yoitisi
January 17th, 2008, 03:29 PM
Post the results of assignment 3 & 4, the cubes, in this thread please. This thread is for my mentees only, unless you've got any tips or hints to share. I won't react on your work if you're not one of my mentees. Thank you :)
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Assignment 3: Cubes
This will actually be the first real assignment complete with deadline and all :) Now that we have the basic idea of lines and perspective behind us, we can start the drawing of shapes in perspective. I'll start with cubes. The reason for this is simple, by combining cubes and some of its cross sections you can already make quite a complicated drawing. Cubes are often used to keep proportions and measurements in check, as foreshortening makes it sometimes difficult to judge these without them as guideline.
You can already get an idea of what I'm going to ask of you in the sketch above, but I'll now explain how to get there in a few simple steps. The reason I want you to follow these steps is that they provide a good way to spread decision making in your drawing. Unlike a mere block shape, cubes have more rules :P For one, a cube measures the same length on all of it's ribs. This makes them ideal to use as a check for proportions. However, judging whether a cube is actually a cube takes some training.
http://i163.photobucket.com/albums/t291/yoitisi/Cube2small.jpg
Above you see 6 steps in which I want you to try to follow through until you end up with the cube. If you feel uncomfortable following these step by step feel free to come up with your own order, but in my experience this works quite well to begin with.
Step 1: Start out with drawing the vertical front rib of the cube. The length of this rib defines the total size of the cube, so you can just put two points on it already to have a guide for the rest. Then, draw a horizontal line on the lowest point. This line doesn't exist in reality, and after you got some cubes down you may drop it completely if you like. The reason for this line becomes clear in step 2.
Step 2: Draw the two base ribs that rest on the ground. Make sure there is an angle between them and the horizontal line you just drew, otherwise you'll end up with a cube in sideview without any perspective. Also, make one of the two angles larger than the others, check with the examples below for the why :) This difference in angle means one of the sides gets more foreshortening than the other. You can choose to make either Alpha or Beta smaller or larger, that is up to you.
Step 3: The next step is to draw one of the two vertical ribs on the corner right or left. It is easiest to start with the side that has the least foreshortening. The place of this line has to be guessed, because as this is not a perfect sideview, the side of the cube will have some foreshortening (and thus appear smaller). To help judge these though, you can measure the length of the front vertical along your pen and then measure the horizontal distance between the two verticals. This should be somewhat less than the total height. The bigger the angle Alpha is in my drawing, the shorter the side will appear to be. Keep in mind that in the end, each side must appear to be a square in perspective.
Step 4: Next step is similar to step 3, now take the more foreshortened side and again, judge the horizontal distance between the lines.
Step 5: Now add the two 'horizontal' lines on top, this way you close the first two sides of your cube. Keep in mind the story about perspective I put up above. Step 4 and 5 are interchangable, you can start finishing one side before going on or you can do it the way I did it.
Step 6: Now finish the cube. Draw all the lines, even those which you can't see. This will be very usefull and even necessary in coming assignments. Again, take the perspective and vanishing points into account. As you can see, I made several mistakes in this drawing but instead of starting over or erasing parts, I simply drew another line to correct my mistake. At this point you might also find some of the points found by the crossing of perspective lines will not line up properly (see the rear vertical rib, it doesn't really end at the crossing of the two rear horizontal ribs at the top). This is fine, as making a perfect cube isn't easy. When you see this happen, try to make your own estimate and see where you can adjust the lines to correct it.
Step 7: This would be the result: a nice cube :) I toned one side with my C3 marker, just to punch out the shape a bit more. I also made the lines where the cube sits on the ground a bit stronger, as a sort of shadow. This works to make the drawing a bit more 3d. In this example you might already have noticed how important the training in line thickness and straight lines is.
http://i163.photobucket.com/albums/t291/yoitisi/Notcubes.jpg
The figure above is to show some examples of, well, not mistakes. But drawing a cube like one of those might give problems you don't want, so try to stay away from these if possible.
You may notice that I do draw the lines slightly longer than need be, and I also start slightly before the actual starting point I need. The reason for this is that it prevents you from doing the opposite. If you do not draw all the lines up to the point you want them to go, you lose information an clarity in your drawing. If you need for example the diagonal line on one of the sides of the cube, you need to make sure it passes through the right point. If you do not draw it through that point but stop somewhere before that, it doesn't always read very well where the line originally came from.I advise to always draw the lines all the way through and even a bit longer than that.
Another important aspect, draw big. This forces you to practice your lines etc. but also gives a better opportunity to correct your drawing withouth having to erase anything or start over. If you draw too small, the drawing will easily become full of lines that start to obscure the actual form you're trying to get across. Try to make all the drawings for this about handsize. This means aim for something roughly 15cm x 15cm.
Now, the first real assignment is for you to draw a couple of cubes. Take about 10-15 minutes for each cube, and make it a total of about 6-8 cubes on one sheet. They all have to be a cube, so no block shapes or anything, but cubes. Also, put a tone on one side like I did in the example nr. 7 (I'll explain more about shadow etc. later on). Then, when you're done with them, put a circle around the two you think are the best cubes. This way you also learn to judge your own drawing. To be delivered in this thread before Saturday 26th.
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Assignment 4: Cubes as a guide for construction
This is the follow up of assignment 3, as that one shouldn't cost you too much time. Now, we'll see that with only a simple cube we can already do quite complicated stuff. Part of drawing these constructions is actually very close to -if not just plain- mathematics.
Below you'll see how we go from a basic cube to a whole range of cubes in the same perspective. Funny thing I noticed, these cubes are all exactly the same, but when I put them in a row they seem to turn towards the viewer as you expect them to have the same vanishing point from left to right :)
The ability to draw straight thin lines becomes important in this assignment, as the construction requires a lot of lines and will quickly become unreadable if all your lines are thick. If you don't feel sure you'll be able to keep them all thin, try drawing the cube bigger so line thickness becomes less of an issue. Keeping the lines straight will become harder of course.
The reason for this exercise is that sometimes when you design something and start drawing it, you might need to find where certain points of your drawing are in space. You could guess them, and eventually you'll learn to do so, but it'll always be less sure than if you make the full construction. Drawing the shape into such a system of cubes is one way to do it (possibly the most difficult at that too). You won't use this construction very often, but it helps to create that feeling for where points are in space and in relation to one another.
http://i163.photobucket.com/albums/t291/yoitisi/Cubes1.jpg
Step 1: Start out with a simple cube. Take care that is has to be a cube and not a block shape, as this will make the construction less of use to measure proportions. If it turns out a block, it gets harder to show things like 'the object is twice as long as it is high' etc. Make the cube large, say 20cm x 20cm so as not to get problems later on.
Step 2: Now, devide the side surface into four squares. To do this properly in perspective, you need to first draw the diagonal lines in this surface. The thing with perspective is that the further away an object is, the smaller it gets. Therefore, the squares at the back should be smaller than at the front, which makes it harder to simply guess the middle. So, draw the diagonals and on the crossing of the two you'll find the middle of the cube. Now, draw the vertical and horizontal line in the surface (the horizontal one will be in perspective. To find it's direction without too much guessing, you might find it usefull to first divide the front rib in two. Since we use only 2 points perspective, this line appears without foreshortening and can therefore safely be divided into two equal halves. See point B in the drawing) Notice how line CD is longer than DE, while AB and BC are of the same length.
Step 3: Now do the same with the front surface. You might find that it already gets a bit difficult to distinguish the lines from each other as the start crossing and run over each other. This is sometimes inevitable, especially in a construction like this and might make it hard to find the right lines and points later on. Try to see through it. Also, sometimes if your lines don't end up real straight or just miss the corners, you'll have to adjust it a bit by eye. This, again is inevitable and require you to train your eye to see these things intuitively.
http://i163.photobucket.com/albums/t291/yoitisi/Cubes2.jpg
Step 4: Repeat the steps above until you've covered all sides of the cube, including top and bottom. Notice that if your point of view is too low on this one (i.o.w. angle Alpha and Beta are too small as seen in assignment 3) you'll have a hard time doing so in the top and bottom surface. We're almost done now, we just need a few more lines.
Step 5: Now devide the cube down the middle as well by drawing the three crosssections as seen in the last drawing above. You already got all the information you need to draw these surfaces from the construction on the sides of the cube, but to be on the safe side you can still add the diagonals as well to find the exact middle of the cube. As you can see, the construction has already gotten quite complex while we're still only talking about a simple cube. In the last figure of this assignment you'll see it gets much better readable again by applying some shading.
The above method is a construction from the outside in, and works well to minimize mistakes in the initial cube. Another method to draw the same figure is by starting out with a small cube and multiply it with the following constructing method. The problem here is that you also multiply any mistake in the original cube, so you might end up with a worse result than above.
http://i163.photobucket.com/albums/t291/yoitisi/cubemultiplyall.jpg
Step 1: Again, start out with a single cube. This time make the horizontal lines in perspective longer than really necessary, as you'll need the extra length later on. Now, divide the rear rib of the cube into two equal halves (point A). Since this line doesn't have any foreshortening, this should be eay :)
Step 2: Draw the diagonals through A from both point B and C. You actually only need one of those, as you'll see that line BD is much harder to get right (it's longer and if only you miss the right spot D the differences are much larger). Line CE is the most accurate as it minimizes any mistakes.
Step 3: Now you can draw the second cube behind the first with help of the point you just found.
http://i163.photobucket.com/albums/t291/yoitisi/Cubesshade.jpg
As you see in the image above on the left, putting some tone on the drawing immediately makes it much easier to read. This is an easy method to cover up any mistakes, or even to show one cube is missing! I did this by simply choosing to put shade on a different surface which I had already found by the earlier construction. Note that even while I originally constructed the whole cube, by putting the shade on the right spot you're able to make things in your drawing 'dissappear'. It is often important however to still construct the whole of the shape, as the lines I now do not use still tell a lot about the overall shape, even while they're not supposed to be there.
On the right you see the actual assignment: Start out by drawing the cube in the fist part, then substract one cube from the total as I just explained. Add another cube to the back or front, choose you're own side I'd say. And last, put another cube on top of it all. How to do that is up to you to find out (it's not difficult at all :P)
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Deadline on both is Friday 25 January.
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Assignment 3: Cubes
This will actually be the first real assignment complete with deadline and all :) Now that we have the basic idea of lines and perspective behind us, we can start the drawing of shapes in perspective. I'll start with cubes. The reason for this is simple, by combining cubes and some of its cross sections you can already make quite a complicated drawing. Cubes are often used to keep proportions and measurements in check, as foreshortening makes it sometimes difficult to judge these without them as guideline.
You can already get an idea of what I'm going to ask of you in the sketch above, but I'll now explain how to get there in a few simple steps. The reason I want you to follow these steps is that they provide a good way to spread decision making in your drawing. Unlike a mere block shape, cubes have more rules :P For one, a cube measures the same length on all of it's ribs. This makes them ideal to use as a check for proportions. However, judging whether a cube is actually a cube takes some training.
http://i163.photobucket.com/albums/t291/yoitisi/Cube2small.jpg
Above you see 6 steps in which I want you to try to follow through until you end up with the cube. If you feel uncomfortable following these step by step feel free to come up with your own order, but in my experience this works quite well to begin with.
Step 1: Start out with drawing the vertical front rib of the cube. The length of this rib defines the total size of the cube, so you can just put two points on it already to have a guide for the rest. Then, draw a horizontal line on the lowest point. This line doesn't exist in reality, and after you got some cubes down you may drop it completely if you like. The reason for this line becomes clear in step 2.
Step 2: Draw the two base ribs that rest on the ground. Make sure there is an angle between them and the horizontal line you just drew, otherwise you'll end up with a cube in sideview without any perspective. Also, make one of the two angles larger than the others, check with the examples below for the why :) This difference in angle means one of the sides gets more foreshortening than the other. You can choose to make either Alpha or Beta smaller or larger, that is up to you.
Step 3: The next step is to draw one of the two vertical ribs on the corner right or left. It is easiest to start with the side that has the least foreshortening. The place of this line has to be guessed, because as this is not a perfect sideview, the side of the cube will have some foreshortening (and thus appear smaller). To help judge these though, you can measure the length of the front vertical along your pen and then measure the horizontal distance between the two verticals. This should be somewhat less than the total height. The bigger the angle Alpha is in my drawing, the shorter the side will appear to be. Keep in mind that in the end, each side must appear to be a square in perspective.
Step 4: Next step is similar to step 3, now take the more foreshortened side and again, judge the horizontal distance between the lines.
Step 5: Now add the two 'horizontal' lines on top, this way you close the first two sides of your cube. Keep in mind the story about perspective I put up above. Step 4 and 5 are interchangable, you can start finishing one side before going on or you can do it the way I did it.
Step 6: Now finish the cube. Draw all the lines, even those which you can't see. This will be very usefull and even necessary in coming assignments. Again, take the perspective and vanishing points into account. As you can see, I made several mistakes in this drawing but instead of starting over or erasing parts, I simply drew another line to correct my mistake. At this point you might also find some of the points found by the crossing of perspective lines will not line up properly (see the rear vertical rib, it doesn't really end at the crossing of the two rear horizontal ribs at the top). This is fine, as making a perfect cube isn't easy. When you see this happen, try to make your own estimate and see where you can adjust the lines to correct it.
Step 7: This would be the result: a nice cube :) I toned one side with my C3 marker, just to punch out the shape a bit more. I also made the lines where the cube sits on the ground a bit stronger, as a sort of shadow. This works to make the drawing a bit more 3d. In this example you might already have noticed how important the training in line thickness and straight lines is.
http://i163.photobucket.com/albums/t291/yoitisi/Notcubes.jpg
The figure above is to show some examples of, well, not mistakes. But drawing a cube like one of those might give problems you don't want, so try to stay away from these if possible.
You may notice that I do draw the lines slightly longer than need be, and I also start slightly before the actual starting point I need. The reason for this is that it prevents you from doing the opposite. If you do not draw all the lines up to the point you want them to go, you lose information an clarity in your drawing. If you need for example the diagonal line on one of the sides of the cube, you need to make sure it passes through the right point. If you do not draw it through that point but stop somewhere before that, it doesn't always read very well where the line originally came from.I advise to always draw the lines all the way through and even a bit longer than that.
Another important aspect, draw big. This forces you to practice your lines etc. but also gives a better opportunity to correct your drawing withouth having to erase anything or start over. If you draw too small, the drawing will easily become full of lines that start to obscure the actual form you're trying to get across. Try to make all the drawings for this about handsize. This means aim for something roughly 15cm x 15cm.
Now, the first real assignment is for you to draw a couple of cubes. Take about 10-15 minutes for each cube, and make it a total of about 6-8 cubes on one sheet. They all have to be a cube, so no block shapes or anything, but cubes. Also, put a tone on one side like I did in the example nr. 7 (I'll explain more about shadow etc. later on). Then, when you're done with them, put a circle around the two you think are the best cubes. This way you also learn to judge your own drawing. To be delivered in this thread before Saturday 26th.
---------------------------------------------------------------------------------------------------------------------------------------------------------
Assignment 4: Cubes as a guide for construction
This is the follow up of assignment 3, as that one shouldn't cost you too much time. Now, we'll see that with only a simple cube we can already do quite complicated stuff. Part of drawing these constructions is actually very close to -if not just plain- mathematics.
Below you'll see how we go from a basic cube to a whole range of cubes in the same perspective. Funny thing I noticed, these cubes are all exactly the same, but when I put them in a row they seem to turn towards the viewer as you expect them to have the same vanishing point from left to right :)
The ability to draw straight thin lines becomes important in this assignment, as the construction requires a lot of lines and will quickly become unreadable if all your lines are thick. If you don't feel sure you'll be able to keep them all thin, try drawing the cube bigger so line thickness becomes less of an issue. Keeping the lines straight will become harder of course.
The reason for this exercise is that sometimes when you design something and start drawing it, you might need to find where certain points of your drawing are in space. You could guess them, and eventually you'll learn to do so, but it'll always be less sure than if you make the full construction. Drawing the shape into such a system of cubes is one way to do it (possibly the most difficult at that too). You won't use this construction very often, but it helps to create that feeling for where points are in space and in relation to one another.
http://i163.photobucket.com/albums/t291/yoitisi/Cubes1.jpg
Step 1: Start out with a simple cube. Take care that is has to be a cube and not a block shape, as this will make the construction less of use to measure proportions. If it turns out a block, it gets harder to show things like 'the object is twice as long as it is high' etc. Make the cube large, say 20cm x 20cm so as not to get problems later on.
Step 2: Now, devide the side surface into four squares. To do this properly in perspective, you need to first draw the diagonal lines in this surface. The thing with perspective is that the further away an object is, the smaller it gets. Therefore, the squares at the back should be smaller than at the front, which makes it harder to simply guess the middle. So, draw the diagonals and on the crossing of the two you'll find the middle of the cube. Now, draw the vertical and horizontal line in the surface (the horizontal one will be in perspective. To find it's direction without too much guessing, you might find it usefull to first divide the front rib in two. Since we use only 2 points perspective, this line appears without foreshortening and can therefore safely be divided into two equal halves. See point B in the drawing) Notice how line CD is longer than DE, while AB and BC are of the same length.
Step 3: Now do the same with the front surface. You might find that it already gets a bit difficult to distinguish the lines from each other as the start crossing and run over each other. This is sometimes inevitable, especially in a construction like this and might make it hard to find the right lines and points later on. Try to see through it. Also, sometimes if your lines don't end up real straight or just miss the corners, you'll have to adjust it a bit by eye. This, again is inevitable and require you to train your eye to see these things intuitively.
http://i163.photobucket.com/albums/t291/yoitisi/Cubes2.jpg
Step 4: Repeat the steps above until you've covered all sides of the cube, including top and bottom. Notice that if your point of view is too low on this one (i.o.w. angle Alpha and Beta are too small as seen in assignment 3) you'll have a hard time doing so in the top and bottom surface. We're almost done now, we just need a few more lines.
Step 5: Now devide the cube down the middle as well by drawing the three crosssections as seen in the last drawing above. You already got all the information you need to draw these surfaces from the construction on the sides of the cube, but to be on the safe side you can still add the diagonals as well to find the exact middle of the cube. As you can see, the construction has already gotten quite complex while we're still only talking about a simple cube. In the last figure of this assignment you'll see it gets much better readable again by applying some shading.
The above method is a construction from the outside in, and works well to minimize mistakes in the initial cube. Another method to draw the same figure is by starting out with a small cube and multiply it with the following constructing method. The problem here is that you also multiply any mistake in the original cube, so you might end up with a worse result than above.
http://i163.photobucket.com/albums/t291/yoitisi/cubemultiplyall.jpg
Step 1: Again, start out with a single cube. This time make the horizontal lines in perspective longer than really necessary, as you'll need the extra length later on. Now, divide the rear rib of the cube into two equal halves (point A). Since this line doesn't have any foreshortening, this should be eay :)
Step 2: Draw the diagonals through A from both point B and C. You actually only need one of those, as you'll see that line BD is much harder to get right (it's longer and if only you miss the right spot D the differences are much larger). Line CE is the most accurate as it minimizes any mistakes.
Step 3: Now you can draw the second cube behind the first with help of the point you just found.
http://i163.photobucket.com/albums/t291/yoitisi/Cubesshade.jpg
As you see in the image above on the left, putting some tone on the drawing immediately makes it much easier to read. This is an easy method to cover up any mistakes, or even to show one cube is missing! I did this by simply choosing to put shade on a different surface which I had already found by the earlier construction. Note that even while I originally constructed the whole cube, by putting the shade on the right spot you're able to make things in your drawing 'dissappear'. It is often important however to still construct the whole of the shape, as the lines I now do not use still tell a lot about the overall shape, even while they're not supposed to be there.
On the right you see the actual assignment: Start out by drawing the cube in the fist part, then substract one cube from the total as I just explained. Add another cube to the back or front, choose you're own side I'd say. And last, put another cube on top of it all. How to do that is up to you to find out (it's not difficult at all :P)
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Deadline on both is Friday 25 January.