okay, I'm going to draw
on each of the faces, the right side view
and the given front view as shown.
So the right side view looks
like I see a solid here, okay?
Whereas on the front view it looks like I see, so if I look
at the correspondence of details in the front view
and the right side view,
it looks like this horizontal part here is corresponding
to the lower part of this hidden incline line,
which means that it's this part here,
is that incline plane there, and the upper part of that plane
over here is therefore this part here.
So this part here or this smaller rectangle is actually
slightly towards, it's actually towards the back.
So that means that only the u-shaped feature,
so I measure this distance here, measure the distance
on the other side also, like so, and then measure the height here
like so and then I'm going to start creating what I see
in the face of the frontal plane.
I'm just doing this by, it's hard to do it on a tablet PC.
So there's my u-shape that's in the front, okay?
And I know that this plane here is not in the same plane
as the u because they are separated by a solid line
and also I've already concluded earlier
that this smaller rectangle actually corresponds
to this incline plane here.
What that means is that somewhere here,
all the way to the back here, okay,
there's maybe my incline plane, okay,
like that, something like that.
So hopefully even if my drawing is not accurate
because it's hard to draw accurately on computer.
So hopefully you understand.
Okay, here's another example here.
The object is a little more complicated.
I will not show you the solution here, instead I want you to look
at tutorial of lab 6, there's actually part of lab 6.
For this particular case the object is a little more
complicated and as you can see here, what I suggest
that you do is instead of going straight
through to visualizing how it looks in 3-D space,
work on the object plane by plane, point by point
as illustrated by the numbered points on the plane here.
But, just watch the tutorial for lab 6.
Oblique sketches, okay, the second group of tutorials, okay,
is based on a system wherein with a perpendicular pair
of axes and 1 receding line.
So you have perpendicular axis like this,
the front is actually showing the correct size and shape
and the third axis is receding.
The frontal projection plane is rectangular
and there is receding lines for the depth dimension are parallel
to each other and can be anything between zero
and 90 degrees although 30 degrees is the most commonly
used angle.
Distances on the frontal planes as well
as the angles are correct or true, okay?
Along the receding lines distances may
or may not be true depending on the type
of oblique that you have.
We have something called a cavalier wherein measurements
along the third axis, the receding axis,
are to scale or full size.
We have cabinet wherein it's half size along the receding
axis and we have general one that's
between half size and full size.
And here's an illustration
on those 3 types of oblique tutorials.
We have the cavalier, okay,
that's full scale along the receding axis, okay?
Take note that if you measure this edge here and this edge
and this length here they're actually equal to each other.
Although, as you can see, it doesn't appear
to be visually accurate because the receding lines were supposed
to be along an incline and therefore should be foreshortened
so it appears that this is not a cube but it has the dimension
that it's longer along the depth direction, okay?
And that's why sometimes you might want to use the cabinet,
okay, which seems to be a little more accurate.
It looks more of a cube even though, okay,
if you take a ruler and measure the distance along the receding
axis it's actually just half of the distances
in the front view, okay?
And that's the cabinet and, of course,
a general oblique is one that's between being half sized
and full sized in the receding direction.
Now, the last type of pictorial is the perspective sketch.
Just like oblique it has receding lines, okay,
but the receding lines are like the oblique,
they're not parallel anymore.
They actually converge to a vanishing point,
which is a point in the horizon.
The reason why this is useful is it's actually more visually
accurate in that objects that are farther
from the observer appear to be smaller,
so this is popular among architects and artists
because they represent, they're closer to reality.
It's not as popular for engineering
because even though it's visually accurate it's more
difficult to get quantitative measurements
of distances and angles.
There's 2 types, we have the 2-point perspective,
which has 2 vanishing points and, as we will see,
looks somewhat similar to an isometric pictorial.
The second type is the 1-point perspective,
which only has 1 vanishing point and it looks kind
of similar to an oblique sketch.
Just to illustrate this roughly, okay,
here is a 2-point perspective.
We have the front edge of our box, okay,
and we have 2 vanishing points.
Let's say vanishing points are always on the horizon.
Vanishing point number 1 is there,
vanishing point number 2 is here and then, as we said,
we attach receding lines and the receding lines actually
intersect or converge in the vanishing points.
So this is vanishing point number 1,
vanishing point number 2,
the reason why it's called 2-point perspective is
because it has 2 vanishing points, okay?
And based on that we can now construct our basic rectangular
prism by connecting this vanishing point there again,
connecting this vanishing point there, and this edge,
this vertex there, okay?
So, as you can see, here is the approximate appearance
of the rectangular box in the 2-point perspective.
It looks like, as I said, it kind of looks like isometric
in that these 2 axes are actually angled there
but they're not 30 degrees, okay?
However, it's not quite isometric
because these distances are, the edges are shown
in the representation as equal to each other.
On the other hand, the 1-point perspective is very similar
to an oblique wherein you have the front view
so the front view is showing the perfect true size
and shape and we only have 1 vanishing point.
Here is our single vanishing point here and then
from that we can create our receding lines that intersect
or converge in the vanishing point
and then we can deconstruct our basic rectangular prism
as the angular prism for 1-point perspective.
Again, it looks like oblique because the front is the same,
however the receding lines are not parallel but converging
into a single vanishing point.
I think that's all I have to say about this topic.
What I suggest you do now is to understand this more
and for more examples look at the tutorials for the labs.