 So, this is an example on perspective view. So, what I will try to do is I will attempt a 3 point perspective of this object and what I will do is I will be using a 2 station point method to draw this perspective. I will not be using vanishing points explicitly, but instead what I will do is I will rotate this object twice, one would be about this axis, I will rotate the top view about this axis and afterwards I will rotate the profile view about this axis. I will do that to ensure that none of these edges are parallel to the picture plane. So, these are the orthographic views of this object. The front view or the frontal plane is this top view, the profile view. So, what I did was I performed one rotation, I rotated the top view like so by some degree, I got the frontal view as well as the profile view, but then things became complicated. So, what I did was the next smart thing, I went to MATLAB, I recorded the 3 dimensional coordinates of all these vertices, I also record the connectivities and then within MATLAB I performed 2 rotations of this object. Once I did that I got 3 views, this was my front view, top view with respect to the front view and the profile view with respect to the front view. So, the trick is to use the true top view and the true profile view to get the perspective of this object. We will try to see how this example goes. So, what I have done is I have copied down the true top view here and the true profile view here and with these 2 views using the 2 station point method I will try to attempt the perspective drawing of that object. Let me first specify the ground line, so the ground line will be passing through this point O little gentle line. Let me also specify the picture plane, now in the top view the picture plane let us assume that it passes through point a vertex G, let me call this P P the picture plane. In the profile view the picture plane is going to be vertical and is going to be passing through this vertex G here. I have to practice lettering, but let us not worry about that for now. Now, let us say I am station somewhere here in the top view and let me mark a point or perhaps somewhere over here the further I stay from the picture plane and further away from the object I will probably getting a nicer perspective, but a smaller perspective. So, I do not want to be too far away from the picture plane and I do not want to be right in front of the object may be I want to maintain some angle between the object and myself in the top view. Let me have my station point somewhere here it is arbitrary and let me encircle it, so that when I am drawing the perspective I do not miss it. Notice that I am using my two edge pencil and let me call this station point with a subscript t to remind me that this is in the top view. Now, in the profile view let us say I would want to see the roof of this object, so my horizon line would be above this portion of the object. And this distance in the top view should be the same as this distance in the profile view. So, let me first choose the horizon line, horizon line could be anywhere in the profile view does not matter it could be above the picture plane or below the picture plane. Let me have my horizon line here well you would notice that after a while I would stop calling this the horizon line, because I will have my station point here. Let us measure this distance it is about 60 millimeters and let me have this distance over here. Let me encircle this point to remind myself time and over that this is the station point in the profile view I use a subscript p, so throughout I will be using the two edge pencil, because there will be a lot of many construction lines there are all chances that I might make a mistake if I am not careful and if I am not focusing. First things first let us identify this vertex g, vertex g in the top view lies on the picture plane. So, I can take the vertical projection I can take the vertical projection down from the top view and perhaps I can take the horizontal projection from the profile view intersection of these will give me vertex g. Now, what I will do is I will start seeing these vertices in the top view from the station point. I will get their projections or their images on the picture plane and I will try to project the images downwards likewise in the profile view I will start seeing the respective vertices I will get their images on this picture plane and I will try to project them horizontally. The intersection of vertical projections and the horizontal projections will give me the respective vertices on this part of the sheet the perspective plane, if I may call that perhaps not a good idea to disturb my drafter. So, I am going to be using this kind of mine the 30 60 90 square and let us perhaps focus on this vertex r this is the range the top view through which I am visualizing r I get its image over here I project it down by some distance I am using very dim line perhaps may be a little darker. So, that you could also see and then from the station point in the profile view I see my vertex r here this is where the image of r will be formed I use horizontal projection from this point here and this is let me mute myself for now and work on these vertices in the top view and the profile view let us see how things go the procedure to get all these vertices on the perspective plane is identical I am working with q I get the image of q here now within. So, whenever I draw the horizontal and vertical projections I need to be careful in correlating them let us take p in perspective have its image down may be it is a nice idea for me to indent these intersection points otherwise I will get confused the image of p is right there this is where p would be in perspective and perhaps o. So, looks like o is going to be line on this vertical line and let me take o from here its image on the picture plane is right there o lies on this vertical line need to be a little careful I do not want to miss these lines perhaps just to get an idea as to how the picture or perspective is getting formed let me join these 6 points to form a plane these 4 points n q r and g n q r and g they will have to be collinear. So, they will have to line on a straight line. So, it seems we cut it right and then n p forms an h likewise o g forms an h and o p forms an h this seems to be looking quite skewed I wonder if I have taken this view right or this view right seems like it was o ok. Nevertheless, let me continue and see where I go from here perhaps maybe it will be a good idea for me to draw this face and see if everything seems ok. So, let me focus on vertex a that connects with o I have labeled these vertices for my own convenience otherwise I tend to forget where these vertices are nevertheless. So, a gets its image formed over here if I look at vertex a from this station point this is where the image of a gets formed projected horizontally and this is where my vertex a is my intended also right little notation. So, o a gets connected let me see where b is looks quite weird to me at this time maybe not a proper choice of station point, but let us see image of b getting formed over here I project that image down and then I look at b here in the profile view from the station point get this ray go in the image of b gets formed over here and I need to intersect the horizontal with this vertical here this is perhaps where my b is looks quite weird looks really weird well let me continue. How about I vertex I here symmetric getting formed here somewhere take this mesh down then it will be many raise one needs to be quite careful from here vertex I forms an image somewhere here on the picture plane take its horizontal projection and get the intersection here indent this point I am not supposed to be doing that, but just to remind myself that this is where I is improper use of grammar should be I am, but this is vertex I let me verify if this is ok seems like this is ok seems like this is ok alright let me have this point I. So, done a b I perhaps h station point here h would be very close to this vertical line very close indeed. So, this is my vertex h in the profile view this is perhaps where the image of h gets formed I take a horizontal projection from here mark it over here. So, this is my point h. So, just to make my sheet looking better I will take a break and I will erase these off shoots and then I will come back later. So, looks like I have all these vertices corresponding to this plane in my picture here perspective picture. So, G O and then I have got I perhaps I should go and orderly fashion. So, G O then A I have A here perhaps I have B here I here and h here. So, let me try to join them maintaining the same connectivity let me keep my drafter way for a while. So, let me join G and A first I will worry about visibility later and then A B and then B I h h is here and h back to G perhaps I made a mistake I should have really joined O and A I will erase that and come back cut joining O A as I mentioned earlier if you are not careful there are chances that mistakes will happen. So, O A A B B I I h and h back to G perhaps I can try to get this face as well at least I will be able to figure if my top view is ok or not. So, I already have p and n I need to get these four vertices let us focus on m or be careful need to use 2 h. So, this where m makes an impression on the picture plane project it down my vertex m is here this where I get the image of m on the picture plane I project this horizontally absence where I get m and then that may be make a little note for myself. Now, for vertex f that is where the image of f is take it down and then f is here makes an impression here very close to m perhaps I lost my projection over here. f coming from here is here and f is making its image very close to m on the picture plane which should be little above I let that line stay. So, two points remain E and L. So, this where the vertical projection is coming for E and this where the horizontal projection is coming for E. So, perhaps this is where E is it is very easy to get lost in perspective finally, L think is where L is let me verify. So, the ray from the station point towards L makes an impression here on the picture plane gets down ok. So, this where I should be and then from here this ray that is making an impression at this point on the picture plane. So, it looks like I am fine. So, I have got L E m and f f is connected to p and m is connected to n let me work on these connectivities m connected to n and then L connected to m L connected to E then E connected to f here perhaps and f connected back to p. It is kind of looking weird, but let us see how this goes further still not a good idea perhaps for now to start making these lines darker because there is still a lot of construction lift. So, if you realize L E d k is making a face d c j k is making another face and c b i j third face. So, I got this edge I got this edge in perspective perhaps if I get these two edges I then will be able to see these three faces and verify if I am really going ok. First let us look at c these are going to be too many lines. So, maybe I will start marking and maybe I will remind myself that this is c take a vertical projection down all right go to c here we let us mark c here get the horizontal projection up till this vertical projection. This point here is c let us look at j now. So, looks like j is going to be very close to this vertical projection it is not going to be very far from that maybe it would be this is j get the vertical projection from here. And let me look at j in profile view let me get the horizontal projection from here and perhaps this is where j is let me indent this point and call it j. So, looks like I have this face b i j c. So, i is connected to j let me make that connection and then b is connected to c let me make that a little darker and then of course, j is connected to c. So, I have gotten this face now what remains is to find k and d. So, I look at k this is where k should be bring down the vertical projection from here my lines are getting darker now that should not happen. And I look at k here this is where k would be take the horizontal projection this is where point k is. So, looks like too many points are close to each other and d this is going to get mess here these days here take the vertical down. And then take the image of d on the picture plane in profile view here that is d usually these markings are not supposed to be done, but I am just doing that because otherwise I know I am going to get last no I know I am going to be last is my drafter k. So, possibly it lies a little above the picture plane project this thing upwards a little looks like my d would be somewhere here. So, now things lot messy here because there is so many points to be careful in locating k which is here and d which is here. So, before we tend to lose ourselves let us go ahead and connect the vertices. So, l is connected to k k is connected to d and d is connected back to e and I have no idea where e is did I get e right I have to figure that out. So, let me go back e should have been here somewhere then e should have been on this vertical projection e should be coming out from here. So, e should have been here. So, I mark this point wrong once again station point to e image of e comes here somewhere take it down all right. So, maybe let me mark e here and then station point to e in the profile view e makes an image here take it is horizontal projection from here and e should be here. So, looks like I got e wrong here. So, this connection is also not proper. So, if you are not careful you know mistakes happen it looks like I am in a mess here. So, many points so many rays horizontal and vertical projections. So, I will take a break try to sort this mess out and come back and then continue with the rest of the perspective projection. So, what I did was I went offline and darkened my construction lines. So, that I do not get confused, but in the process it looks like I am little more confused anyhow. So, I got this part all right. So, this was the region where I started to make mistakes if you realize this is point c this point j what x k what x d would be somewhere here. And if I look at this space here c j k d make this space. So, c j k d let me complete this space and then move further at this time it looks little messy, but hopefully when the final drawing is done things will be a lot more clear. Now, look at what x l what x l is behind the face c j k d and so is vertex e. So, one of the options is to let go of them second option is to you know make this space, but if we do that things would be a little more messy. Well let me try it out let us see how it goes now that we are in a mess already and later on we will work on the visibility part and try to finalize this drawing. So, looks like I have this face done pretty much and then on the back side e and f would be connected. So, it is a very skewed line, but let me have it and let me darken b c just to get an idea as to how skewed the perspective is. So, before we work on the rip part perhaps it could be nice if we can figure out the visibility of this. So, let me go back to my front view right here and realize that face h g n m is on top h g n m it is on top. So, these lines they need to be dark p o is at the bottom. So, this part can be omitted and o a is visible. So, this is visible and so is g o. So, let me work on this part first and try to darken these edges before I start getting more confused. So, here we go and to darken I am going to be using my h pencil I hope I would not be making mistakes from now on. If I do well I do now this part will probably not be visible because this edge would hide that. So, maybe I will just make a partial face or maybe let me not work on this for the while because I am not sure if the rib that we are going to be working with will further hide it or not. So, let me omit this part and perhaps darken this part of the perspective. So, these faces are going to be visible anyways whether or not the rib is there only a part of the rib is going to be behind these faces. So, let me darken these faces I am not supposed to be using the pencil over itself. This is what happens if I do overlap of lines which is something that I do not recommend. But, just to show you how the perspective is going to look like I am darkening these lines as much as I can. So, that they are clearly visible when compared to the construction lines around them. Well, now that I am working with dark lines let me make these lines as dark as I can just to have them in contrast with the lines rather many lines in the neighborhood that looks better. And of course, this face is also going to be visible let me mark it looks all right to me and of course, the back face E f. So, now let us work on the rib notice that rib is composed of these vertices u v, t s and q r none of which have been well q r are there. But, other than that these four vertices they are not there slightly that t s is within this region anyhow we will have to get them let us first focus on u and v let us get back to construction. U is here let me join that to the station point and looks like the projection of u and the projection of v are pretty much the same over here or perhaps over here. So, let me use my drafter extend this up a little need to switch my pencils for that and then mark little u here. Let me go back to the profile view what takes u from the station point get its image on the picture plane right here. Now, notice that I have started using darker construction lines this is by u s take my drafter this would where my u would be now have to be extremely careful as u and then looking at v going to the top view looking at v from the station point getting its image on the picture plane in the top view. Now, that these lines are dark enough I do not have to worry about the darkness to construction lines though I need to make them as light as possible and as clear as possible. Fortunately in this example things have been little messy especially in this area. Now, back to v this is where v would be let me draw vertical projection slightly extended upwards. So, that I can mark v here now let me look at v in the profile view from the corresponding station point draw construction drawing perspectives as no way easy and then use the corresponding horizontal projection and perhaps get it reach the corresponding vertical projection here. So, this v let me intend that a little v. So, let me pull out my front view for reference. So, v is connected to q and u is connected to r let me make those connections put the drafter away for a little while and only a part of this rib will not be visible let me make this connection here q with v and you see that this part of n m now is hidden behind the rib. Well perhaps I can now see this perspective more clearly let me draw this line a stick line few strokes back and forth and then it looks like both these edges of the rib they are going to be visible. So, I am going to darken them I will start with the top one first and then I am going to go only till this point only up to this point. I still do not have much idea as to how this perspective is going to look definitely looks much weirder than I expected, but well and then perhaps what we can do is starting from r. So, this edge would be visible. So, perhaps if we can locate s on our perspective we can draw this edge and hopefully finish this diagram. Let us not worry about t because t is going to be behind. So, it is not going to be visible. So, let me take this off and worry about s switch pencils look at s in the top view get its corresponding image on the picture plane it is going to be very close to this projection here. Let me extend this little upwards just in case of these two projectors call this s little small note and then in the profile view let me get the image of s on the picture plane here somewhere it is want to make sure I do not lose it bring my drafter there make a horizontal projection and follow these projections perhaps this is where my s is make a little note s and then join r with s again this part of the rip will be behind it is not going to be visible. So, perhaps I can use a dark line directly well as I said many many times it looks like a very weird perspective and one of the reasons why this is. So, it is possibly because the vanishing points are very close to the image let us try to look at the vanishing points. So, this is one of the axes this is the second one and this is the height axes. So, corresponding to this axis if I try to draw if I try to extend these edges and I am going to be using a different colored pencil would look a little weird, but if I try to extend these edges this is the first vanishing point that I get somewhere here and if I extend the height edges this is the second vanishing point that I would get over here somewhere and if I extend edges along this direction these directions I will possibly be expecting the third vanishing point over here somewhere. So, vanishing point 1, vanishing point 2 and somewhere over here the vanishing point 3 let us see if these vanishing points are indeed correct because if they are not then of course, there is something wrong with this perspective. It is always a good idea to verify if you have made a mistake or not there is nothing wrong with making mistakes. So, to get the vanishing point along this direction you will probably have to look along this direction from the station point. So, let me now start adjusting my drafter align my horizontal along a scale along this along this edge look at an object at infinity along that direction. Let me use the blue pencil for that and of course, this will be making an impression over here on the picture plane. Now I will do the same thing I will look at an object at infinity along this direction this will perhaps explain why the perspective is this sphere anyhow. So, if I look at an object along this direction at infinity from this station point I will probably be getting the image of that object over here. Let me mark these vertices let me now straighten my drafter and drop verticals. Now let me take the vertical from here I will extend it along both directions and also let me take a vertical from here again I will extend it along both directions. Now in the profile view the x and y directions they are along these edges and the z direction the depth or the height direction is along this edge. I will do precisely the same thing as I did over here set my drafter to be parallel to one of these edges from the station point I will look at an object at infinity the image of which is going to be getting formed on the picture plane somewhere here. And likewise I will set my longer scale in the drafter parallel to this edge and I will look at an object at infinity along this from the station point in the profile view and that image is going to get formed over here. I need to be a little careful rather I need to be quite careful now because little mistake will not ensure that my perspective is indeed right or incorrect possibly here somewhere you know little change in angle makes so much of a difference. So, looks like these vanishing points are quite sensitive to these edges I will have to be very careful. So, anyhow so taking this and drawing the horizontal from here and the horizontal from here extending that extending the horizontal is from here up till both these vertical blue lines. I see that my vanishing point is here and my another vanishing point is there. So, if I set my scale accurately along these lines I should probably be very very close to that vanishing point. So, looks like I should have really drawn them a little later I was maybe in a hurry know as I said a little error could make so much of difference. Now, looks like this is not aligning properly. So, could be that I may have gotten these edges wrong is it that let me go back let me check my construction clearly I got the O wrong because if you look at O it is getting. So, this ray starting from this station point is hitting the picture plane over here somewhere and if I extend this right there vertically downward my O should be on this vertical projection clearly I got my O wrong. Let me verify from here. So, this is where the ray from S B P towards O it is a picture plane this is a corresponding horizontal projection. So, this seems ok, but just that my O needs to be slightly displaced towards left having said that realize that both these vanishing points get affected let me go back make this correction and join with you shortly. So, realize that these mistakes are going to happen that is one of the reasons why I keep repeating that is always never a good idea to start drawing dark lines one needs to be very very careful and focused nevertheless. So, this is where my point O is well as I said nothing wrong in making mistakes while I am saying that I am still using my edge pencil, but hopefully I get things right now let me join these edges rather this edge using a dark pencil. So, this thinner than last time now if I align my set square to one of the edges it would realize that I am actually approaching that vanishing point which is good news. So, maybe I will just you know extend that. So, this vanishing point is incorrect, but perhaps that one is more reasonable there you go there you go this is wonderful. And if I come back I need to erase this part as well which is because I do not need this edge in my perspective all I need is this point P let me darken these lines probably get back our perspective just as it was before or perhaps not pretty much there anyhow. So, let me mark this using a thin line switch pencils it does not really matter now, but anyhow. So, now if I extend this line this is also pretty because now I am hitting the second vanishing point. So, this vanishing point was incorrect now this better all right. So, how about the third vanishing point? So, in the profile view I was looking at an object at infinity along this duration that is a z duration. So, this is corresponding blue line I got that image there I extended it horizontally, but then the top view I did not do that exercise. So, this is the z duration I should be looking along this duration at infinity and get the image of the object on the picture plane. So, this is where the image of the object is over there and perhaps I can extend that downward. So, it looks like this would be my third vanishing point. So, again I probably did not get this correctly possibly because I did not align my scale of my ruler probably along these two edges. Let me verify if indeed this point is the third vanishing point and if that is the case then I can verify that this perspective of mine even though it is not neat and I admit that I have made a lot of mistakes, but that is ok that is how people learn. If I align my ruler properly along these edges hopefully I will be getting close to this vanishing point. Now, before that let me verify if this indeed is the vanishing point that I should be looking at. So, little error in alignment and you could expect many errors happening. Now, this suggests that these vanishing point should be upwards let me look at a little longer edge may be align myself parallel to that may be even longer is this. So, if I go back to my station point it looks like there is a minor deviation I can effort to go down a little further perhaps over here somewhere and then I straighten my rafter I can possibly expect my vanishing point to be a little more down then it was suggested before well things are messy, but you know this is a nice learning exercise if not final. It looks like I can get this edge to align with this vanishing point this of course is not correct and may be then there is something incorrect with this edge. So, let me see if I have gotten these two points right first point h. So, I look at what x h in the profile view from the station point is where the image is getting formed and of course, this is the correct horizontal projection where h should lie how about the vertical projection I am looking at this vertex here. So, you know this is quite close and a little sensitivity in the image of h over here could make quite a bit of difference. So, if I expect my h to be slightly towards a right and if I expect my h to be here possibly perhaps I can get this right and looks like I do. So, may be a little deviation in this edge along this direction permits me to have this vertical edge of mine converge to this vanishing point right there. So, let me erase this vertical edge join s and the new found vertex h be a few more strokes look at this also smooth in this edge out. So, here we are the three vanishing points corresponding to the three orthogonal directions found let me mark them. So, this is the right vanishing point v p r this is the left vanishing point v p l and this is what people tend to call as another point because tends to be below v. So, although this perspective looks quite awkward looks like the construction seems because the three vanishing points although I have not use them when I actually started drawing the perspective tends to conquer or agree with the vanishing points that I found assuming that I was looking at objects at infinity parallel to this direction which is this edge object parallel to this direction at infinity which is this edge. And then object along z direction the height direction which is this direction here and the profile view this direction. So, summary too many mistakes, but that is how people learn rather I believe that people learn better by mistakes than by not committing them at all. Because of reason that three point perspectives could be awkward it is usually preferred to draw two point perspectives perhaps better choices of the station points in the top view and profile view would have allowed me to draw this perspective a lot better. So, last time I had mentioned that I was not very happy with this perspective drawing for two reasons reason number one was that I probably had chosen my station point poorly with respect to the top view of this object. And reason number two was that I made many many mistakes perhaps I was not focusing well anyhow. So, I was not very happy. So, after I drew this I stayed back in the studio and I redrew the perspective with the same top and profile view with a different station point. So, my station point in the top view was this point over here correspondingly I chose my station point in the profile view over here. So, that this distance from the picture plane of the station point was the same as this distance. So, this was the picture plane in the profile view and of course, this was the horizon line. So, you could see how nicely the three point perspective of this object has shaped up. I like this one particularly better before drawing the perspective of this object I also kind of got an idea of the vanishing points using the same method. So, you know from the station point look at infinity along this direction look at infinity along this direction. Let the two rays hit the picture point over here somewhere make a vertical projection and do the same thing over here. Look at an object at infinity along this direction which is the z direction the x and y directions and get the corresponding horizontal on the picture plane over here. Let the horizontal and the vertical intersect at these two points. So, this was how the vanishing points were identified. Nevertheless, choosing the station point properly in the top view will give you a very nice picture a very nice perspective of an object that you are trying to draw. So, this was the point that I wanted to make.