 So, if you understand perspective raise your hands, if you think you understand perspective raise your hands. So, maybe I will try to devote some time to revise whatever we have covered in the last two or three lectures. And I will also talk about a new method that I got introduced to by professor N. N Kishore yesterday evening and I will talk about that. So, you know quite a few of you guys came to me yesterday and said sir, I mean maybe it will do us a lot good if we can have an extra session and I was like fine. So, after the class yesterday I went to the lecture hall office spoke with Mr. Verma about the availability of any of the halls. He said L 16, 11 o clock I said great fine. So, then I start thinking man I mean I am not prepared for today what am I going to be doing. So, maybe I will just revise whatever we have covered and then I met professor Kishore in front of director's office. And then he explained a method which seemed very logical to me and then I am going to talk about that today. So, this scene let me animate the scene. So, stay with me here let us say that face of the cube in top view is this table. Let us say the face in top view over there is this table. This is the position of the viewer that is me. So, if you are looking from the top you would be looking at somebody's head. And imagine that I as a viewer I am standing here and you are looking at me as well as this table from the top. And let us say that this table is at an angle I am here this table is there you guys are looking at me as well as the table from the top. So, you see my head which is that point the position of the viewer that is me viewing the table in the top view. Now, the picture plane how about the picture plane? The picture plane is going to be a vertical plane that would be in between the object as well as myself fine all right good. So, this is me the viewer object and the picture plane is in between me and the object the picture plane is vertical in the top view that would appear as a line which is here fine all right. Now, my eye would be looking at different aspects or different features of the object the vertex on the left top right bottom right top and the vertices below. And those would be represented by the rays going from this point here up till all these four vertices. So, much so for the top view. So, you get this site information you get this site information from the top view now forget about the top view for now let us go to the front view. So, of course you are looking at the profile view of the site view of the object this is not the true site view this is the site view that is enough to give you the height information of the object fine this is where the ground line is. So, this is where the object is stationed all right horizon line. So, imagine that if I am standing on the ground this height corresponds to the distance between my feet and my eye level this is where my eye is going to be and so happens that in perspective views we do not need this information. So, we let go this information all we need from the front view is a ground line and the horizon line this is where my eye is and we can get the true height information from the profile view of the object. Now, does not really matter where the ground line is if you push the ground line below the object gets pushed below by the same amount and the horizon line gets pushed below by the same amount does not really matter where you position this what is important is how you are positioning your horizon line. So, this again the line that differentiates between the sky and the ground your eye level. So, what matters is how you are positioning your horizon line with respect to the ground line that is what is important. Now, the important thing for you to do is to combine the top view and the front view like. So, the picture plane the top view of the object and the viewer position a point we call it the station point these are parts of the top view with me and the ground line and the horizon line they are the part of the front view you are going to be getting the slight information by projecting the rays from this point to different vertices of the object and you are getting the height information by projecting horizontal lines lines which are parallel to the horizon line from this object. Now, I have already covered this example. So, I will quickly go through this. So, if you are looking at a point far away at infinity along a line parallel to this you will be getting this point as the vanishing point now imagine just in case in the isometric drawings that we have drawn you have the projection lines are too light is it let us worry about that let us worry about that never let us see how it goes. So, if you are looking at may I so if you are looking at an object along this direction far away you will get the image over here on the picture point projected down you get the vanishing point. So, just imagine that you are drawing something very similar to an isometric view. So, you can imagine that this thing is the direction along the x axis this thing is direction along the y axis and the height is coming out of the screen. So, with that this would be the vanishing point for all the edges that are parallel to the y axis. And likewise this would be the vanishing point for all the lines which are parallel to the x axis cannot see those construction lines now all right let us see how it goes. So, you know that this edge is on the picture plane it will be in true length projected down get the true length of this edge right. The corresponding x lines they vanish let me be here the corresponding x lines they vanish at VP x the corresponding y lines they vanish at VP y we cannot see the construction lines can we give me a moment you have seen this example before. So, you know where the lines are going to be do not worry about that it is going to be hard time to get this thing fixed anyhow. So, you see that this vertical edge corresponding to this it would be lying at it would be lying in between these two rays vanishing towards VP y this edge would lie in between the two rays vanishing towards VP x and then draw two more vanishing lines complete the block this is something that we have seen before not a problem something that you understand hopefully right. So, keep this in mind this is where I am going to be introducing you to what I say plus a Kishore's method I am going to making a few changes and I want you guys to be attentive over here I am going to making a few changes change number one I will not draw the perspective where pre specified vanishing points or pre found vanishing points I will not be using vanishing points at all instead what I will do is I will use the true profile view. So, the top view remains the same from there I use projections like we do in orthographic projections I name these vertices as A E. So, A is on the top E is at the bottom those as B F B on the top F at the bottom C G not the center of gravity, C G C on top G on bottom and D H D on top and F on bottom once again number one I will not use vanishing points number two I will use the true profile view of the object and I will see if I can make a perspective a nice perspective of course that is the picture plane there. Now, if you are looking at the picture plane and the object in the front view your picture plane will passing through the edge A E all right. If you are looking at the picture plane in the profile view how would your picture plane be look looking like it will be a line and be a line that passes through so it will be a vertical line that passes through A E that picture plane is not visible here, but let us try it is visible now. Now, the second thing that you want to keep in mind look at this point here what is this point station point in English it is the position of the viewer with respect to the picture plane in the top view. So, you would know this distance from here towards the picture plane you will know this distance how would this distance show in the profile view in the profile view if you use the same distance from here to here rotate it come over here and plot the position of the eye on the horizon would be this point once again this the position of the viewer in the top view. So, this is where the viewer is position with respect to the picture plane this is what the distance is from here to here the same scenario if you want to capture in the profile view how would you want to do that I am here from the top you see my head you see my station point the head position with respect to the picture plane what you guys see now is the profile view this is my line of horizon this is what I am standing of course and that is where the picture plane is what is this distance from here to the picture plane is that distance the same as this distance yeah yeah all right. So, if you know this point if you know the position of picture plane the top view you know the distance use the same distance to locate the station point or the position of the eye of the viewer in the profile view. So, this is where the eye of the viewer will be in the profile view this distance is the same as this distance from here to here and of course the eye is going to be lying on where the horizon line right now comes interesting part and a very logical very reasonable part and follow me carefully position of the eye of the viewer in the profile view all right. Let me use the short forms SPT station point in top view SPP station point in the profile now what I am doing is I am looking at vertex a and vertex e from here this is very dim I am sorry about that, but just imagine that I am looking from here at vertex a and vertex e man it is going to be difficult for me to explain let me see if I see those lines this helps. So, picture plane this is the picture plane here I am looking at vertex a and vertex e from the station point in the profile view it. So, happens that a e lies in the picture plane. So, I use horizontal projections directly and then I look at the vertex a e from the station point in top view. So, it lies in the picture plane over here I take those projections and what I have over here is a vertical edge a e in perspective straight forward here comes the interesting part. If I look at BF from the station point in the profile view now this ray is going to be cutting the picture plane at this point. So, this means that the image of point B will be here on the picture plane in the profile view likewise the image of point F will be here on the picture plane in the profile view B prime F prime I project these guys horizontally and then I use the site information from the top view what do I do I tell you what. So, follow me and I will make certain revision the slides and then post it on the web for you guys. So, just imagine that I am looking at B from here if I look at B from here it will be crossing the picture plane here somewhere I take the horizontal projection down just in case that you have been doing in case of your conventional 2 point projections and then I look at F same thing. So, this ray would be cutting the picture plane here somewhere I project it down and this is what my BF is going to be it is going to be vertical again. So, this is the new thing this is the new thing this is the same thing that we have covered in the previous lectures. So, D prime H prime they will be lying at the same 2 points as B prime and H prime on these 2 rays take the horizontal projections same thing from the station point here look at D H over there that would be cutting the picture plane somewhere over here project it downwards and then you will be seeing D H. The same thing with CG you are looking at C from the station point SVP this would be the image of C in the picture plane on the picture plane this would be the image of G on the picture plane in the profile view project them horizontally. Now, look at CG from this position use the ray that ray is going to be intersecting the picture plane somewhere project that intersection downwards let that ray cut these 2 points or these 2 lines and essentially you will be getting this edge CG. You have all the 8 vertices that you need in your perspective figure that is it you know what the interesting part is you know what the interesting part is you do not. If I extend the edges along the x and y directions oh I can see those projection lines now if I extend these I will be getting the same vanishing points that I have been using. So, this is the perspective using the new method this is the perspective using the old method new method old method exactly at the same locations. Now, you have a lot of questions regard to how to choose the vanishing points over here etc. This actually sounded a lot more reasonable and logical to me. So, I would recommend this method to be used for even single point perspective and 3 point perspective that hopefully I am going to be covering today with me now are you with me good clear I am really sorry about the projection lines I thought they would be visible, but anyhow difference in the 2 methods in the new method that I had introduced to you today I did not use the vanishing points rather I chose to use the true profile view of the object in the previous method that we had covered we had used the vanishing points information, but we had not used the true profile view of the object. So, that is the difference. So, a hexagonal block prismatic block using the new method again I have a feeling that projection lines will not be visible let us write. So, the view is a hexagon a g b h c i d j e k and f l of edges going into the screen a b c d e f are vertices on the top face g h i j k l are vertices on the bottom face a g f l b h e k c i d j your station point in the top view s b t remains the same with respect to the picture plane here it is. So, frustrating for me I mean I can imagine. So, imagine that you have a picture plane over here let us see it is better all right. So, station point s b p you are looking at edge a g. So, it is going to be. So, these 2 rays are going to be intersecting with the picture point or with the picture plane here at these 2 points take the horizontal projections you would actually know that face a g f l will not be in true shape because the face is on the picture plane top view. So, get that face directly no problem a g l f all right now. So, yesterday I made a mess by showing too many construction lines. So, I try to avoid showing additional construction lines. So, I start the new construction lines. So, I am looking at edges b h and e k b h and e k where will these 2 rays intersect I get the images of e and b here and h and k here take the horizontal lines. Now, I look at the edge b h from the station point in top view that would intersect the picture plane over here I make the projection downward essentially. So, vertical line I believe just about close to vertical line. So, this is my edge b h all right I look at e k I get the intersection here project the intersection downward get the intersection between these 2 rays and that vertical projection here and create n edge e k. Now, I look at the images c i and d j the images of which are going to be formed on these points and these points take the horizontal projection from the station point in the top view I look at c i get the intersection between this ray and the picture plane over here take that intersection downward allow this vertical projection to intersect with this and this horizontal ray and create the new edge c i likewise I look at d j from s p t same thing same thing I have got 6 vertices at the top and 6 vertices at the bottom without using vanishing points I can join these vertices you get a hexagonal prismatic solid without the use of vanishing points pre pretty nice very logical very reasonable method. Do you want to see whether vanishing points are they have to lie on the horizon line stay with me stay with me they have to lie on the horizon line and so happens that they do you get the right vanishing point here and the left vanishing point over here now if you draw a ray that passes through s p t and this vanishing point that would be parallel to what a b and if you draw a ray which is passing through s p t and this vanishing point that would be parallel to what what what what come again which one why fine here we did not use the vanishing point but what we are doing is we are saying how these guys are going to be vanishing what we are doing is just the reverse we drew this perspective where the true profile view the truth of you stay with me true profile view truth of you got this perspective and then we are trying to figure whether vanishing points are how do we figure the vanishing points by looking at a pair of parallel edges vanishing at a certain point. So, what I draw is a ray passing through this a ray passing through this these three guys apparently are what concurrent they intersecting same point and likewise this horizon line and the ray which is along this edge and the ray which is along this edge they are also intersecting the same point yeah now using the same method I am going to try to construct a three point perspective you can try constructing a single point perspective using this method simple examples I am going to be using the example of a cube to construct a three point perspective using same method. So, what you see is the third angle orthographic projection the front view the top view and the profile view. So, the top view in the top view the cube is rotated by certain amount let us say 45 degrees. Now, how would I get a three point perspective rule number n in perspective all lines have to be running away from the picture plane none of the lines should be parallel to the picture plane only then I can get a three point perspective otherwise not right right. So, what do I need to do for that I need to make another rotation. So, it is so happens that you would be getting a two point perspective in this because you have you still have an edge or rather you still have four edges one two three and four parallel to the picture plane which is here. So, I need to make one more rotation what would I do is I would rotate the cube in the profile view and get the respective views in the top and the front view like this use projections go back rotate this cube in the profile view by a certain amount when I rotate this what happened to this gets rotated about this axis and this also gets modified accordingly you have done orthographic view. So, it should be very difficult for you now I am going to be using this picture and this picture to draw a three point perspective the top view and the true profile view these vertices one two three and four they correspond to these four vertices over here right where are these vertices in the top view these guys or those guys careful careful careful you know I was making this animation at eight o'clock in the morning the set of vertices below or the set of vertices above look at the projections these four vertices are getting projected over here these four vertices are getting projected and coming back here look at the projections. So, these four vertices they will appear at the bottom or at the top in the top view at the bottom. So, that is one thing that you need to keep in mind which is where I struggle for half an hour almost 45 minutes this morning. So, a b c d is the bottom phase e f g h is the top phase in the top view a b c d is this phase here e f g h is this phase here in the profile view clear look at the position of the picture plane in top view it is passing through the vertex e this time in this example the picture plane is passing through the vertex e correspondingly in the profile view the picture plane is going to be a vertical line that passes through this vertex e. I choose a station point in the top view s p t this can be any point and the same rule whatever this distance is I am going to be using the same distance from this picture plane in the profile view and have my i or the station point in the profile view on the horizon line fine here s p p and then the drill remains exactly the same exactly the same no changes look at these vertices from the station point in the profile view draw horizontal projections look at the corresponding vertices in the top view from the station point s p t draw corresponding vertical projections find the intersections find the vertices and that is it let us get started looking at a e I am looking at a and I am extending this ray because the image of phase being formed over here on this picture plane take that horizontal I look at a e now I need to extend this ray because the image would actually form on the picture plane over here draw the verticals find the intersections and get the vertices the same thing for all edges all what x pairs look at b f extend this s p p b ray to intersect with the picture plane draw horizontal from here draw horizontal from here f gets formed here the image of that look at the corresponding vertices in the top view in the sections between the ray and between the rays in the picture plane draw the verticals let them intersect with the corresponding horizontals get the vertices again same thing this is for d h and this is for the center of gravity 4 edges of a block of a cube I do not know what perspective it is I join these vertices and get a perspective we are looking thing yeah fine fine fine I still need to convince you that this is a 3 point perspective option 1 word your block look like that or would your block look like this it would look like this yeah or this have you heard of something called a knickers cube illusion have you heard of something called a knickers cube illusion yes no no yes all right for those who have not all right look at this vertex E and look at this vertex C and tell me which one is in front of the other so if you are looking at this object if you are looking at this object at one time it will appear to you that vertex E is in front at the other time it will appear to you that vertex C is in front careful careful so that is that is what the knickers cube illusion is yeah that is that is what the illusion is anyhow so if this is the true perspective of this cube let us try to figure out by the where the vanishing points are draw lines parallel this is my first vanishing point sorry got it wrong yeah yeah this is not the correct what I got this wrong all right I got this wrong let us see let us see where I made a mistake I have three vanishing points all right but two of them they happen to lie on the picture plane not the horizon line which is strange so right can you help me figure where I have made a mistake can you help me figure where I have made this mistake where I have made a mistake the entire thing all right fine think about it yeah picture plane would be more towards the left side look but my picture plane I decided my picture plane to pass through E I decided my picture plane to pass through E well this distance I thought was the same as this distance no idea where did I go wrong the orientation the other alternative no no this nothing to do with the knickers cube illusion where did I go wrong yeah are the distances between SPT and the corresponding picture plane okay all right okay are these distances equal yeah looks like they are where did I go wrong you know the only problem with this is that I am getting the vanishing points on the picture plane and not the horizon line yeah so this is what I'll do yeah a b c d on same plane on the same plane a b c d a b a b e f all right so a b e f okay so what a b e f yeah got that plane I'll tell you what I'll tell you what I'll post these slides on the web you can take a look and if you have found my mistake share with me in the next class