 TA 101 think and analyze, but actually it is technical arts. So, this is lecture number 3 on orthographic views. So, first few corrections in lab 1. So, I realize that these dimensions are lot smaller for you to work. So, you might want to consider these dimensions. So, replace 20 mm by 100 mm over here 15 mm by 75 mm here over there 20 mm by 100 15 mm by 75 here 100. So, 10 by 100 and 8 by 80 just scale it up and over there 10 mm by 100 mm. So, these corrections they should help you draw these ellipses better. So, let me or let us revisit the construction of the ellipse using the 4 center method. So, here we have a rhombus or let us say here we have a palogram. So, this edge is at 30 degrees with the horizontal. So, as I said the first thing that you would need to do is draw the longest diagonal first and then from this vertex join or draw a line segment joining the midpoint of the opposite edge from here again the same thing draw a line segment join the midpoint of the opposite vertex. So, this is center C 1 center C 2 with this is radius draw an arc with this is radius draw another arc over here center C 3 draw this arc center C 4 draw this arc over here. Of course, this arc would be of radius this length and this arc would be of radius this length. Now, let us try to figure something out here. So, this length is let us say L. So, as I said this is a rhombus. So, this length is 2 L let us assume that this distance is T. Now, what is this angle theta here? Now, if you look at this construction carefully if you want this arc to be tangent to this line segment here and this line segment here. So, it so happens that this triangle here has to be a right angle triangle. So, the cosine of this angle will be L over 2 L or theta would be the arc cosine of half which is 60 degrees. So, if this is 60 degrees this angle over here would be 60 degrees and this and this these two angles are going to be 120 degrees. You know just the other way around just the transformation rotation transformation. So, now this edge of the rhombus is at 30 degrees to the horizontal this is 120 degrees same thing draw the longest diagonal first from here join the midpoint from here join or rather from here join the midpoint you will get the centers as c 1 c 2 c 3 c 4 you know the construction you can go ahead and you know construct this approximate ellipse not a problem. Now, if this angle is anything other than 60 degrees then what happens? If you follow the same construction procedure you know identify the longest diagonal from here join the midpoint of the opposite edge from here join the midpoint of the opposite edge identify the centers four centers and you know complete the construction of the ellipse. What will happen is a part of this arc is going to be a way or is going to be lying outside this paragraph this is something that you would not want and this would be an exercise that you will be doing extensively when you are drawing circles as ellipses and isometric drawings or projections. So, this angle has to be equal to 60 degrees otherwise this construction is not going to work. So, let us get into orthographic projections second week third lecture alright this is now my 11 year old then I think he was about maybe a few months old in joint has quite a bit of task ahead trying to you know look at us and trying to figure well find orthographic views what they are let us see. So, we have the first object here and let us try to look at this object from different directions. So, let me take this object on to the top right corner of my screen let us look at this object from this side how does it look this heart looks it is actually a rectangle. Now, let us look at this object from the top how does it look again pretty much like a rectangle and if I look at this object from this side it looks like a trapezium. Let us take another object and let me take it back to my top right corner again and again try to investigate how this object looks from the three sides. If I look at this object from this side looks like a sector there is a Shuklaji behind the object he is not a part of the object definitely. If I take a look at the object from the top how do you think this object is going to look like well you are right looks like pretty much like a rectangle. And if I take a look at the object from behind again looks pretty much like a rectangle. The third example more complex you know this object is basically a flat plate over here a rectangular block over there and a semicircular block over here all glued up together in that fashion all right. So, if I take a look at this object from this side how does it look to you yeah. So, it looks like a rectangle here and this would also show up as a rectangle pretty much like this bigger rectangle and a smaller rectangle. And there would be a rectangle corresponding to this block over here on the top yeah. So, ignore all the other entities behind the object yeah anything else possibly not. If I take a look at this object from the top how would it look to me yes is all right. So, corresponding to this main block I will see a rectangle and with regard to this block I will see a rectangle somewhere on the top left of this one. And with regard to this semicircular block over here I would actually see a semicircular pretty much like this yeah. So, you have this rectangular big block and a small rectangle here and a semicircular here. And if I take a look at this object from behind how would it look well. So, this part would show up as a rectangle this part would again be a rectangle and corresponding to the top block will see a rectangle over here. Well these are actually not perfect rectangles why because you know the eye is very very close to the object it is not very far, but if the eye is quite far from the object you would probably not see the top face as you see in this figure. So, the point I am trying to make is let me go back yeah the point I am trying to make is you know if you have any object at hand and if you try to look at this object from three mutually perpendicular directions orthographic you will essentially get different impressions of the object or above the object. And orthographic projections essentially pertain to those impressions that you have if you look at this object from three mutually orthogonal directions. This is the first direction second direction and third direction yeah. The first step to comprehension so given an object what you do let us take an example. So, this is a victory stand gold silver bronze just an example. So, it is a pretty nice very simple example so it is easier for me to locate the three perpendicular axes. Let me call this axis as x that one is y and third one is z. And if I want to investigate how this object looks from different directions again. So, the point is that I am trying to capture the impression that this object is going to be giving in three mutually orthogonal planes. You know in this case x y y z and x z yeah alright. So, the first thing that you know if I take any object you know I feel like you know rotating translating to whatever with this and try to look at this object from different angles yeah. So, happens that only three angles are adequate for me to completely describe this object something very similar here. So, probably I would be rotating this object about the z axis and see how the object looks like or the x axis see how the object looks like or the y axis and you know get the impression of the object. So, let us do this first let me rotate the object about the z axis and try to figure how the object looks like. So, if I rotate the object about the z axis which plane am I looking at I am looking at the x z plane. So, I am looking at the object from this direction. So, let us draw the axis. So, when you are going to be drawing the orthographic views I mean this just for your understanding this is just for your comprehension, but essentially when you are drawing the orthographic views you will not be drawing these axes it is just for you to understand alright. So, let us look at what we see on the x z plane do we see this edge what would this edge correspond to it would correspond to the bottom edge of the object. How about the vertical edge here this would correspond to this edge of the object how about this edge will correspond to this edge and then the vertical from here to here and then another horizontal will correspond to this edge vertical downward here a horizontal downward well rather a vertical downward upward from here and then a horizontal that would represent this edge. Do you see anything else possibly not how about if we rotate this object about the x axis and see what we see see what we see essentially how would the object look if we place our eye over here from the top. So, we are looking at now the x y plane here you go now what would this edge correspond to it is essentially be corresponding to this edge this edge and this edge together. So, this edge would essentially be appearing as a point somewhere on the edge here and this vertical edge also will be as a point somewhere on this edge. Now, what would this edge correspond to here right. So, it would be this edge and then this would correspond to the edge over here the vertical over here we are not worried about that because it will show up as a point about this edge. So, essentially we will be extending this edge further this vertical again will show up as a point here and this edge would essentially be shown like this and then about this edge will be here and essentially you will get an outer loop anything else yeah. So, you will be seeing this edge as well and this edge as well. So, this how the victory stands going to be looking from the top now how about we rotate this about the z axis and try to look at the object from this side you know standing over here what do we see you are essentially going to be looking at the y z plane there you go the y z plane what you see you would see first this edge then the two vertical edges then this edge essentially over here. So, this loop is represented over here and then about this part you will have another vertical edge this one over here and the horizontal edge there representing this loop. Now, would there be anything that you would be seeing from this side yeah possibly not. Now, what if I tell you that let this not be a solid box, but be a box made of say glass. So, instead of this being a solid box this is actually a transparent box now focus on this edge would you be seeing this edge looks like you would be and this edge would be at some height and from this edge. So, we already have captured this edge here now this height is different and since this edge is not directly visible to us we are going to be using a convention we are going to be representing that using a dashed line all the other edges which are visible to us they are being represented as solid lines all the features which are not directly visible to us, but they are there they are going to be visible or they are going to be depicted using dashed lines anything else possibly not because this edge is concealed behind this edge this edge here is concealed behind this edge you know and this edge is actually hidden behind this edge. So, we are fine now. So, let us imagine that we have an object over here and that is enclosed by let us say a glass box or a box or may be just three planes you know this vertical plane here the vertical plane here the horizontal plane here and all these three planes happen to be mutually orthogonal or perpendicular to each other I just follow the animation I just imagine that we have light bulbs on all these edges and they are emanating light in such a way that this light is essentially going to be going in three mutually perpendicular durations along this duration along this duration and along this duration. So, there are special kinds of light bulbs. So, if you look at the rays which are parallel to this edge you will essentially be having this loop getting captured on this vertical plane likewise if you have rays emanating from these special light bulbs along this direction then you will have one loop getting captured there another one there and the third one here and in case the light is parallel to this edge from you know this box essentially you will be having this big loop getting captured the smaller loop getting captured and if you look at this edge over there it is kind of not visible from this side, but still there is always a nice idea to represent what is also not visible but there. So, even this edge is going to get captured. So, the object from this side is going to look like this the object from the top is going to look like this the object from this side is going to look like this we do this exercise at home. So, pretty simple exercise for you all right. So, once we have captured these images from three different directions I will rip this edge off and I will rotate these planes. So, that they happen to lie on the same plane two dimensional plane. So, if I rotate this plane about the same line and if I rotate this plane you know. So, this vertical plane is like here the horizontal plane is like this I am rotating the horizontal plane like this and this one over here I am rotating it you know like this like this all right. So, if we flip these planes. So, that they lie on the same two dimensional plane let us see what we are going to get. So, this vertical plane will be over here the horizontal plane is going to be on top of the vertical plane and the right hand side plane the plane on the right hand side will be over here on the right hand side of this vertical plane all right. So, we will see this part over here these three loops over there and this part over here. So, this is the front view if you are viewing the object from the side the top view if you are viewing the object from the top and the right hand side view if you are viewing the object from this direction all right. So, this is the hinge line that separates the horizontal and vertical plane this one here and another hinge line that separates the vertical plane and the plane on the right which is this hinge line here. So, let us get rid of these planes and this is how we are going to be you know seeing the representation of the object in three different orthogonal directions the object the three different views of the object. So, these are the orthographic views of the object all right. Of course, this was the first exercise on orthographic views for you. Now, let us try to correlate different vertices and different edges of the representations in the three planes. So, you know of course, these vertices and the edges will get correlated. So, with these these and these all right and if you correlate the edges and vertices in these two views we will have this correlation here this correlation this correlation and if you look at this edge this edge will get correlated to this hidden or dashed line there of course, there would be a correlation between the top view and the right side view as well. Now, try to figure what angle this is guesses this would be precisely 45 degrees y because this distance is the same as this distance. So, that is the x y plane the top view the x z plane the front view and the y z plane the right side view I said before you do not need to do. In fact, you will not be requiring to depict these planes in your orthographic views this just for your understanding just for your comprehension. So, given the views. So, by the way I make a lot of mistakes. So, there is this projection line which is missing over here anyways. So, think and analyze there is a question for you. So, given the views can one uniquely determine a three dimensional object for you to answer and a related question do I need to have all the three views. So, the answer of this question is yes do I need to have all the three views to be able to uniquely represent a three dimensional object or in all cases or perhaps in some cases only two views would be adequate. Going back to the examples that we were discussing you know quite a while ago. So, this object if I look at this object from the front this is what the view is from the top this is what the view is and from the side this is how the object looks like and if we correlate using the projection lines you know this is how you would want to draw these projection lines. Second object the front view the top view the right side view and if you correlate different features of these objects in different views this is how your projection lines are going to show up in a drawing. Third object if this is the front view this is how the object is going to look like in the front view the top view and the right hand side view if you again correlate different features of the object in three different views this is how the projection lines are going to look like in every instance this angle of this line will be making a 45 degree angle with the horizontal line. So, if you recall I had talked about Gaspard Mange engineer in French military who was the inventor of descriptive geometry and he was a person who you know could formalize drawings by means of orthographic views. So, this is the thing which is of importance to us Mange formalize the technical drawings what we know as orthographic projections you know if you are given the three views of different objects it is possible for you to reverse engineer and you know try to estimate how not try to estimate or predict, but try to actually exactly know what the object is going to look like in three dimensions like in this case for example, if this is the front view the top view the right side view this is how the object looks like there is just a pen front view top view the right side view this is how the object looks like it is pretty much like a stool front view top view the right side view the object and the front view of a personal computer the top view the right side view this is how you know 3D objects would look like. So, it looks like if you are given these three views it looks like I say I mean I could be wrong and something that you need to answer for yourself. So, given three views given three orthographic views it should be possible for you to exactly extract the three dimensional information of an object. So, this was an exercise that one of my students Amitayesh Mishra did quite some time ago in probably 2005 2006 he did a fantastic job one thing I would always emphasize throughout this course sketch sketch sketch sketch sketch sketch sketch sketch and sketch and sketch keep sketching because that is how you practice the more you practice the better you become in drawing always a good idea to sketch before you start representing an object via its orthographic views and other views as well. So, let us take an example. So, this is a three dimensional object we have this is about 100 units millimeters 80 millimeters the height is about 60 millimeters over here. So, this is a you know feature which is cut from the block and we would like to represent this object by means of orthographic views. So, let us see how. So, the arrow means that this is the front view. So, the moment this is the front view in the third angle projection we are going to be talking about that later this would become the top view and this would become the right hand side view. So, with the front view given how would the object look like if we visualize the object along this direction again. So, mark the way I am representing these edges. So, this time just constructing I am not constructing the final drawing at this time. So, if I am using construction lines I am going to be using a 2 H pencil or 2 H lead ensuring that my lines are very dim. So, barely visible. So, this horizontal edge would correspond to this edge the vertical edge would correspond to this edge. If I look at this object along this direction this entire feature will be represented by this edge and of course, there will be a horizontal edge this guy here always a nice idea to start with the bounding boxes in the corresponding view. So, this actually is the bounding box for the front view let us also draw the bounding box in the top view. So, the length is 100 in the top view I am going to be representing this edge. So, this is about 80. So, this block is 100 by 80 and I will draw a vertical hinge line separating the front view from the right hand side view I will draw the projection lines. So, this height is 60 now this length would correspond to this length over here which is this length it is about 80. So, this the bounding box of the object if I am visualizing it from the right hand side. So, this of course, boxes 100 by 60 in dimensions the length and the height. So, once I have identified the bounding boxes let us try to sketch all the features of course, I complete the entire schematic including the projection lines. So, this edge is this one vertical edge is this one and then this is about 20 from there then I am going down I am going up from here I am going left forward from here. So, what would be this length it is about 80 and then I am going vertically upward yeah. Now, what is do I see I see these steps at heights 40, 50 and 60, but we come back to that later let us try to look at the object from the top I have drawn this edge. Now, it is always a nice idea to work with the projection lines because you are kind of sure which entities or which features of the object you are representing in whichever view. So, I project this point upwards and then I show this edge and then I have got to show this edge over here or you will come back that later shown this edge here this edge here this edge and then I am going down from here to here this edge all right and then of course, this edge is going to show like a vertical edge in the top view and of course, this entire thing. So, this edge would be this and this together. Now, this one here corresponds to this edge it is about 20 plus 25 20 plus 25 downward and I have got this edge right there which is 20 further downward. So, looks like I have been able to capture all features of the subject in the top view once I have done that I will start using my projection lines I am working with the right side view this edge this edge here and then I am projecting this feature or to the right again that feature and this feature all these three features and then I am going to be projecting these features downward. I am going to be ensuring that I maintain the heights. So, this height is about 60 this height is 50 here this height is 40 here correspondingly I will go to the front view and draw these lines finish the vertical edge which would correspond to this edge in the front view. Of course, I should have drawn these projection lines a little earlier and then I will finish of the right side view am I done yet possibly not because I am missing this edge and this edge there I go anything else that I am missing you know there are lot of chances that you are going to be making mistakes when you are drawing you know when you are working with these technical drawings. So, these projection lines are going to be helping you out in identifying those mistakes. So, if you are missing any feature in any one of these views after you have drawn these projection lines you will know for sure what you have missed. So, you got to be a little careful you have to be very careful and sketch sketch sketch sketch and sketch practice and keep practicing this is what the golden rule in technical drawing is done all right relax keep thinking and analyzing.