 Let us get started, can you hear me, M 4 have you heard that joke before, A 4 apple, B 4, B 4 apple, C 4, B 4, 2 2 apple, E 4, A 4 apple, yeah so M 4, M 10, M 4 max, what is M 4 again, what, what is M 4 again, M T, M T, one more word, relate these 4 words now, let go of the Maya, let go of the Maya, 4 max and rather look at, yeah so remember these 2 words think and analyze, most of you are 18 plus, so you are adults, you have the right to vote, let go of the idea that you should be running for max, learning is what is more important later on, important thing is you have to be thinking and analyzing, so mid semester results, this is where clapping starts, we have had quite a few century makers, quite a few century makers, those who have scored 100 and more, so what I will do is I will project their names and roll numbers and they need to stand up and raise their, so to speak bat, so for them the bat would be a mechanical pencil or a normal pencil or if they do not have it just a pen, and then you guys can clap, the first one, yeah raise it high, second where is the pen, guess his or her max, 1 1 3, guess his roll number or her roll number, and his name is of course, you know I feel very happy, I feel very happy and privileged to be teaching this batch, it is one of the smartest batches that I have seen in a long time, so clap for yourself, having said that these are the numbers that you guys are in precedent, scary, what I can say about this row is something very simple, just 25 percent in your hand, rest is again in your control, 25 percent for your labs, I think 5 percent for your homeworks, 10 percent for your homeworks, 35 percent there, and then of course, 40 percent for your instance, so plenty of still plenty of runs on the pitch, so you guys can score, so do not worry about this, maximum of courses, full marks in all questions, wait, wait, wait, I make a lot of mistakes, do not worry about it, so that 113 should I think be 120, that should be 120, these are the averages, so about 199 of you plus 1, 200 are above average, 220 are below average, which is again not a reason to worry, you still have about a lot of things in your control, you can always score plenty of runs, plenty of marks, and again keep my and Moksha in mind, so let us continue with perspective views, Shikant Singh, is he still there, yeah Prajapati, oh by the way a few comments, so they got to the Mitsana exams, I had requested you guys to not bring your cell phones and bags, it was wonderful to know that only 11 of the 420 that I have, they brought their cell phones, the rest of you did listen to me, which is a wonderful thing, thank you. Of course, I gave the cell phones back to them, I thought they were present to me, but they wanted it back, so I gave it to them, this belongs to someone in here, we will talk later, we will talk later, so perspective views, so last time I guess I was a little bit technical, I probably did not explain very well how to draw perspective views, can close the door please, and can you close that door, thank you, so I thought maybe I will explain perspective views in a slightly different perspective, so I have this hollow box in front of me, looks like this, so each of you will have a slightly different view about this, because your station points, your respective station points are different, but what is something that I want you guys to observe are the inner vertices, can you see those inner vertices, can you see these guys from there, not quite, maybe if I bring this closer to you inner vertices, try harder, these guys, these guys from this window, you can possibly see this, and one another observation that you would make is that these guys, if they these lines, these vertical lines, if they run to infinity, they would converge to a point, that is some observation that you can make easily, so with that said, let the green plane be the picture plane, and let this plane be on the front face of the object, so this is where this loop is, this hollow box is, and the picture plane is right here, touching the space of the object, and of course, this is your view direction, you are viewing at this hollow box straight through, so your perspective is essentially going to be looking like this, so what we will do is work this example backwards, given the perspective, get all the essentials that are required to make this perspective, so it is a slightly backward example, I will be a little slow for you guys to stay with me, this is how the top view of this object is going to look like, please straight forward, this is how the top view is going to look like, and of course, as I said the picture plane is on the front face of the object, so the green thing is going to be the picture plane P P, now profile view, and this is ground line G L, which is this face of the object, it is this face, and since this face is exactly precisely on the picture plane is going to be in true shape, two dimensions of all the four edges and true shape, because this face is right there, how about this face, this face is the back face, what you have to say about this face, is it going to be in true shape, careful is it going to be in true shape, good is it going to be in true size, good the back face is going to be in true shape, but it is going to be scaled, why, because all the edges of the back face are parallel to the picture plane, but not on the picture plane, that is the reason why is going to be in true shape, yet they are not going to be in true size, this is the back face of the object, how about these edges here, the four ones, what you have to say about this, what you have to say about this, are they converging to a point, and they correspond to those depth edges of the object, those green ones or those black ones here, what do you observe about these edges, are they on the picture plane, are they running away from the picture plane, if they are running away from the picture plane, in perspective they are going to be seeing, they are going to be showing up as a lines, a set of lines which are converging to a point, these black lines correspond to these depth edges of the object, and one observation that you guys make is, the depth lines they have to recede to a vanishing point. So, four observations, let me repeat the front face of course, is in true shape, so anything of the object which is on the picture plane is going to be in true shape, and is going to be in true size, anything which is on the picture plane, by the way this picture, what would this picture correspond to, any area, this scheme is something very similar to orthographic views, you have a front view, you have a top view, you have profile view, but what would this guy correspond to, this guy is going to be corresponding to the image of the object on the picture plane, in the front view of course, so that is the picture plane, this is the object stationed relative to the picture plane. So, you will see some image of the object, and if you kind of rotate this thing, this is what you are going to be see, so keep that keep that mind. So, of course, these guys are converging, and they are converging to a single point, it is called vanishing point, and then based on these observations, we kind of frame a set of rules, so thanks to my conversation with Prasakishore, so he had dropped by my office, I guess two or three days ago Prasakishore was it, two or three days ago, and then we had this little discussion from where I kind of summarized these rules for you. Lines parallel to the picture plane always remain parallel in perspective, lines parallel to the picture plane, so these are the lines which are parallel to the picture plane, what else lines which are into the screen, they are also parallel to the picture plane, so they will always remain parallel in perspective. Rule number one, lines on the picture plane will always remain in true scale, rule number two, rule number three any line not parallel to the picture plane has to recede to a vanishing point, so these are three rules that you need to keep in mind, as I said this guy here is the image of the object on the picture plane in front view, that is my vanishing point, vanishing point has to lie where horizon line, this is my horizon line H L, so remember I am working this example backwards, starting with the perspective I am trying to figure different features that are required for me to draw that perspective, I have the horizon line and then what, look at this face, this face is going to be in true shape and you can get the true shape directly by projection from the top view as well as the profile view, look at this face it is going to be scale of course, how do you get that scaling, how do you get the scaling, you need one more parameter, what is that parameter the station point, how do you get the station point like so, if you look carefully this face is the image of this edge in top view carefully, if you look at the top view this is what you are going to be seen for that face, image of the back face of the object on the picture plane project these guys upward towards top view, so this point is the image this point here, this point is the image of this point extend the two lines the intersection of these two lines will be what the station point, do you have everything now, do you have everything with regard to this perspective view, yes or no, no serious faces, serious eyes all the energy gone, what do you have to say about this guy this line here, what do you have to say about this line, if you stand at the station point and look along this direction, which is parallel to the dead direction at infinity focus on object at infinity the image of that object will be what, image of that object will be what a point this point is going to be there project that point back to where the horizon line that is why your vanishing point is deep stuff, deep stuff yes no one more time real quick, real quick keep these three rules in mind lines which are parallel to the projection plane of the picture plane, they remain parallel in perspective lines on picture plane they will remain in true scale any line which is not parallel to the picture plane has to vanish to a point. Now, look at the top view, how many lines do you think are not parallel to picture plane, 4 they will all have to vanish they will all have to vanish to a single point or to two points, single point why not 2, why not 3, why not 4, why not 2, why not 3, why not 4, we will come to that question later. The image of the object is on the picture plane front view that is a vanishing point horizon line look at this face, this face is going to be in true shape, you can get this face directly by projecting pictures from the top view and the profile view look at the back face, the back face is going to be the image of this edge in top view, how do you get this edge, you have to have a station point for that to get the station point project these guys back, remember we are solving this example backwards project this guy back. So, this point here is the image of this vertex, this point here is the image of this vertex, this point is the image of this vertex join these two guys, the intersection of these two guys would be the station point. And if you look along the depth direction, there is only one depth direction here, if you look along the depth direction towards infinity look at the object, the image of that object on the picture plane will be a point. And if you project that point back to the horizon line, you will be getting the vanishing point, so all these guys are related to each other. Now, what if I move the station point, instead of having the station point here in the middle, what if I move the station point to the right, back to the loop this is where your loop is, what you saw was a bunch of you guys looking at the perspective of this. Now, the new perspective corresponds to a bunch of you guys looking at this, station point picture plane the loop top view right there. Let us look at that, we have a station point first let us get the vanishing point look in the depth direction, which is a single depth direction look at an object at infinity, the image of that object will be a point on the picture plane project that point downwards to the horizon line, this is your vanishing point. Once you have this vanishing point of course, the front face of the object is on the picture plane get the true shape from the profile as well as top view. And then and then from here to here the edge is going to be vanishing where, from here to here the edge is going to be vanishing like so. And how about the bottom edges the bottom of this is going to be vanishing like so, and this one is going to be vanishing like so. So, you have to figure out these edges in the front view and remember this rule, any line which is not parallel to the picture plane has to be see to a vanishing point. One this edge is what the top edge this guy here yeah how about this edge this guy how about this one and finally, this one right let us get the back face for that we need the top view. Look at the back face from the station point. So, the back face is essentially an edge in top view what is the corresponding image of the back face it is going to be this line project this guy downwards. And the intersection of this line and this line will give you one vertex this line and this line will give you the second one this line and this one the third one. And I need to project this thing back over here so, this will be my fourth one. So, the first edge the second one first edge the second one and would this be a partial edge or a total edge would this be a partial edge or a total edge. And then I get the depth edges done done now just imagine if you just let go of these projection lines how the perspective is going to look yeah with me. Any questions so far Vardhwaj, Yemi any questions so far nine yeah come over here turn around what do you want to know like what is this h l g l and k b when I am looking at that how to walk stand here turn around turn around face the class. I need a person taller than him take your sleepers off you just face the class alright. So, he is the station point are you shakery of course, he has a top view and front view stay close to him tall enough a little forward a little forward a little forward yeah alright. So, let us say that he is looking at that light over there. So, rather forget about the light you are looking at that pillar column over there this guy is looking at this guy looking at the pillar from the top. So, he has what is your name Aditya has a view of this guy is head and that pillar and again that pillar is going to be in top view for Aditya. So, just imagine Aditya is in the sky flying he does not have wings, but still. So, he would have the top view of this guy is head Ayush's head and that column which is what is this. So, Aditya is going to be looking at Ayush standing here and the column there fine. Now, you are looking at that right, but you see one of those edges going into the wall yeah which is this edge for you will you see the switch fine forget about the wires just a column focus alright. So, look at the dead direction of the column which is this right. Now, look at an object just imagine the wall is not there look at an object which is far away along that direction you will see a point you will see a point where at what level will you see that point at this level yeah. So, Ayush is going to be seeing an object which is at infinity along that direction along the line of his eyesight Aditya is observing everything and he is nodding his head. So, before that the picture plane would be just kind of coinciding with the column just going to be it just going to be attached to the column the picture plane the front face of the column is the picture plane. So, this point which is what the image of the object which is far away along this direction on the picture plane Aditya will be able to see that the top you guy he will be able to see that and if I project this thing back onto your horizon line which is your eyesight this is where the vanishing point is going to be your ground line yeah down below down below. So, that is that is what his ground line is and what else do you want to know you got it did you get it no in the top view in the top view you have no height. So, guys this entire thing is in the top view this entire thing is in the top view. So, it is pretty much like orthographic projections happening just that you are recording the image of this object on this picture plane and you are projecting the image of you are projecting this image over here that that would be your perspective how is your no this is the story in the front view ground line horizon line in top yes, but in the front view no no not in the front view in the front view you are the boss in the top view who is the boss. So, remember that this is a story of two views interacting with each other station point upwards is the top view station point below vanishing point horizon line ground line they all form apart of the front view got it two point perspective same story same story look at the same example I am going to be making a slight change in that example instead of having this face of the object on the picture plane instead of having this face of the object on the picture plane I rotate the object in the top view. So, that I have only a single edge on the picture plane now stay with me here it is going to be important stay with me it is not the front face, but the front edge of the object that is on the picture plane and remember this line below any line which is not parallel to the picture plane has to receive to a vanishing point how many lines you see are not parallel to the picture plane careful careful how many lines are not parallel to the picture plane eight are not parallel to the picture plane two four six eight all the edges which are going into the screen corresponding to these four vertices they will remain or they will stay parallel to the picture plane those which are parallel to the picture plane will remain parallel in perspective those which are not parallel to the picture plane has to receive or they have to receive to a vanishing point. Once again any line which is not parallel to the picture plane has to receive to a vanishing point stay with me here now look at the object look at the pair of lines how many vanishing points you think you will have two. If Ayush Shekhar is standing here and if Aditya is observing as a bird then if Ayush is going to be looking at an object along this direction at infinity well for that let us let us go over to the rules lines parallel to the picture plane will remain parallel in perspective now back to that Ayush Shekhar is standing at the station point and if he is looking at an object which is at infinity along this direction the image of that object will be formed on the picture plane and the image is going to be what the image is going to be a point Ayush is about one inch or two inch taller than me so his eye level is here if he projects that image from the top view on to this horizon line he get the first vanishing point or the right vanishing point R B P. If he looks along the other direction at something which is at infinity the image of that object will again be a point on the picture plane project that thing down you will get the second vanishing point which is the left vanishing point. So, the two views are interacting with each other the top view and the front view now focus on this vertex and focus on the corresponding edge what you have to say about that it is going to be in true length you will get the true length from the profile view this is what the edge is going to look like all the other eight edges which are not on the picture plane they will vanish towards the respective vanishing points. So, these edges where will they vanish right or left right correct and these edges they will vanish to the left. So, let us focus on this edge which is this one and the edge below this they both will vanish at R B P this thick edge and the other one will vanish at the left vanishing point. So, what you have you have this edge in perspective this edge in perspective this edge in perspective here and this edge in perspective here what is left this vertex is going to be where on this edge yeah and this vertex is going to be on this edge as well as on this edge two vertices one below the other. Now, if Aditya observes Ayush in top view looking at that vertex this would be the line of sight the image of that vertex on the picture plane will correspond to this point. So, this is how the image of that edge will be in picture plane project this point down on both the edges you will get the first edge you will get the second edge correct and of course, you will have a vertical edge joining these two vertices again if Ayush looks at this vertex from the station point in top view this is how he would be seeing the image of that edge on the picture plane. If you project that image down you will have this edge and you have this edge how about this guy will it be visible or will it not be visible it will not be visible all right, but if you do the same if you do the same exercise if you do the same exercise this would be the corresponding image right there right there this would be the corresponding image project that thing down if you do that exercise of course, these lines are going to be behind this, but you would see that the edge which is into the screen at that vertex will essentially be this vertical edge although these lines are not very important for this perspective. So, I will just let go of now the question is you see those two rules below satisfied lines which are not parallel to the picture plane they have to vanish lines which are parallel to the picture plane they remain parallel is that true true again to emphasize we are combining two scenarios again to emphasize we are combining two scenarios one the top view the other one in the front view this is a slightly different example the station point at different position you get the site information essentially these rays intersecting with the picture plane. So, these rays intersecting with the picture plane in the top view and then you get the height information from the profile view you have the ground line you have the horizon line you have the station point. So, you get the height information from here. So, if the technique is clear to you I will not say anything from now on just observe this is what left vanishing point right vanishing point true height the edges which are not parallel to the picture plane they vanish you take the projections from different vertices or different points in the top view and get the perspective real nicely. So, remember it all depends on where your station. So, for you the perspectives are going to be different for you the perspective is going to be different for you the perspectives are going to be different. So, it all depends on how you are stationed with respect to the object as well as the picture plane something important. If one of your edges or if the object is not on the picture plane then what if the object is not on the picture plane or if any part of the object is not on the picture plane then what what you do in this case. How do you get the true height let us say how do you get the true height of this edge which is passing through this vertex and into the screen can I know no idea one option of courses to extend one of the edges extend this guy and imagine that imagine that this edge over here has moved to this edge has moved has moved along this edge here. Now, if this edge has moved along this edge which is now on the picture plane you can get the true length of that edge right. So, this would be in true length now you would know that this guy is going to be vanishing now along where R V P yeah you go to your station point of course you are the station point you look at this edge now here you look at this guy here the image of this point on the picture plane is this projected downwards. So, this edge which is here will be in true length, but this edge here will show up like this one more time stay with me. So, if any feature of the object is not on the picture plane use extension get a feature of the object on the picture plane. So, just imagine that this edge extends this edge would vanish towards R V P the right vanishing point this edge will vanish towards the left vanishing point. And if you draw the line of sight from the station point and look at this vertex here the image of this vertex on the picture plane will be this point project that point in the front view. And this would be the perspective image of this edge that is something that you need to keep in mind rest should not be very difficult should be straight forward just follow those 3 rules. And you should be able to draw a nice perspective now just imagine the cube on the left of the station point the cube on the right of the station point differentiate the perspective images of these 2 cubes. So, they will be different just an example I think this is going to be an animation yeah this is going to be an animation those who want to stay back stay back those who want to just watch well you wanted me to quit. Yeah you have the slides also yeah fine. So, just one point you know reminds me of one very nice story I was one last point I want you guys to appreciate the difference between this figure and this figure ok.