 So, can I have 2 volunteers on stage please? Can I have 2 volunteers on stage? You, you, you, you. Yeah, ok, stand here. And stand there, place the audience. And what you have is the 3 dimensional line in your hand and raise your both hands. And orient this line in any way you can. Yeah, it is good now, statue. So, we are discussing auxiliary method last time. So, we were given a three dimensional line of course, we are working with sketches on two dimensional paper and we essentially have the front projection or the projection of a three dimensional line on a vertical plane and the horizontal plane. So, what is the name? Siddharth, what is yours? Neeraj. Neeraj. So, Siddharth and Neeraj are volunteers who are holding two three dimensional lines in different ways. What you see is essentially the projection of Siddharth's line on the frontal plane and Neeraj's line on the frontal plane. And imagine that this projection looks like this and if you get a chance to develop wings and if you tend to fly and if you tend to hit the roof, you would essentially be seeing the top view of these projections. So, now the question is how do I find the true length of this three dimensional line given the two projections which are what you see on the screen. So, what I have over here on the right is a little three dimensional box where of course, this projection all right. So, this projection is on the horizontal plane and this projection is on the vertical plane and if I extend the two projections, I would be in a position to get the three dimensional line in a box all right. So, somebody asked me yesterday well I mean what is the use of for doing all that exercise that we have been doing because we have been able to capture this line anyways within box ok. So, the answer to that is well have you actually captured can you actually see that three dimensional line? No, although the box is something that you can see it is still visible on a two dimensional vertical plane right it is not tell anyhow what do we do? So, the idea is for so ok. So, maybe I will probably need one more can you come yeah the GC number five I do not know your names I am sorry as much as I would want to know your names ok. So, stand in front of Mirage. So, Shashwat Shivam Shashwat and Shivam are able to see the frontal projections of these three dimensional lines ok. Now, what they would do is to get the true picture of the line they would try to reorient themselves ok. Now, can you try to reorient themselves so that you can see the actual three dimensional line yeah yeah yeah you are you are ok you are ok can you can see that no can you yeah now can you see how about you no no no no you have to yeah yeah what have they done? What have they done? If you look at that red plane over there they have essentially oriented themselves to be parallel to that plane ok is not that is not that true Shivam yeah. Now, once they have oriented themselves to stay parallel to the plane on which or on a plane parallel to which that projection lies and therefore the actual three dimensional line lies once you have captured that plane all you need to do is draw a hinge line and flip that plane over as simple as that ok. Everybody with me here ok can I over yeah over statue over that game ok clear now stay with me here stay with me this is important. So, that red plane is actually a plane that is parallel to another plane which is containing this projection as well as this actual three dimensional line. So, once you have captured both of these all you need to do is flip that plane over like you do in case of orthographic projections ok. So, these distances are the same because that red plane is parallel ok. So, you have and then what would this distance be would it be the same as this distance great how about this one the same as this distance right ok all you need to do is now figure out. So, this is the true line that you have captured on the plane figure out the hinge lines and flip this red what we call the auxiliary plane over as far as visualization goes this should be now clear to you ok. You know wait wait wait wait wait wait wait I am running behind in schedule and I need to do this ok because otherwise you have problems with your next lab. So, I need to do this. So, extra class Friday 12 to 1 is 17 feel free if you want to come great I will be there if you do not want to come fine. So, what we will do now is we will flip this plane over with respect to this horizontal plane ok this is the hinge line that suppress the vertical plane from the horizontal plane that is the blue line stay with me. Now, if you notice this purple hinge line this one has to be parallel to the projection in the horizontal plane right yeah ok. And of course, the projections are going to be perpendicular to the hinge line. Now, pay attention to this distance we are trying to flip this plane over. So, what would this distance be over here. So, should I be measuring this here or here yeah ok and likewise the smaller green distance I measure it there and I have this green line capture sorry red line capture there. So, essentially what I have done is I have rotated this red plane about the hinge line maintaining these two distances as this and this ok. And I have the true length of the line on the auxiliary plane do you agree do you agree good the easier way to remember this is this why this how I remember you essentially have three views of the line the frontal view the top view and the auxiliary view ok. Which view is common which view is common the frontal the top of the auxiliary the auxiliary sorry the top view is common. So, this one is common between this view and this view ok. Now, just in case if you are confused where to take the distances from this would have just let go of the common view measure the distance in one of the given views and transfer that distance in the third view as simple as that ok. Now, let us see if you can exercise this in a slightly different manner. Now, I really do not need to have the auxiliary plane associated with the horizontal plane I can have it associated with the vertical plane as well this of course, in true length hinge line that separates the front from the horizontal or the top ok. This is something that we have seen it does not really matter where the distance of that hinge line is from the projection will essentially be getting the same will essentially be getting the same true length of that line this was the line that was parallel to the line from before. Now, hinge line now instead of drawing a hinge line which is parallel to the projection in the horizontal plane I am going to draw my hinge line over here same concept same concept then what have the projections come out perpendicular from which view horizontal or vertical vertical like these ok. Now, this view is going to be common this view is going to be common between this view and the auxiliary view ok, where are you going to be measuring the distances from the horizontal. So, you would measure this distance there and these distances have to be from the hinge line ok, these distances they have to be from the hinge line. So, you would be measuring that distance over there and transferring that distance where left projection or the right projection left projection right projection this one again this would be measured from this hinge line measure that distance in the horizontal plane again from the hinge line and transfer it over there and you have the true length. Now, if you go back to your method of rotation and if you go even further back I had introduced certain formula right. So, if one of the projections is horizontal or rather parallel to the hinge line then the other projections going to be giving the true length of the line right right. Do you see some something very similar over here do you see something very similar over here this projection is parallel to this hinge line and therefore, the other projection will be giving the true length of this three dimensional line and this is going to be true in case of auxiliary plane as well right with me with me alright. Now, in this one we had taken the auxiliary plane from the top view the vertical plane and the other example we had done the same thing from the horizontal sorry from the vertical plane from the front view they both give you the true length of the line. Are you convinced would the length be the same or would be different same just in case if you are not if I transfer this line over there ok and draw an arc this confirms it ok. So, whether you use the top view or the front view ok draw the auxiliary plane from there get the true length it will be the same. So, far with me so far with me ok choose any orientation stun somewhere ok alright the first thing Shubham did Shibham did was to orient himself in such a way that he captured a plane on which the actual three dimensional line was there to get the true length ok. Now, the question is if I want to get the point view of a line in other words if I want to orient myself to a plane where I can see the point corresponding to this line what would I do yeah how would you see the line as a point yeah statue stay there that is how precisely that is how ok. So, he is looking at or he is on a plane which is so he is on a plane which is which is perpendicular to the line ok. So, I have a plane where I capture this line in true length now I have to look at this line from a direction perpendicular to it ok for that what do I need to do if I want to draw a hinge line and flip that plane over where would my hinge line be where would my hinge line be at this kind true length at this kind true length if I want to get the point view of this where would my hinge line be perpendicular to this ok yeah ok and the same concept of transferring distances now this view becomes common between this view and the view that we are going to draw right and we are going to be transferring distances we are going to be transferring distances from where to where from the top view to the second auxiliary view this is the first auxiliary view this is the second auxiliary view ok and do now kind of see whether we are going to be getting a point there will be a single projection there will be a single projection here right there and we are going to be measuring distances from the top view and these distances they will be the same and I need to transfer that distance over there and essentially I will be seeing the point view of a line agreed agreed no why not this distance is the same as that distance three views two views are associated with a single view ok drop that view take the distances from the first view transfer them to the third three views one two and three this view is common between this and this drop this view ok take the distances from here and transfer it over here lost do you agree that if I draw a hinge line perpendicular to the true length view of the line ok here and if I take a projection here somewhere over here I will be seeing the point view of the line do you agree with that do you agree with that all right where would that point lie where would that point lie where would it lie I mean you are following the same steps right you are creating another auxiliary plane aren't you aren't you so the principles that we have learned from before of transferring distances you are going to be transferring distances from this view to this view right where is this point where is this point take this distance transferred over there same principles questions can you come here well you have to see it for yourself take this go over there so the red line which is the true length of a line that lies in the red plane this one absolutely ok so if you want to get the point view of this line absolutely absolutely so so your black hinge line will be perpendicular to this one rather yeah it would be lying on the plane which is perpendicular to this wanted wanted so if my plane that contains the true length is here ok how would you orient to get the point view of this you will have to go perpendicular over there let me see if I can explain this better so as far as visualization goes so how would you where are you yeah how would you describe this inch line with respect to let us say this inch line so what you have done is you have flipped the auxiliary plane plane from this inch line right so your auxiliary plane was kind of here somewhere you just kind of flipped it over right now your this plane is kind of down here and you are flipping this up like this so remember you are working everything on a two-dimensional plane so when you flip you transfer distances ok I can do the same thing from the other side so remember I had taken this hinge line over here I had associated this auxiliary plane with the frontal plane if I want to draw the point view of a line ok then I have to figure a hinge line which is perpendicular to the TL line right take a projection which is perpendicular to the hinge line and then transfer distances now from where am I going to be transferring distances from where am I going to be transferring distances from here so this distance is the same as this distance ok so if I transfer this distance over here ok so this guy is sitting over here somewhere ok and this guy is just behind this guy ok but the same distance from the hinge line this is a point view think about this so this guy so these two points are one behind the other these two points are one behind the other which one is closer to you the one which is closer to the hinge line yeah and this is right at the back so if you imagine that this is pretty much like the true length ok and if you kind of flip it like so you see this point ok and then you see this point exactly or precisely behind this point it is what the point views yeah with me a little lost completely lost ok was that I cannot hear you I cannot hear you why did we take this distance the same as this distance this example ok your true length is going to be lying on these projections why are we taking this distance the same as this distance why why yeah so if you go back to that three dimensional box you will kind of make that relation right so those distances are they are going to be the same you do the same exercise and you will get you will get your answer do the same exercise you will get your answer yeah which two planes intersect to get the black line you have the answer right there you have your answer right there shift this plane back let it pass through the blue projection line over there so this plane will be containing the black line so the blue line oh we will probably have to work out the queue for that ok perhaps I will do that tomorrow ok for now I will just take my word for it but it should be very difficult I mean so once once you have this true line over here imagine that this is there on the frontal plane ok now what now what you are going to be looking at a plane which is perpendicular to this line and then you are flipping that plane over on this plane you are going to be seeing the point view of the line you are flipping this plane same thing but I will I will try to explain it better tomorrow perhaps anyhow so if this is not clear maybe take my word for it I will try to do a better job tomorrow I was here somewhere I was here somewhere yeah all right so just take my word for it but you are essentially doing the same exercise now you are essentially doing the same exercise of transferring distances they will come with practice ok so an example ok this is a little difficult for you to understand so you have the projection you have the projection on the frontal plane you have the projection on the horizontal plane front view the top view ok and this is something that you would need to keep in mind that the three views ok just ignore the common view take distances from one and transfer them to the other so take distances from the views which is not common from the view which is not common ok so for example this is the hinge line that separates these two projections maybe it will be a nice idea for you to sketch this while I am working with it so you will probably get a better idea so what I will do is I will draw some arbitrary hinge line somewhere here ok stay with me here eyes on the screen please what I will do is I will draw an arbitrary hinge line ok ideally I should be drawing this hinge line parallel to the projection but I am trying to make a point so I will draw this hinge line arbitrary ok in a sense I am free to choose the auxiliary plane that I want I am frankly speak I can view that line or that projection from anywhere I want ok follow that rule take distances so this view is going to be common this view is going to be common the distances are available from here ok and of course if I am viewing these two vertices my projection lines they have to be perpendicular to this hinge line right I take the distances from below ok and transfer them over there ok I get one vertex I take the distance from that vertex down there and transferred over here ok I get two vertices I get a line ok let me go forward I will take another arbitrary hinge line again this is not parallel now this guy is common between the view that I am going to be making and this view so I am going to be taking the distances from this one here and transferring it over here ok and this time my projections are going to be parallel to sorry perpendicular to this hinge line like this like this I take this distance transferred over there this distance transferred over there I get some other projection ok all right just a just a so to speak physical exercise ok not even mental now if I draw a line or a hinge line which is parallel to this projection do the same exercise now this time this view is common so I have to take the distances from here transfer them over there ok I take this distance yeah this distance transferred over there that distance transferred over there I get this projection now here notice that the hinge line is parallel to one of the projections so therefore you would expect this to be the true length of the line ok ok what I did in one go over here had I taken this hinge line to be parallel to this projection I would have gotten the true length of the line immediately but I prefer to take a few steps I ensure that these hinge lines they are not parallel to any of these intermediate projections ok essentially essentially I was free to choose the auxiliary plane that I wanted I am just trying to make a point I will essentially be getting the true length of a line whose vertical and horizontal projections are given over here right now let me call it TL 1 had I gone this had I done this in one step had I made my hinge line parallel to one of these projections ok now this view is common between this and the view that I am going to make I would be transferring this distance over here and this distance over here I would expect this to be the true length of the same line because my hinge line is now parallel to this projection let me call it TL 2 one shot multiple shots I should be getting the same result isn't it so this is my TL 2 this is my TL 1 same orientation TL 1 TL 2 and if I let one of the vertices of these two lines coincide drawn arc I confirm that I will be getting the true length of the line ok alright with me so what was initially a mental exercise now becomes a physical exercise you can switch off your minds and you know draw this blindly yeah so the point was that I don't need to use just one auxiliary plane I can use as many auxiliary planes as I want but of course that is not going to be efficient anyhow next one instead of one line now let's say we have two lines whose projections are given in the vertical and horizontal planes ok now V the subscript V is for vertical the subscript H is for horizontal two lines whose projections are given on the vertical plane and the horizontal plane ok question do they intersect do the actual lines intersect they may or may not how do you know and how do you find find that whether they intersect or not how do you find whether they intersect or not two lines here if they intersecting if they intersecting if you happen to look at the point view of one of the lines that has to lie on the other line right if you look at the point view of one of the lines that has to lie on the other line if it doesn't they are not intersecting if the point view of one of the lines is not on the other line that means that they are not intersecting ok let's confirm hinge line follow these steps carefully I choose to figure out the true length of cd line cd and that's the reason why I am going to be making an auxiliary plane where this projection of cd is going to be parallel to this hinge line ok I am just focusing on cd draw my projectors perpendicular to this hinge line ok this view is common so I measure distances from here transferred over here ok now this is the projection where c would lie and this is the projection where d would lie which distance am I going to be taking this one great transferred there ok now I take this distance and transferred there ok this is cd is this in true length why because one of its projections this one is horizontal or is parallel to this hinge line so you would expect c 1 d 1 to be in true length ok now to get the point view of that you have to draw a hinge line which is perpendicular to this but before that I have to transfer these two points as well like just like I did cd c and d ok so my a b they are going to be lying on these projectors which are perpendicular again to this hinge line ok this view is common so I measure distances from here transferred over here so I take this distance ok measure this over here this is my a 1 for example I take that distance transferred over there that is my b 1 and that is the corresponding projection of a 1 b 1 now a 1 b 1 will not be in true length because of course this guy is not parallel to this yeah now once I have this scene once I have this scene which pretty much corresponds to one of the lines being in true length and the other one not being true length you still see the projection of that line ok so this guy is in true length this guy may not be in true length ok now what I would do is I would just turn myself and have you look at one of these lines in point view yeah this was what the previous scene was now this would be the new scene rather this would be the new scene so that this line would be in point view now for that you would draw a hinge line which is perpendicular to what c 1 d 1 ok now c 1 d 1 view is common so you are going to be measuring distances from where from the horizontal plane take this distance and both these distances they are going to be the same so take that distance and this would be the point view of line c d which one is going to be closer to you c or d d would be closer to you true length this is your plane where you would be seeing the point view yes alright do the same exercise for a b ok now take distances from where from the which plane from which plane horizontal plane take that distance transfer there take that distance transfer there this is your a 2 b 2 auxiliary plane 1 and therefore the subscript 1 auxiliary plane 2 and therefore subscript 2 now do you figure if the lines are intersecting or not you know that they do not intersect because the point view of c d does not lie on the corresponding projection of a b ok another thing slightly modified example the same exercise hinge line unless I am going to be going a little faster hinge line a hinge line which is parallel to c h d h ok projectors measure distances from yeah transfer there this distance transfer there this is c 1 d 1 in true length do the same thingy for a b take the projectors perpendicular to this hinge line ok measure distances from here transfer there measure this distance transfer there you get the corresponding projection of a b say a 1 b 1 now c 1 d 1 is in true length so if you look at a view perpendicular to it you will get the point view of c 1 d 1 hinge line perpendicular to that measure this distance transfer there you get the point view of c d ok do the same thing for a 1 b 1 measure this distance take that distance transfer over there you get a 2 b 2 now the point view of c d lies on a 2 b 2 that means that these two lines in space they intersect ok hold on hold on hold on clearly this is the point of intersection clearly this is the point of intersection if you project it back this is where your intersection is happening if you project that back onto the top view this is where the intersection is happening and if you project that down ok this is where the intersection is happening ok so just by looking at this view and this view and realizing that the point of intersection over here and over here if they lie on the projector or projection which is perpendicular to this hinge line only then the two lines will intersect otherwise they won't so in the first example that was not the case in the second example these two corresponding intersections they lie on the same vertical projection yeah a little test yes your question done ok