Technical Arts 101

Prof. Anupam Saxena

Department of Mechanical Engineering
Indian Institute of Technology, Kanpur

Lecture - 34
Lab 06

(Refer Slide Time: 00:19)

This is an example on perspective view. So, what I will try to do is I will attempt a three
point perspective of this object and what I will do is, I will be using a two station point
method, to draw this perspective. I will not be using vanishing points explicitly, but
instead what I will do is, I will rotate this object twice, one would be about this axis, I
rotate the top view above this axis and afterwards I will rotate the profile view above this
axis.

I will do that to ensure that none of these edges are parallel to the picture plane. So, these
are the orthographic views of this object the front view or the frontal plane is this, top
view the profile view, so what I did was I performed one rotation.
(Refer Slide Time: 01:54)

I rotated the top view like, so by some degree I got the frontal view as well as the profile
view, but then things became complicated. So, what I did was the next smart thing I went
to MATLAB, I recorded the three dimensional coordinates of all these vertices, I also
record the connectivitys and then within MATLAB, I performed two rotations of this
object.

(Refer Slide Time: 02:40)

Once I did that, I got three views this was my front view, top view with respect to the
front view and the profile view with respect to the front view. So, the trick is to use the
true top view and the true profile view to get the perspective of this object, we will try to
see how this example goes.

(Refer Slide Time: 03:18)

So, what I have done is I have copied down the true top view here and the true profile
view here and with these two views using the two station point method, I will try to the
attempt perspective drawing of that object. Let me first specify the ground line, so the
ground line will be passing through this point o little gentle line, let me also specify the
picture plane. Now, in the top view the picture plane, let us assume that it passes through
point a vertex g, let me call this p p.

The picture plane in the profile view the picture plane is going to be vertical and it is
going to be passing through this vertex g here, I have to practice littering, but let us not
worry about that for now. Now, let us say I am station somewhere here, in the top view
and let me mark a point or perhaps somewhere over here, the further I stay from the
picture plane and the further away from the object I will probably be getting a nicer
perspective, but a smaller perspective.

So, I do not want to be too far away from the picture plane and I do not want to be write
in front of the object may be I want to maintain some angle between the object and
myself in the top view. Let me have my station point somewhere here it is arbitrary and
let me encircle it, so that when I am drawing the perspective I do not miss it. Notice that
I am using my two h pencil and let me call this station point with the subscript t to
remind me that this is in the top view.

Now, in the profile view let us say I want to see the roof of this object, so my horizon
line would be above this portion of the object and this distance in the top view should be
the same as this distance in the profile view. So, let me first choose the horizon line,
horizon line could be anywhere in the profile view does not matter it could be above the
picture plane or below the picture plane.

Let me have my horizon line here, where you would notice that after while I would stop
calling this is the horizon line because I will have my station point here. Let us measure
this distance it is about 60 millimeters and let me have this distance over here, let me
encircle this point to remind myself time now here that this is the station point in the
profile view, I use a subscript p. So, throughout I will be using the two h pencil, because
there will be a lot of many construction lines there are chances that I might make a
mistake if I am not careful and if I am not focusing first things first.

Let us identify this vertex g, vertex g in the top view lies on the picture plane. So, I can
take the vertical projection down from the top view and perhaps I can take the horizontal
projection from the profile view intersection of these will give me vertex g. Now, what I
will do is I will start seeing these vertices in the top view from the station point, I get
their projections or their images on the picture plane and I will try to project the images
downwards.

Likewise in the profile view I will start seeing the respective vertices, I will get their
images on this picture plane and I will try to project them horizontally. The intersection
of vertical projections and the horizontal projections, will give me the respective vertices
on this part of the sheet, the perspective plane if I may call that.

Perhaps not a good idea to disturb my drafters I am going to using this kind of line the
30, 60, 90 swiss square. And let us perhaps focus on this vertex R, this is the ray in the
top view through which I am visualizing R, I get its image over here I project it down by
some instance I am using very dim line perhaps may be a little darker, so that you could
also see. And then from the station point of the profile view, see my vertex I here, this is
where the image of the R will be formed, I use horizontal projection from this point here
and this is R.
Let me view myself for now and work on these vertices the top view and the profile
view, let us see how this go, the procedure to get all these vertices on the perspective
plane is identical, I am working with Q I get the image of Q, here now within. So,
whenever I draw the horizontal and vertical projections I need to be careful in correlating
them. Let us take P in perspective have it is image down maybe it is a nice idea for me to
indent these intersection points otherwise I will get confused, the image of P is right
there and this is where p would be perspective and perhaps O.

So, looks like O is going to be lying on this vertical line and let me take o from here, it is
image on the picture plane is right there, O lies on this vertical line need to be little
careful I do not want to miss these lines, perhaps just to get an idea has to have the
picture of perspective is getting formed. Let me join these 6 points to form a plane, these
4 points N Q R and G they will have to be collinear.

So, they will have to line a straight line, so this seems we got it right and then in P forms
an edge likewise O G forms an edge and O B forms an edge, this seems to be looking
quite queued. I wonder if I have taken this view right or this view right, seems like it was
((Refer Time: 19:07)), nevertheless let me continue and see where I go from here
perhaps may be it will be a good idea for meet to draw this face and see if everything
seems.

So, let me focus on vertex a that connects with O, I have labeled these vertices for my
own convenience otherwise I tend to forget where these vertices are nevertheless. So, a
gets it is image formed over here, bring it down if I look at vertex A from this station
point, this is where the image of A gets formed project it horizontally and this is where
my vertex A is I indented also right a little notation.

So, O A gets connected, let me see where B is looks quite weird to me at this time, may
be not a proper choice of station point, but let see image of B getting formed over here, I
project that image down. And then I look at B here in the profile view from the station
point, get this ray go in the image of B gets formed here and I need to intersect the
horizontal with this vertical here, this is perhaps where my B is looks quite weird looks
really weird.

Well let me continue about I, vertex I here image getting formed here somewhere take
this down then go to many, many, many, many rays one needs to be quite careful from
here vertex I forms an image somewhere here picture plane, take it is horizontal
projection an get the intersection here indent this point. I am not supposed to be do that,
but just to remind myself that this is where I is you proper use a grammar should be I am,
but this is vertex I.

Let me verify if this is, seems like this is seems like, this is all right let me have this point
I. So, I have done A B I perhaps H look at this station point here, H would be very close
to this vertical line, very close indeed. So, this is my vertex H in the profile view, this is
perhaps where if the image of h gets formed, I take a horizontal projection from here and
mark it over here, so this is 1 point H.

So, just to make my sheet looking better, I will take a break and I will erase these objects
and then I will come back later. So, looks like I have all these vertices corresponding to
this plane in my picture here perspective picture. So, G O and then I have got I perhaps I
should go in an ordinary fashion, so G O then A I have A here, perhaps I have P here, I
here and H here.

So, let me try to join them maintaining the same connectivity let me keep my drafter for
while. So, let me join G and A first, I will worry about visibility later and then A B and
then B I, I H, H is here and H back to G. Perhaps I made a mistake, I should have really
joined O and A, I erase that and come back got joining O A as I mentioned earlier if you
are not careful there are chances that mistakes will happen.

So, O A, A B, B I, I H and H back to G, perhaps I can try to get this face as well, at least
I will be able to figure if my top view is okay or not. So, already have P and N I need to
get these four vertices let us focus on M, going to be careful me to use 2 h. So, this where
m makes an impression on picture plane, project it down my vertex m is here this is
where I get the image of m on the picture plane I project this horizontally perhaps this is
where I get m intend that may be make a little note for myself.

Now, for vertex F that is where the image of F is take it down and then F is here make
celebration here very close to M perhaps I lost my projection over here. So, F coming
from here S here and F is making its image very close to m on the picture plane, well it
should be little above that one more time, I let that line stay. So, 2 points remain E and L,
so this is where the vertical projection is coming for E and this is where the horizontal
projection is coming for E.
So, perhaps this is where E S, so very easy to get last in perspective finally, I think is
where I is let me verify, so the ray from this station point towards L makes an impression
here on the picture plane gets down. So, this is where I should be and then from here this
is the ray that is making an impression at this point on the picture plane and so looks like
I am fine.

So, I have got L E M and F and F is connected to P and M is connected to N, let me work
on these connectivitys M connected to N and then L connected to M, L connected to E
and then E connected to F here perhaps and F connected back to p, it is going to looking
weird. But, let us see how this goes further still not a good idea perhaps for now to start
making these lines darker, because it is still lot of construction left.

So, if you realize L E D K is making a phase, D C J K is making another phase and C B I

J third phase. So, I got this edge I got this edge in perspective perhaps if I get these two
edges, I then will be able to see these three phases and verify if I am really going. First
let us look at C these are going to be true many lines. So, maybe I will start marking and
maybe I will remind myself if this is C take a vertical projection down all right go to see
here, may be lets mark c here get the horizontal projection up till this vertical projection
this point here is C.

Let us look at J now, so it looks like J is going to be very close to this vertical projection
it is not going to be very far from that or may be it would be, let me mark this is J get the
vertical projection from here. And let me look at J in the profile view, let me get the
horizontal projection from here and perhaps this is where J X, let me intend this point
and call it J. So, looks like I have this phase B I J C, so I is connected to J let me make
that connection and then B S connected to C, let me make that a little darker and then of
course, J is connected C.

So, I have gotten this phase, now what remains is to find k and T, so I look at K this is
where K should be bring down the vertical projection from here my lines are getting
darker now, that should not happen. And I locate K here, this is where K would be take
the horizontal projection and this is where point J is. So, looks like too many points are
close to each other and D E this is going to get mess here, these takes here take the
vertical down.
And then take the image of D on the picture plane in profile view, here mark that as D
usually these markings are not supposed to be done, but I am just doing that, because
otherwise I know I am going to get last I know I am going to be last it is my drafter. So,
possibly it lies a little above the picture plane and I need to project this thing upwards a
little looks like my D would be somewhere here.

So, now, these looking messy here because there are, so many points I need to be careful
in locating K, which is here and T which is here. So, before we tend to lose ourselves let
us go ahead and connect the vertices. So, L is connected to K, K is connected to D and D
is connected back to E and I have no idea where E is did I get E right and how to figure
that out.

So, let me go back E should have been here, somewhere and then E should have been on
this vertical projection E should be coming out from here. So, E should have been here,
so I marked this point wrong, once again station point to E image of E comes here
somewhere take it down right. So, may be let me mark E here and then station point to E
in the profile view, E makes an image here take it is horizontal projection from here and
E should be here, so looks like I got E wrong here.

So, this connection is also not proper, so if we not careful you know mistake happen here
looks like I am in a mess here, so many points, so many rays horizontal and vertical
projections. So, I will take a break try to sort this mess out and come back and then
continue with the rest of the perspective projection. So, what I did was I went up line and
darkened my construction lines, so that I do not get confused, but in the process it looks
like I am little more confused anyhow.

So, I got this part all right, so this was the region where I started to make mistakes if you
realize this is point C this is point J vertex K, vertex T would be somewhere here and if I
look at this phase here C J K T makes phase. So, C J K T let me complete this phase and
then move further this time it looks little messy, but hopefully when the final drawing is
done things will be a lot more clear.

Now, look at vertex L vertex L is behind the face C J K T and s, its vertex E. So, one of
the option is to let go of them second option is to you know make this phase, but if you
do that things would be a little more messy, well let me try it out let see how it goes.
Now, that we are in the mess already and later on we will work on the visibility part and
try to finalize this drawing. So, looks like I have this face done pretty much and then on
the back side E and F would be connected, so it is a very cute line, but let me have it and
let me darken B C just to get an idea has to how cute the perspective is.

So, before we work on the ray part, perhaps it could be nice, if we can figure out the
visibility of this. So, let me go back to my front view right here and realize that phase H
G N M is on top. So, these lines they need to be dark P O is at the bottom, so this part
can be vomited and O a is visible, so this is visible and so S G O. So, let me work on this
part first and if I to darken these edges, before I start getting more confused.

So, here we go and to darken I am going to be using my h pencil I hope I will not be
making mistakes from now on, if I do well I do. Now, this part will probably not be
visible, because this edge would hide that. So, maybe I will just make a partial phase or
may be let me not work on this for little a while, because I am not sure if the ray that we
are going to be working with will further hide it or not, so let me vomit this part and
perhaps darken this part of the perspective.

So, these phases are going to visible anyways rather or not the ray is there only a part of
the ray is going to be behind these phases. So, let me darken these phase, I am not
supposed to be pencil over itself, this what happens if I do overlapping lines, which is
something that I do not recommend, but just to show you how the perspective is going to
look like and darkening these lines as much as I can. So, that they are still visible when
compare to the constructional lines around them, well now that I am working with dark
lines.

Let me make these lines are dark as I can, just to have them in contrast with the lines
rather than many lines in the neighborhood, it looks better. And of course, this phase is
also going to be visible, let me mark it looks all right to me and of course, the back phase
F. So, now let us work on the rep, notice that rep is composed on these vertices U, V, T,
S and Q, R none of which have been well Q, R are there, but other than that these four
vertices they are not there slightly dark T, S is with this region, anyhow we will have to
get them lets first focus on U and V.

Let us get back to construction U is here let me draw that in station point and looks like
the projection of U and the projection of V are pretty much same over here or perhaps
over here. So, let me use my drafter extend this circle little, need to switch my pencils for
that and then mark little u here, let me go back to the profile view, u vertex u from the
station point get it is image on the picture plane right here.

Now, notice that I have started using darker construction lines, this where u is take my
drafter and this what where my u would be now I have to be extremely careful as u and
then looking at V going to the top view looking at V from the station point, getting it is
image on the picture plane in the top view. Now, that these lines are dark enough I do not
had to worry about the darkness of the construction lines though I need to make them as
light as possible and as clear as possible, unfortunately in this example things have been
little messy specially in this area.

Now, back to V, this where V would be let me draw vertical projection, slightly extended
upwards. So, that I can mark V here, now let me look at V in the profile view from the
corresponding station point, draw construction line drawing perspectives is now very
easy. And then use the corresponding horizontal projection and perhaps can V reach the
corresponding vertical projection here, so this is v let me intend that and mark a little v.

So, let me pullout my front view for reference, so v is connected to Q and U is connected
to R, let me make those connections, let me for the drafter verify a little while. And only
a part of this rep will not be visible, let me make this connection here, Q with V and you
see that this part of N M, now is hidden behind the rep. Well perhaps I can now see this
perspective little more clearly let me draw this line as thick line a few strokes back and
forth and then it looks like both these edges of the rep they are going to be visible.

So, I am going to darken them I will stop at the top one first and then I am going to go
only till this point and then only up till this point I still do not have much ideas to have
this perspective is going to look definitely looks much weirder than I expected.

But well and then perhaps what we can do is starting from R, so this edge would be
visible. So, perhaps if we can locate S on our perspective, we can draw this edge and
hopefully finish this diagram let us not worry about T, because T is going to be behind,
so it is not going to be visible. So, let me take this off and worry about S switch pencils
look at S in the top view get it is corresponding image on the picture plane, it is going to
vertical close to this projection here.
Let me extend this little upwards, just in case of these two projectors call this s, little
small note and then in the profile view, let me get the image of S on the picture plane
here somewhere, it is going to make sure I do not use it bringing my drafter there make a
horizontal projection. And follow these projections perhaps this is where my S is make a
little note S all right and then join R with this again this part the rep will be behind it is
not going to be visible, so perhaps I can use a dark line directly.

Well, as I said many, many times it looks like very weird perspective and one of the
reasons why this is source possibly, because the vanishing points are very close to the
image, let us try to locate the vanishing points. So, this is one of the axis this is second
one and this is the height axis. So, corresponding to this axis, if I try to draw, if I try to
extend these edges and I am going to E using a different color of pencil going to look
little weird, but if I try to extend these edges, this is the first vanishing point that I get
somewhere here.

And if I extend the height edges this is the second vanishing point that I would get over
here somewhere and if I extend edges along this direction these directions I will possibly
be expecting the third vanishing point over here somewhere. So, vanishing point 1,
vanishing point 2 and somewhere over here, the vanishing point 3, let us see if these
vanishing points are indeed correct, because if they are not, then of course, there
something wrong with this perspective. So, always a good idea to verify if you have
made a mistake or not there is nothing wrong with making mistakes.

So, to get the vanishing point along this direction, we will probably have to look along
this direction from this station point. So, let me now start adjusting my drafter, align my
horizontal a longer scale along this, along this edge and look at an object at infinity along
that direction. Let me use the blue pencil for that and of course, this will be making an
impression over here on the picture plane.

Now, I will do the same thing I will look at an object at infinity along this direction this
will perhaps explain why the perspective is this weird anyhow. So, if I locate an object
along this direction at infinity from this station point, I probably be getting the image of
that object over here. Let me mark these vertices, let me now straight my drafter and
draw verticals. Now, let me take a vertical from here, I will extend it along both
directions and also let me take a vertical from here again I will extend it along both
directions.

Now, in the profile view the x and y directions they are along these edges and the Z
direction the depth or the height direction is along this edge. I will do precisely the same
thing as I did over here set my drafter to be parallel to one of these edges from the station
point I will look at an object at infinity the image of which it is going to be getting
formed on the picture plane somewhere here. And likewise I will set my longer scale in
the drafter parallel to this edge and I locate an object at infinity along this from the
station point in the profile view and that image is going to get formed here.

I need to be little careful, rather I need to be quite careful now, because little mistake I
will not ensure that my perspective is indeed right or incorrect possibly here somewhere,
you know little tangent angle makes, so much of difference.

So, looks like these vanishing points are quite sensitive to these edges, we will have to be
very, very careful. So anyhow, so taken this and drawing the horizontal from here and
the horizontal from here, extending that and extending the horizontals from here up till
both these vertical lines, I see that my vanishing point here and my another vanishing
point is there. So, if I set my scale accurately along these lines I should probably be very,
very close to that vanishing point.

So, looks like I should have really drawn them a little later, I was may be in a hurry, you
know as I said a little error could make, so much of difference now looks like this is not
aligning properly, so could be that I may have gotten these edges wrong is it that. Let me
go back let me check my construction here, I got the o wrong, because if you look at O it
is getting. So, this ray starting from this station point is hitting the picture plane over here
somewhere and if I extend this right there vertically downward, my O should be on this
vertical projection clearly I got my O wrong.

Let me verify from here, so this is where the ray from S B P towards O it is a picture
plane this is a corresponding horizontal projection. So, this seems, adjust that my O
needs to be slightly displaced towards left, having said that realize that both these
vanishing points get effected. Let me go back make this correction and join with these
shortly. So, realize that these mistakes are going to happen that is what the reason why I
keep repeating that is always never a good idea to start drawing dark lines, one needs to
be very, very careful and focused nevertheless. So, this is where my point O is, well as I
said nothing wrong in making mistakes, what I am saying that I am still using my h
pencil, but hopefully I get things right now.

Let me join these edges rather this edge using a dark pencil, so this is thinner than last
time. Now, if I align my swiss square to one of the edges to realize that I am actually
approaching that vanishing point, which is good news. So, maybe I will just you know
extend that, so this vanishing point is incorrect, perhaps that one is more reasonable,
there we go this one. And if I comeback I need to erase this part as well which is because
I do not need this edge in my perspective all I need is this point P.

Let me darken these lines probably get back a perspective just as it was four perhaps not
pretty much there anyhow, so let me mark this using a thin line, switch pencils does not
really matter, now but anyhow. So, now, if I extend this line this is also pretty, because
now I am hitting the second vanishing point. So, this vanishing point was incorrect, now
this better all right, so how about the third vanishing point.

So, in the profile view I was looking at an object at infinity along this direction that is the
z direction. So, this is corresponding blue line, I got that image there I extended it
horizontally, but then the top view, I dint do that exercise, so this is the Z direction I
should be looking along this direction at infinity and get the image of the object on the
picture plane. So, this is where the image of the object is over there and perhaps I can
extend that downward.

So, it looks like this would be my third vanishing point, so again I probably did not get
this correctly possibly because I did not align my scale or my ruler properly along these
two edges. Let me verify if indeed this point is the third vanishing point and if that is the
case then I can verify that this perspective of mine even though it is not need and I admit
that I have made lot of mistakes, but that is okay, that is how people learn if I align my
ruler properly along these edges hopefully I will be getting close to this vanishing point.

Now, before that let me verify if this indeed is the vanishing point that I should be
looking at, so little error in alignment and you could expect many here is happening.
Now, this suggest that these vanishing point should be upwards, let me look at a little
longer edge, may be align myself parallel to that may be even longer ((Refer Time:
1:18:33)). So, if I go back to my station point, it looks like there is a minor deviation I
can effort to go down little further, perhaps over here somewhere and then I straighten
my drafter, I can possibly expect my vanishing point to be little more down, then it was
suggested before well things are messy, but you know this is a nice learning exercise if
not fine.

It looks like I can get this edge to align with this vanishing point, this of course, is not
correct and may be then there are something incorrect with this edge. So, let me see if I
have gotten these two points right first point H. So, I look at vertex h in the profile view
from the station point, this is where the image is getting formed and of course, this is the
correct horizontal projection, where H should lie above the vertical projection I am
looking at this vertex here.

So, you know this, this is quite close and a little sensitivity in the image of H over here
could make quite a bit of difference. So, if I expect my H to be slightly towards the right
and I expect my H to be here possibly perhaps I can get this right and looks like I do. So,
may be a little deviation in this edge along this direction from it is me to have this
vertical edge of mine converge to this vanishing point right there.

So, let me erase this vertical edge and perhaps join S and the new found vertex H, may
be a few more strokes, let me drawn this and let me also smoothen this edge out. So, here
we are the three vanishing points corresponding to the three orthogonal directions found
let me mark them. So, this is the right vanishing point V P R, this is the left vanishing
point V P L and this is what people tend to call as another point, because just be below V
P N.

So, although this perspective looks quite awkward looks like the construction seems,
because the three vanishing points although I have not use them when I actually started
drawing the perspective, tends to conquer or agree with the vanishing points that I found
assuming that I was looking at objects at infinity parallel to this direction, which is this
edge object parallel to this direction at infinity, which is this edge.

And then object along the C direction the height direction, which is this direction here
and the profile view this direction here. So, summery to any mistakes, but that is how
people learn, rather I believe that people learn better by mistakes than by not committing
them at all. Because if reason that three point perspectives could be awkward it is
prepared to draw two point perspectives, perhaps better choice is of the station points in
the top view and profile view what I allow me to draw this perspective a lot better.

So, last time I had mentioned that I was not very happy with this perspective drawing for
two reasons reason number 1 was that I probably had chosen my station point purely
with respect to the top view of this object. And reason number 2 was that I made many,
many mistakes perhaps I was not focusing well.

Anyhow, so I was not very happy, so after I drew this I stay back in the studio and I
redrew the perspective with the same top and profile view with a different station point.
So, my station point in the top view was this point over here, correspondingly I chose my
station point in the profile view over here, so that this distance from the picture plane of
the station point was the same as this distance. So, this was the picture plane in the
profile view and of course, this was the horizon line.

So, you could see how nicely the three point perspective of this object has shaped up, I
like this one particularly better, before drawing the perspective of this object, I also kind
of got an idea of the vanishing points using the same method. So, you know from the
station point look at infinity along this direction look at infinity along this direction, let
the two rays hit the picture point over here somewhere, make a vertical projection.

And do the same thing over here locate, an object that infinity along this direction which
is the Z direction the X and Y directions and get the corresponding horizontals on the
picture plane over here. Let the horizontals and the verticals intersect at these two points.
So, this was how the vanishing points were identified, nevertheless choosing this station
point properly in the top view, will keep you a very nice picture a very nice perspective
of an object that your trying to draw, so this was the point that I wanted to make.