Converting Iso Ortho

So today we're going to talk about a few different strategies that are available to you for converting from a isometric pictorial to an orthographic projection. And the outline is we're first gonna talk about using the infinite perspective properties of the orthographic drawings to be able to create an orthographic projection from an isometric pictorial. We are then going to look at the glass box approach and track some points around and some surfaces around. And before we get into these, I just want to say that it's not necessarily that one of these is better than any of the others. They can be useful in different circumstances. I actually use all of them when converting, depending on what type of objects that I'm dealing with. So they can work better for different people, they can work better for different objects, No one is significantly better than any other. So we're going to first look at the infinite perspective property of the orthographic projection. So when I am creating an orthographic projection, what I am doing is imagining that I am this little guy here and I am standing really, really, really far back from my object. Now why am I standing really far back? Well if I am this little eye here and I am looking at a tree, and I am up fairly close to the tree, my lines of sight are going to do something like this, so you see them at an angle and this is where you get the perspective you see in real life. The further back I stand, The shallower and shallower these perspective lines get. So that as I'm infinitely far back, they are effectively parallel to one another. So that's why its called an infinite perspective. Its as if I was standing infinitely far away so that my perspective lines are virtually horizontal and perpendicular to the object that I'm looking at. So I'm this little guy, I'm standing really far away and I am looking at this front surface. And all I'm going to do is draw what I see. So I see a few different edges here. I see the front surface here. So I draw that in down here. I see this surface here. And I draw that in here. And then I see the circle so I draw that in as well. When it gets down to it there are three major reasons that I will be drawing a line on a drawing. And the first one is that I am seeing the edge of a plane. So here I have this plane up top and I'm seeing its edge right here. So that's where this line comes from. I have this plane over here and I'm seeing its edge over here. So that's kinda where this line comes from. So the lines that I'm drawing are the side view, basically, or the edge view of a plane. Another reason I could be drawing a line is if I have the intersection of two surfaces. So if I have something that looks kind of like this. So I have this kind of triangular prism. And I am for some reason drawing it from this perspective, which doesn't make a whole lot of sense but let's just say I am. I'm drawing it from this perspective. So then the view that I would be seeing would look something like this. And Let's change ink colors... So now if I look at it, this line here is represented here. And what that is, actually, is the intersection of this surface with this surface. So our first type of line was the side view of the surface. Our second type of line was the intersection of two surfaces. There's a third type of line that we may draw that may not be quite as obvious. And that is, basically, the limiting element of a curved surface. So if instead of a triangular prism, I had a circular prism. And now I am looking at it again from this perspective. What I would draw is essentially a rectangle. Now where this top line and this bottom line comes from is the limiting element of this cylinder. So I have the top line here. I have this bottom line here. The very, very extreme part of the cylinder is what I'm seeing in these two lines. So these are the three different types of lines I'm really encountering. I'm encountering the edge view of a surface. Like there. I'm encountering the intersection of two surfaces, like I am here. Or I am encountering the extremes of a cylinder, which is what I have here. So I draw these lines based on my infinite perspective. And for a lot of shapes, they're simple enough that I can do that by imagining myself standing here, imagining myself standing here, and imagining myself standing there. Another way to think about something very similar is this glass box approach. So here I have a glass box and I put an object inside of it. And what I want to do is project the things that I see from a certain view of that object onto that glass box. So lets look at that. So here if I'm standing at the front surface of this glass box looking in, I project forward the points and the vertices that I can see. And now I get this view you see now on the front face. Top face: I get something similar, and the side view I get something similar. So then what I do is I unfold my glass box. And now what I end up with is something that looks somewhat like this. So this looks very similar to the infinite perspective view. You don't draw perspective lines, you don't worry about perspective. You just project in a certain direction the points and vertices that you see. You project it onto the front face, the top face, and the right side face in this case. It could also be a left-side face, that's just not what I did here. So this is the glass box approach. And you can see that in this kind of video that I have playing here; so you have a front face, that's being projected, a top and a right-side face, which become the front view, the top view, and the right-side view. This drawing has a bit more detail in it. You can see on this drawing that we've included centerlines and hidden lines. You didn't need that on the object that we looked at a few slides ago. Okay, now we are going to talk about point tracking. So we've talked about the infinite perspective, we've looked at the glass box, now we're going to look at point tracking. So what I do with point tracking is I basically assign a coordinate system to my object. So we all know that if you have a coordinate system and I create an x-axis and I create a y-axis then by the right-hand rule this would be my z-axis. So this is what we're going to be using for this object. So if I look at my object over here in the orthographic views I can figure out which axis is in which direction. So this part I have a y-axis going this way, and I have an x-axis going this way and down here I have a z-axis. And an x-axis, and here I have a z-axis and a y-axis. So you can see that roughly z is the height axis, x is the width axis, and y is the depth axis. So now, what I'm going to want to do is figure out the coordinates of each of these. So I have x, I have y, and I have z. And I have, for instance, lets say points A, B, C and D. And I would end up doing this for more than just these because I have lots of different points on this object. But we're just going to look at a few of them for an example. So we're gonna say that the A point is at our origin. Now what I want you to do is I want you to pause the video and I want you to figure out the coordinates of B, C, and D. And then once you figure them out, play it again and we'll go over what the answers are. Okay so now that you've figured out what you think the coordinates are for B, C, and D, let's check ourselves. So B in the x direction is 1...2...3... away from the origin. So I have three And then I'm gonna have to look at a different view than the front view to figure out the y-axis, so lets do the z direction next. So in the z direction I am 1...2...3... 4...5 units in the z direction. And then if I hop over to the right-side view I am 1...2...3... 4...5 units in the y direction. Similarly, I can figure out that C is 4, 1, 2 and D is 7, 1, 0. So I've figured out the coordinates for all these different points. Now what I would do is I would go ahead and plot them on my isometric grid here. So I would figure out what my axes were, put them on the isometric grid and plot them. So here, I've done that here. So let's remind ourselves. So now I can check and make sure that I've actually drawn this correctly. So let's look at this... So this is my x direction, this is my y direction, and this is my z direction and right here is my origin. So this would be my point A. And A is at 0, 0, 0. Now lets plot out where point B would be. Point B would be 1... 2...3 units in the x direction. 1... 2...3...4... 5 units in the y direction. And 1...2...3...4... 5 units in the z direction. So this is point B and I can see that down here, it looks like I've actually drawn the right point. I can look at the C and D points as well. C ends up being right here. And D ends up being right there. And so what I would do is I would either draw the isometric based on what I'm visualizing from the three orthographic views or I would actually start plotting these points out one by one, figure out where B is and plot it, figure out where this point is and plot it, figure out where this point is and plot it. And then basically connect the dots together. And that's how I could go back and forth between the orthographic and isometric. Now we're going to track surfaces instead of tracking points. Before we do this we need to know the three types of surfaces we tend to encounter when we are drawing objects. So our three types of surfaces are principal surfaces, inclined surfaces, and oblique surfaces. So here's a principal surface. And what makes a principal surface a principal surface is that you see it as its true size and shape in one view and you see it as a line in two other views. You see its edge, which shows up as a line. So here I have the shape showing up as a rectangle in the top view, as a line in the front view and as a line in the right-side view. So with a principal surface, I can look at any of these views to get the dimensions of this shape. So if I look—I can look at the top view to get the distance between 4 and 3, or I can look at the front view to get the distance between 4 and 3. I can look at the top view to get the distance between 2 and 3 or I can look at the right-side view to get the distance between 2 and 3. So this is a principal surface. An inclined surface shows up as the characteristic shape in two views and then as a line in the third view. So here I have the inclined surface showing up as a rectangle in the top view and in the right side view. It doesn't have to be a rectangle, that's just what it was this time. It could be a circle, it could be a triangle, it could be anything. In this case its a rectangle. And then I also have it showing up as a line in the front view. So here if I want to get true dimensions, if I want to get the distance between 2 and 3, I could do that in the top view, or in the right-side view. And that would be the same deal for the distance between 4 and 1. If I wanna get the distance between 4 and 3 or 1 and 2 I can't do that in the top view or the right-side view because its on an incline. So if I wanna get the linear distance between 4 and 3 I need to do that here in the front view. Our third type of surface is an oblique surface. And here it shows up as its characteristic shape in all three views. So here its a triangle, it could be something else, but it shows up as a triangle in all three views. I never see just the edge, that's how I know I have an oblique surface. If I wanna get true distances between 1 and 2, I would be up here in the top view. Between 1 and 3, I'd be here in the front view. And between 2 and 3, I'd be here in this right-side view. None of these other distances are the true distances between the points. They are all shortened because of the way that I'm looking at them. So now that I know my three different types of surfaces I can use them to solve a problem and figure out something about a drawing. So here I have an orthographic drawing and I want to draw the isometric and I want to figure out what line I'm missing. I'm missing something. I'm missing a line and I want to figure out what line it is that I'm missing. So what I'm going to do is look at each of these surfaces, draw them in my isometric and use them to figure out what information is missing and what line I need to add. So here I've blocked out my object. It is roughly a 9 x 5 x 5 rectangular prism. And I'm going to within that blocked out rectangular prism, draw my different surfaces. So I have a principal surface here because it shows up as its true shape in one view and as an edge view in two other views. Here I have a surface that shows up as a rectangle twice and as a line the third time, meaning its an inclined surface. I have another principal surface. Here I have an oblique surface because I see it as a triangle in all three views. I have a few more principal surfaces. And now I find out where I'm missing my information. So I'm missing my information here where I see two rectangles. Now it looks to me like it probably isn't going to be an oblique surface. It would be very difficult to fit an oblique surface into this cavity. So because I'm seeing two rectangles its a pretty safe assumption that I'm dealing with an inclined surface. So if I draw in my inclined surface, I can draw in my associated line down here on my side view and now I have figured out my missing information by tracking surfaces. So here's my finished example. One thing I want you to do is to convince yourself that this surface here needs to be an inclined surface and that it can't just be a notch. If you can't figure out how to convince yourself that it couldn't just be a notch back into the object then ask your instructor about it because its an important thing to be able to understand. There's actually one other shape this technically could be. It technically could've been some sort of curved surface and it would've shown up similarly. So in summary, we've looked at using infinite perspective and the glass box approach to just look at an object and be able to draw it. We've looked at point tracking and we've looked at surface tracking. And any of these different strategies could be useful at different times. You don't have to use all of them, but they are very useful.