 So, this is what I would do if you can sell down and let me speak that will be one full thank you. So, this is what I would do I would briefly explain the cutting plane method and there was little bit of confusion in fact there was quite a bit of confusion with regard to how to determine the visibility using the cutting plane method. I would actually tell you not to worry about that, so find the intersection between the two planes using the cutting plane method and then use the projection method to figure out the visibility. So, I will talk about that, so let me get started cutting plane method, so stay with me. So, given two planes A B C and D F we figure the line of intersection between these two planes using the cutting plane method. So, the trick is very straight forward pretty much along the lines of what we had discussed when we studied the interaction between a line and a plane, just imagine that you have to treat one of the planes as planes and the other plane as a set of three lines. For example, you can treat plane A B C as plane A B C and D E F as a set of three different lines. Now, for example, if I treat D E F as a set of three different lines, let me pass an imaginary cutting plane through the edge D V and let me call it C P 1. Now, this edge D V is going to be intersecting with A B C at this point and this point, so between an imaginary cutting plane and the plane A B C what do you expect, do you expect a line of intersection or a point of intersection line. Project this point up, so this point will be lying on A B project this point up, it lies on A B this point it lies on B C project that point up this would be the line of intersection between the imaginary plane that passes through D E and the plane A B C and that would be the projection of that line. Now, this line is going to be intersecting the edge D E at this point, so this point would represent the point of intersection between the line D E and the plane A B C fine with me so far no yes good take another plane that plane passes through D F. Let me call this C P 2 this plane is going to be intersecting A B C at this point and this point, so this point lies on A B this point lies on B C project this point up on A B lies over here project the other point from here lies on B C this would be the line of intersection between the plane A B C and the imaginary plane C P 2. Now, the corresponding point of intersection will have to lie on D F, so to get that point of section you have to extend D F and get this point of intersection. So, it is for that point of intersection to not lie on a plane and a line as of now, so this is your first point of intersection this is your second point of intersection join these 2 guys and the line segment that would be the line of intersection between the 2 planes has to be common between both planes. So, this would be the line of intersection drop that down and you would get the corresponding projection in the front view straight forward with regard to computing the line of intersection between the 2 planes now to get the visibility go for projection. Now, I chose this view for absolutely no reason I could have chosen the top view I could have performed the same thing and I could have expected the same result I could as well well I could have treated A B C as a set of 3 lines instead of D E F I could have still expected the same result I could have as well chosen this as my cutting plane the result would have been the same. So, keep that in mind are you with me now yes now to figure out the visibility using projection method. So, a few lectures ago I said that I did not get in logic behind the projection method, but looks like there is some logic and the logic is as follows first things first you realize that all these edges they are going to be visible all these edges they will be visible even the line of intersection will be visible. So, keep that in mind. So, we need to figure out the visibility of this segment this segment this segment this segment this one this one here and this one this one this one this one this one and this one here. Now, look at this point for example, vertical what would this point represent what would this point represent is it a common point between 2 edges is it a common point between 2 edges no they just may be intersecting at that point may not be intersecting at that point. So, the edges are D E and B C. So, D E is like so for example, and B C is like so for example, now what you see is a top view and what you see is this point here look at my finger and the thumb of the right hand and finger and the thumb of the left hand. So, these 2 points they are at the same position in both edges in top view. Now, which of the sticks is visible to you or is it closer to you the one on my right hand the one my right hand or the one my left hand right hand it is visible you could see that, but there it is not clear. Now, what I would do is I would just flip this over. So, that you could see the front view of this once again I would just flip it up. So, that you could see the front view containing the projections these 2 lines which of the points is up this guy here. So, that is up here it is visible here it is up once again it is visible here in the top view in the front view it is above this point the logic is precisely the same. If you drop a vertical from here whichever edge is up in height in the front view will be visible in the top view logic is precisely the same. So, if you drop a vertical from here d e seems to be getting hit before b c. So, it is this portion of d e that would be visible and therefore solid agreed. How about this one if I drop a vertical from this intersection point. So, now that is intersection between e f and b c which of the edges will be encountered first by this vertical b c. So, that means that b c is going to be visible here. So, this portion is going to be visible here and therefore it is going to be solid with me. Now, if you look at this one back again. So, it is d e which is visible when this portion is visible this portion of a b c should be hidden one thing more that you would want to notice what is what has this intersection line of intersection done to this edge it is changed the status of that edge. So, this edge was visible from b up till the point of intersection and from here it is hidden. Likewise also you can expect something very similar over here. So, this is visible here and from this point onwards edge d e should be hidden. You can verify that for this vertical what do you expect what do you expect for this vertical point of intersection between d e and a b a b gets hit first. So, it is a b which is visible and of course, this will be hidden and likewise you can figure out visibility same thing from this view also. So, extend a vertical upwards from any of these points of intersections see which of the corresponding edge is hit before and that edge is going to be visible this same logic with me everybody absolutely confident. So, this is what I would do this is what I would do I would distribute the question papers I have them I have them question 1, question 2, 2 questions relax I have given time to solve these questions. So, I will give you a single paper and these 2 questions are on the 2 sides of that paper while you are solving that for reference I will keep this slide in front of you. So, that if you are stuck you can refer to this and solve. So, this is the front view of the object this is the auxiliary plane 1 auxiliary plane 2 and looks like I will be able to show the 2 shapes only in or only using auxiliary planes not otherwise. Now, the question is this given the partial auxiliary views of this object containing 2 shapes of the planes of faces. If we have to draw the orthographic projections like the full top view and the side view of this object is it possible for us to do that that is what the question is. So, this is the object and we would like to draw the full top view of this and full side view of this. Now, this part is straight forward I can always take vertical projections draw the square or rectangle whatever. So, this part is going to be visible this edge will be hidden and likewise I can take the vertical projections from these edges. So, likewise this edge is going to be hidden over there I can take the vertical projection from there this edge is going to be visible likewise this edge and over here vertical projection up horizontal horizontal the center line and now the question is how do we transfer the features over here on to this part of the drawing in top view. How do we do that? Step 1 break this arc into a number of segments and then look at these projections transfer these projections over here and from here up to the top view. So, these 2 points they get transferred over here let us first look at the bottom face from here transfer them up right there second thing transfer these 2 points over there likewise the center line up there and here comes the critical part. Now, of course these 2 views they are going to be separated by a hinge line how do you find the position of this hinge line. Now, to do that look at this feature and compute the distance or take the distance of this point from the hinge line over here this feature is going to be lying where over there take it up this feature is going to be lying over there measure that distance and then look at the hinge line. So, once you have the hinge line now it becomes a lot easier for you to transfer whatever distances you are going to be measuring over here up to here same thing the concept of auxiliary planes. So, this view happens to be the common view get the distances from the auxiliary plane and then transfer all of them on to the top view straight forward clear clear. So, I do not have to speak much get this distance now this point lies on this vertical projection this one measure that get that distance this one lies over here measure that get this distance from here to here this guy lies over here measure that straight forward. Now, take this distance and place it over there likewise take this distance place it over there. So, looks like you have gotten these points to lie on some sort of arc this is how the arc is going to look like. So, this is the bottom arc remember that. So, this is the arc corresponding to this part of the object you could do the same thing for the top part of the object real quick same thing for the top part of the object. So, the top part the top arc is going to be visible. So, it is going to be solid the bottom arc apparently is also going to be visible look at this. So, this part is going to be visible therefore, solid this part is also going to be visible therefore, solid and then this edge is going to be visible. How about this circle. So, there is a wide over here at the bottom surface there is a wide over here at the top surface treat them one by one same thing same distances concept. So, divide the circle also into equal parts and take distances of the points lying on the circle from the hinge line and transfer them. So, once you understand the basics it is all straight forward procedure transfer the distances and this corresponds to the circle on the top face or the bottom face top face. Likewise do the same for the bottom face I am just transferring distances they are going to be many lines I am just transferring distances. So, this is possibly this part of the circle and a part of which is going to be visible in the top view. So, this would be solid the other part the same thing transfer distances a part of this circle is going to be visible. So, this would be solid the rest will be hidden do precisely the same thing on the other side. Now, for that you are going to be using this auxiliary view precisely the same thing measure distances and transfer distances. When you do that you would get that part of the arc now this part of the arc is going to be visible this arc on the top face is going to be visible how about the bottom face the arc corresponding to the arc lying on this face not visible that be hidden how about the circles or circular voids same thing. So, the void on this face is going to be visible the void on this face a part of it is going to be visible a part of it is going to be hidden. So, this part is visible this part is hidden now you can do a smart thing observe the following the shape of this arc and the shape of this arc what you observe are they the same or different they are the same. So, if you get one arc all you need to do is transfer the corresponding points over here by equal distances and then get the other arc likewise from the other side. So, once you get this arc just shift this arc by some amount what is that amount going to be what is that amount going to be that amount is going to be this is it is it yes or no it gets. So, this arc gets shifted inward by about this amount now yeah likewise from there. So, this arc gets shifted by about this much amount right side view again the same thing yeah of course, finish the top view by adding center lines. So, side view against very similar concept. So, I will not say much just that I will show you the animation. So, if you had asked what we had been doing in the last 5 or 10 lectures we actually had been preparing a primer for such problems what if the planes are not parallel to the conventional orthographic planes x y y z and x z what happens then. So, we have to take the help of auxiliary views and that is the reason why we call them auxiliary planes helping planes. So, unless until you get the true features in the auxiliary views you will not be able to capture them in conventional orthographic projections any questions any questions are you with me on this everybody. So, I have made the speed of this animation quite slow. So, that I can follow what is going on the lab next time that you are going to be doing I think that is going to be after the mid same break is it or after mid same break. So, that is that is when you are going to be solving these problems John 25th with me. So, while you are watching this I have the benefit of having not many of you. So, we can talk about the exam it is going to be a 4 r exam the n sense 7 questions 4 r exam the first batch is going to be writing the exam between 9 and 1 4 hours the second batch is going to be writing the exam between 2 and 6. We will do something very similar to what we did last time we have to quarantine batch 1 for half an hour and then we will have to let batch 2 in and only then batch 1 gets released. Now, this time what I have done is I have just reverse the batches. So, batch 1 in the mid same is now batch 2 and batch 2 is batch 1 the questions are going to be tough the questions are going to be tough it might happen that 4 hours may not be adequate for you to solve these questions. I will think about whether I should be providing you some sample questions or sample paper or not I will think about that, but I would request you guys to practice and practice hard because these concepts are difficult to follow. So, unless you practice you will not be able to get these concepts and if you do not get these concepts you will not be able to solve the questions no. So, the questions will be from perspective till development perspective, one question on perspective, three questions on lines and planes, one question on this, one question on intersection and one question on development, seven questions. Oh, you have to wait for 5 more lectures. So, we have not yet discovered we have not yet discussed interpenetration of solids and development. So, 5 more lectures yeah none this was the bonus quiz 10 marks straight out 10 marks getting added to your score straight out what 200, 200 marks 7 questions 40, 35, 35, 20, 20 I can give you the paper if you want. What is the meaning of a bonus question to me it means you get extra credit for extra work it is more. So, if you have let us say 8 questions for example, essentially you can get 120 out of 100 as in the mid sem exam. So, I must warn you if you are not careful in the labs that you are going to be working now or if you are not careful in the lectures to come, if you are not attentive it might be a little difficult for you. In your position I would probably try to understand everything that I learnt from now I am here I am committed. So, I can give you n number of extra classes I am committed the question is are you I just want to make sure that you understand what you guys are already tired of TA 101 is it this something interesting a few days ago myself and two colleagues of mine professor Sudhir Mishra and professor Jwadeep Datta mathematics and civil engineering. So, we are having dinner and we are having conversation. So, TA 101 sprung up and we started discussing TA 101 and I was I am on camera, but I will be honest ok. So, you know I kind of confessed that I was having a hard time teaching TA 101 looks like I am not able to deliver the concepts properly and my students are having a hard time I mean I look at their faces I look at their eyes and they are like and I really wonder if I am doing a good job in teaching TA 101 and they said well I mean things become a little difficult starting from space geometry a lot of imagination a lot of visualisation and professor Jwadeep Datta he is a mathematician. So, he is like what is the use of TA 101 I mean why are you teaching TA 101 and professor Sudhir Mishra is like you know you have to teach the language of drawing I mean you have to teach the language of drawing I mean you have to be able to convey without using words what you mean when you have conceived a design. For example, what you want to convey when you have when you have conceived a design you should not be able to use a single word like for example, if a designer from there comes to a manufacturer from here he or she would come with a drawing and he or she would be able to interpret without an exchange of a single verbal word that is what he meant seemed ok, but then I began thinking and I was like you know the first thing that you conceive first idea that you conceive if you want to convey to yourself and if you want to develop it further what you do you take a paper you take a pen and you draw a line you draw a curve you draw a sketch that is the first thing you would do when you want to conceive an idea and develop it further this heads you with that this heads you with that no numbers involved no words involved only drawing it heads you imagine things a lot better if you are doing it right. So, it is important take rithi for example, or you know galaxy you know this is art production in galaxy you build structures I have seen that you build huge structures many of them are new ones many of them are new constructs what you do in there you imagine things you try to convey new ideas, but this is where this is your foundation this is where you develop this is your factory this is where you develop the ideas build it convince yourself that your idea is going to work and then implement your idea this is how important here one on one is one on one is basic course to thinking and analyzing think and analyze only to jump, but I still convey I still I still have this feeling that I am having a hard time conveying what I know or what I do not know to you. So, hopefully things will get better from here with only five lectures to spare all right. So, I want I would I would release you because you have a quiz at 6 o clock.