yoitisi
January 29th, 2008, 05:10 PM
Post here your results for assignment 5: Ellipses and Cilinders. This thread is for my mentees only, if you want to post your work but are not my mentee please go to the space for Lurkers.
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Assignment 5: Ellipses
Now that we have covered straight lines and cubes, it is time to start on some ellipses. As you probably know, circles in perspective turn into ellipses. Below you can see this in some everyday life situations:
291050291051291052
However, before we venture into all the fiddly bits of construction such objects, lets start by the actual drawing of ellipses.
The funny thing with ellipses is that you will find that drawing them is quite a natural movement for the arm. The important thing here, even more so than with straight lines, is to involve your whole arm into drawing the ellips, otherwise you end up with a flat pancake or even worse. Again, this has to do with the fact that the range of a wrist movement or an elbow movement simply doesn't allow for anything big.
Another important aspect of drawing ellipses is to draw several of them to form one complete ellips. If you only do one 'round', you end up with the top drawing in the figure below. This ellips has an open space on top because quite often when doing only one pass the two ends don't connect properly to form the total ellips. This might seem not too much of a problem, but once we start doing constructions with ellipses you'll see you miss a lot of information because of the open end.
The top ellips also doesn't allow for any correction while drawing it, as it is pretty much a single shot to get it right. Imagine you not only need to draw an ellips, but also have to put it in a defined space through predefined points. The best way to draw the freehand ellipses is by drawing it in the air for a couple of times first before you put your pen to the paper and when you do put your pen to the paper continue the same ellips about two or three times in one fluent movement (round and round and round :)). If you find the first round is a bit flat or has other problems, try to correct it on the go in the second round and so on until you feel the ellips is there. You see, the ability to draw thin lines is again very useful. Also, don't overdo it by going over it ten times, this will only make the lines thick and wonky. After three or four times you usually have the ellips right, if not you need to practise more (even true for me, my examples are a bit rusty here and there I'm afraid :P).
291049
You'll notice that no matter how wrong your first attempts were, the eye almost naturally picks the ellips out of the knot of lines. Overdoing the ellips counters this a bit as I said before. Also, going over it one more time to make a thick line from the right ellips often makes it look unnatural and wonky, as the quick movements of the inital cluster of ellipses create a much smoother image. I have gone over a couple of my ellipses in this assigment to make them stand out a little more, but you might notice they seem a bit wobbly already because of it. Leave it out for now I advise.
So, the first thing I want you to do is by taking a fresh sheet A3 size and start drawing as many ellipses as you can fit on it. Differ the angle of the ellipses, so not only horizontal ones as my examples above but do all kinds of angles. Try not to turn the paper though. Also, don't make them all as flat as above but experiment with more rounder ones up to full circles as well. Overlap and drawing through other ellipses is not a problem, the point is to do as many as you can to get a feeling for the movement. No need to post it either, as the rest of the assignment will prove how well you took it in.
Okay, now that you have some sort of feeling for drawing ellipses, it is time to throw in some science :) Nothing fancy, but it will be a huge help for drawing ellipses. An ellips is in fact a mathematical describable figure: a collection of points on a flat surface of which the distance to two points A and B (the total length of the lines AC + AB) is always the same. Might sound a bit official and all, but you might have heard of or seen the example of the two nails and a piece of string tied loosely between them. With this instrument it is possible to create a perfect ellips (see the figure below).
292439292440292441
There is one important thing, 'ovals' and 'ellipses' aren't the same thing. Ovals are made up of parts of circles, while ellipses don't actually have anything of a circle in them. Also, ovals aren't always symetrically, an important aspect of ellipses as you'll see in the next paragraphs.
292438292436
As you can see in the figure above, ellipses are symetrical in two directions: the upper and lower half and the left and right part are symetrical. This follows from the mathemathical description of an ellips and can probably be proven scientifially, but for now I think you can just believe this.
The important aspect you have to get from this is the vertical and horizontal line. These will be a huge help for drawing the ellips later on. Please note that these two lines are always, no matter what, perpendicular to each other. Even if the cilinder is rotated, drawn on its sides, whatever. Other points that may be of help later on are the points where the ellips intersects the diagonal lines as seen in the figure below:
292437
The upper image here is a circle (or as much a circle as I could manage at the moment :P). Notice the intersection where circle meets the diagonals AC and BD, this is roughly a small third of the line A1 in the drawing, measured from the corner. About 3/4 is also fine, in the end it's mainly about checking whether your ellips is more or less right.
The drawing above is actually the second part of the assignment: draw two long vertical lines, roughly the length of your sheet of paper, and in between first create a square (make it a perfect square, measure the distance between your two verticals with your nail on the length of your pen) and draw a circle in there. Doing this in one go is sometimes hard, especially since we're drawing big here, so it might be handy to draw it in quarters. Make sure the end result is a circle though, and I advise you to only do this with full circles as ellipses are far easier the other way.
Then, underneath this, draw rectangles of declining height (check the example) and start drawing in the ellipses and its corresponding points. Try to draw the ellipses the way I told it in the first part of this assignment.
The above is actually still the basics of ellipses but doesn't really tell you how to use them in cilinders and all. The next step by step description will explain something about that. We will start out with a simple cilinder that stands on it's bottom (or top) surface, as these are easier to start with.
295852
Step 1: Start out by drawing the two dividing axis as described earlier. Make it handsized, so the vertical line is about 15cm. The vertical axis has two functions here, the first being it divides the ellips in two equal halves, the second is that it is the central axis around which your whole cilinder will revolve around. There's a little snag here which I'll explain later on. On the two axis, set out the points already through which the line of the ellipse will go (again using the information I described above).
Step 2: Draw the ellipse. As you can see, my first two attempts only managed to touch a couple of point while missing others completely. The third is still off mark here and there. This is not a problem, somewhere in there is the right ellips. Don't stop during the drawing of the ellipse but continue to make the full turn two or three times.
Step 3: Now add the axis for the ellipse on top. Also, add the outlines of the cilinder already. This makes it easier to aim the ellipse than by having to aim for only two points. I also already added the points on the vertical axis. I chose the distance between those points slightly smaller than the bottom ellips, as flat surfaces closer to the horizon appear more flat (when on the horizon they appear as a line only). Don't overdo it though, this cilinder isn't huge so the horizon is well above the edge of your paper, so the difference in the two ellipses isn't all that big.
Step 4: Now draw in the top ellipse. Again, don't try to do it perfect the first time around, but give it a few goes. Also, hitting all the points isn't a holy task, getting an ellipse that looks like an ellipse is more important here :) Basically, what you have now is a cilinder. However, some more work is needed to make it read like one for everyone.
Step 5: Again you'll see that using some variance in line wheight is quite useful. I made the bottom line where the cilinder stands on the ground a bit thicker as the connection with the ground often isn't a neat fit. Also, note that I didn't stop the line at the horizontal axis but continued a bit 'around the corner'. This is to prevent yourself from giving the ellips a pointy end. I also made the vertical outlines a bit thicker. This isn't always necessary but in this case helps to set it apart from the surroundings. The top ellips doesn't recieve any extra attention, see the next step.
Step 6: Now add some shade. To do so with a marker, we face a problem. Markers don't really allow you to make a nice gradient unless you have the whole range of grays from 0 to 10. Even if you posses these, we're not going to use that yet. The reason is once again speed. Opening and closing all of your ten markers to get a gradient on something cheap and simple as this cilinder just isn't worth it. Therefore, we only use one gray (mostly I use the C3 of Copic for this, just don't use anything too dark yet). As you can see, I filled in a shade on one side of the cilinder and added a small stroke next to it to suggest a gradient there. This is a shortcut for markers, when doing this with pencils or on the computer feel free to make a nice gradient. We're almost done now, there's only a couple more things to point out here.
295853295854
In the figure above I added a couple of things. The most important aspect is the 'core shadow' (I'm aware this sounds like nuclear stuff, but that's the best translation I can come up with :P). Once the first layer of marker was almost dry -almost but not completely so the second layer gets to blend a bit with the first- I added another stripe of shade just a small distance from the outline of the cilinder. Two layers of the same marker gives a darker result. The reason for this is bounce light from the surrounding, which often makes the outline a bit ligther again. This doesn't necessarily always happen, but works well to sell this as a cilinder. I also made the cilinder hollow by adding a shade on the inside and by playing around with the linewheight again. Notice that this is a great way to correct earlier mistakes in the cilinder. You might notice the weird shape of the shade on the inside, this will be explained when we get to shadow construction later on.
The image to the right is a summary of some important terminology and info about cilinders. I suggest you try out a couple of them to get a feeling for it.
The image to the right is a summary of some important terminology and info about cilinders. I suggest you try out a couple of them to get a feeling for it.
Something you might have been missing with the cubes as well is the use of the horizon and vanishing points. I mentioned them as something you have to keep in mind while drawing the objects but not draw them. The reason for this is basically speed and complexity. While you could draw the horizon and vanishing points and neatly connect all the lines with them, this won't really help you in the end as it takes too long and when drawing a complex object it will become messy rather fast. Another reason is scale. Although you might not be aware of this consciously, most of the time you look at the world at eye height. In your drawings, this means the horizon is often around 1.7 meters from the ground. If we would draw a cilinder in this perspective with horizon and all (see below) we would easily end up with something rather bigger than you want.
295874
Check the figure standing next to it. Now imagine a little can standing at his feet. Now imagine drawing just that can with horizon and vanishing points on a single sheet of paper. You would end up with a lot of horizon and empty space and a rather small can somewhere at the bottom of the page. Of course, when zooming in on an object the horizon isn't at 1.70 meters from the ground and the vanishing points shift etc. etc., but it helps to draw things in the old perspective to convey the cilinder isn't as big as a castle tower.
In the assignment of next week you'll see that as soon as you've drawn the ellips, you can actually extrapolate the vanishing points and direction of perspective from it without having to draw them.
For now, the real assignment for this week is a small one, but combined with the ellips exercises above I think you've enought to do for now. The assignment is to draw me three rolls of toilet paper (see below :D). Draw two of them as standing on the flat side, the other one has to be lying on its side. You might want to do this from life, so you could make a sort of still life if you like. Make the cilinders and not the wobbly shape some of the real life toilet paper rolls have though. You don't have to add all the details either, it's about the cilinders here.
I didn't explain yet how to draw a cilinder lying on its side, but if you paid attention you might already know how to do so. Next week I'll explain more about it, but I want to see how you all tackle it. Also, there's another snag which I didn't tell yet, again I'll explain later on. The pizza below might give it away actually if you look at it more closely :)
295875295876
Deadline: Monday February 11
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Assignment 5: Ellipses
Now that we have covered straight lines and cubes, it is time to start on some ellipses. As you probably know, circles in perspective turn into ellipses. Below you can see this in some everyday life situations:
291050291051291052
However, before we venture into all the fiddly bits of construction such objects, lets start by the actual drawing of ellipses.
The funny thing with ellipses is that you will find that drawing them is quite a natural movement for the arm. The important thing here, even more so than with straight lines, is to involve your whole arm into drawing the ellips, otherwise you end up with a flat pancake or even worse. Again, this has to do with the fact that the range of a wrist movement or an elbow movement simply doesn't allow for anything big.
Another important aspect of drawing ellipses is to draw several of them to form one complete ellips. If you only do one 'round', you end up with the top drawing in the figure below. This ellips has an open space on top because quite often when doing only one pass the two ends don't connect properly to form the total ellips. This might seem not too much of a problem, but once we start doing constructions with ellipses you'll see you miss a lot of information because of the open end.
The top ellips also doesn't allow for any correction while drawing it, as it is pretty much a single shot to get it right. Imagine you not only need to draw an ellips, but also have to put it in a defined space through predefined points. The best way to draw the freehand ellipses is by drawing it in the air for a couple of times first before you put your pen to the paper and when you do put your pen to the paper continue the same ellips about two or three times in one fluent movement (round and round and round :)). If you find the first round is a bit flat or has other problems, try to correct it on the go in the second round and so on until you feel the ellips is there. You see, the ability to draw thin lines is again very useful. Also, don't overdo it by going over it ten times, this will only make the lines thick and wonky. After three or four times you usually have the ellips right, if not you need to practise more (even true for me, my examples are a bit rusty here and there I'm afraid :P).
291049
You'll notice that no matter how wrong your first attempts were, the eye almost naturally picks the ellips out of the knot of lines. Overdoing the ellips counters this a bit as I said before. Also, going over it one more time to make a thick line from the right ellips often makes it look unnatural and wonky, as the quick movements of the inital cluster of ellipses create a much smoother image. I have gone over a couple of my ellipses in this assigment to make them stand out a little more, but you might notice they seem a bit wobbly already because of it. Leave it out for now I advise.
So, the first thing I want you to do is by taking a fresh sheet A3 size and start drawing as many ellipses as you can fit on it. Differ the angle of the ellipses, so not only horizontal ones as my examples above but do all kinds of angles. Try not to turn the paper though. Also, don't make them all as flat as above but experiment with more rounder ones up to full circles as well. Overlap and drawing through other ellipses is not a problem, the point is to do as many as you can to get a feeling for the movement. No need to post it either, as the rest of the assignment will prove how well you took it in.
Okay, now that you have some sort of feeling for drawing ellipses, it is time to throw in some science :) Nothing fancy, but it will be a huge help for drawing ellipses. An ellips is in fact a mathematical describable figure: a collection of points on a flat surface of which the distance to two points A and B (the total length of the lines AC + AB) is always the same. Might sound a bit official and all, but you might have heard of or seen the example of the two nails and a piece of string tied loosely between them. With this instrument it is possible to create a perfect ellips (see the figure below).
292439292440292441
There is one important thing, 'ovals' and 'ellipses' aren't the same thing. Ovals are made up of parts of circles, while ellipses don't actually have anything of a circle in them. Also, ovals aren't always symetrically, an important aspect of ellipses as you'll see in the next paragraphs.
292438292436
As you can see in the figure above, ellipses are symetrical in two directions: the upper and lower half and the left and right part are symetrical. This follows from the mathemathical description of an ellips and can probably be proven scientifially, but for now I think you can just believe this.
The important aspect you have to get from this is the vertical and horizontal line. These will be a huge help for drawing the ellips later on. Please note that these two lines are always, no matter what, perpendicular to each other. Even if the cilinder is rotated, drawn on its sides, whatever. Other points that may be of help later on are the points where the ellips intersects the diagonal lines as seen in the figure below:
292437
The upper image here is a circle (or as much a circle as I could manage at the moment :P). Notice the intersection where circle meets the diagonals AC and BD, this is roughly a small third of the line A1 in the drawing, measured from the corner. About 3/4 is also fine, in the end it's mainly about checking whether your ellips is more or less right.
The drawing above is actually the second part of the assignment: draw two long vertical lines, roughly the length of your sheet of paper, and in between first create a square (make it a perfect square, measure the distance between your two verticals with your nail on the length of your pen) and draw a circle in there. Doing this in one go is sometimes hard, especially since we're drawing big here, so it might be handy to draw it in quarters. Make sure the end result is a circle though, and I advise you to only do this with full circles as ellipses are far easier the other way.
Then, underneath this, draw rectangles of declining height (check the example) and start drawing in the ellipses and its corresponding points. Try to draw the ellipses the way I told it in the first part of this assignment.
The above is actually still the basics of ellipses but doesn't really tell you how to use them in cilinders and all. The next step by step description will explain something about that. We will start out with a simple cilinder that stands on it's bottom (or top) surface, as these are easier to start with.
295852
Step 1: Start out by drawing the two dividing axis as described earlier. Make it handsized, so the vertical line is about 15cm. The vertical axis has two functions here, the first being it divides the ellips in two equal halves, the second is that it is the central axis around which your whole cilinder will revolve around. There's a little snag here which I'll explain later on. On the two axis, set out the points already through which the line of the ellipse will go (again using the information I described above).
Step 2: Draw the ellipse. As you can see, my first two attempts only managed to touch a couple of point while missing others completely. The third is still off mark here and there. This is not a problem, somewhere in there is the right ellips. Don't stop during the drawing of the ellipse but continue to make the full turn two or three times.
Step 3: Now add the axis for the ellipse on top. Also, add the outlines of the cilinder already. This makes it easier to aim the ellipse than by having to aim for only two points. I also already added the points on the vertical axis. I chose the distance between those points slightly smaller than the bottom ellips, as flat surfaces closer to the horizon appear more flat (when on the horizon they appear as a line only). Don't overdo it though, this cilinder isn't huge so the horizon is well above the edge of your paper, so the difference in the two ellipses isn't all that big.
Step 4: Now draw in the top ellipse. Again, don't try to do it perfect the first time around, but give it a few goes. Also, hitting all the points isn't a holy task, getting an ellipse that looks like an ellipse is more important here :) Basically, what you have now is a cilinder. However, some more work is needed to make it read like one for everyone.
Step 5: Again you'll see that using some variance in line wheight is quite useful. I made the bottom line where the cilinder stands on the ground a bit thicker as the connection with the ground often isn't a neat fit. Also, note that I didn't stop the line at the horizontal axis but continued a bit 'around the corner'. This is to prevent yourself from giving the ellips a pointy end. I also made the vertical outlines a bit thicker. This isn't always necessary but in this case helps to set it apart from the surroundings. The top ellips doesn't recieve any extra attention, see the next step.
Step 6: Now add some shade. To do so with a marker, we face a problem. Markers don't really allow you to make a nice gradient unless you have the whole range of grays from 0 to 10. Even if you posses these, we're not going to use that yet. The reason is once again speed. Opening and closing all of your ten markers to get a gradient on something cheap and simple as this cilinder just isn't worth it. Therefore, we only use one gray (mostly I use the C3 of Copic for this, just don't use anything too dark yet). As you can see, I filled in a shade on one side of the cilinder and added a small stroke next to it to suggest a gradient there. This is a shortcut for markers, when doing this with pencils or on the computer feel free to make a nice gradient. We're almost done now, there's only a couple more things to point out here.
295853295854
In the figure above I added a couple of things. The most important aspect is the 'core shadow' (I'm aware this sounds like nuclear stuff, but that's the best translation I can come up with :P). Once the first layer of marker was almost dry -almost but not completely so the second layer gets to blend a bit with the first- I added another stripe of shade just a small distance from the outline of the cilinder. Two layers of the same marker gives a darker result. The reason for this is bounce light from the surrounding, which often makes the outline a bit ligther again. This doesn't necessarily always happen, but works well to sell this as a cilinder. I also made the cilinder hollow by adding a shade on the inside and by playing around with the linewheight again. Notice that this is a great way to correct earlier mistakes in the cilinder. You might notice the weird shape of the shade on the inside, this will be explained when we get to shadow construction later on.
The image to the right is a summary of some important terminology and info about cilinders. I suggest you try out a couple of them to get a feeling for it.
The image to the right is a summary of some important terminology and info about cilinders. I suggest you try out a couple of them to get a feeling for it.
Something you might have been missing with the cubes as well is the use of the horizon and vanishing points. I mentioned them as something you have to keep in mind while drawing the objects but not draw them. The reason for this is basically speed and complexity. While you could draw the horizon and vanishing points and neatly connect all the lines with them, this won't really help you in the end as it takes too long and when drawing a complex object it will become messy rather fast. Another reason is scale. Although you might not be aware of this consciously, most of the time you look at the world at eye height. In your drawings, this means the horizon is often around 1.7 meters from the ground. If we would draw a cilinder in this perspective with horizon and all (see below) we would easily end up with something rather bigger than you want.
295874
Check the figure standing next to it. Now imagine a little can standing at his feet. Now imagine drawing just that can with horizon and vanishing points on a single sheet of paper. You would end up with a lot of horizon and empty space and a rather small can somewhere at the bottom of the page. Of course, when zooming in on an object the horizon isn't at 1.70 meters from the ground and the vanishing points shift etc. etc., but it helps to draw things in the old perspective to convey the cilinder isn't as big as a castle tower.
In the assignment of next week you'll see that as soon as you've drawn the ellips, you can actually extrapolate the vanishing points and direction of perspective from it without having to draw them.
For now, the real assignment for this week is a small one, but combined with the ellips exercises above I think you've enought to do for now. The assignment is to draw me three rolls of toilet paper (see below :D). Draw two of them as standing on the flat side, the other one has to be lying on its side. You might want to do this from life, so you could make a sort of still life if you like. Make the cilinders and not the wobbly shape some of the real life toilet paper rolls have though. You don't have to add all the details either, it's about the cilinders here.
I didn't explain yet how to draw a cilinder lying on its side, but if you paid attention you might already know how to do so. Next week I'll explain more about it, but I want to see how you all tackle it. Also, there's another snag which I didn't tell yet, again I'll explain later on. The pizza below might give it away actually if you look at it more closely :)
295875295876
Deadline: Monday February 11
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