This thread is for my mentees to post their work. If you're not one of my mentees but want to show your practice on these exercises or have questions, please check the Lurkers thread or general discussion thread.
Assignment 6: Cilinders again
Time to explain the pizza example from the last exercise As I mentioned in the thread of the assignment, something about the way a pizza is cut up and how we see it in the image tells us an important fact when drawing ellipses. To show it a bit more clearly I made the image above on the right. As you may notice, the midpoint where all the slices meet and the point where the major and minor axis of the ellipse meet are not in the same place. How did that happen? To show this isn't caused by a badly cut pizza or by my not-so-precise ellipse construction I made the following construction:
Step 1: Start out by drawing a circle again. Do this by first constructing the square, divide it using the diagonals and horizontal and vertical lines and draw in the circle. Try to get it as precise as you can because it's important to keep the construction as acurate as possible to get the best result.
Step 2: Draw the horizon somewhere above 3/4th of the height of the square and add a vanishing point in the vertical middle of the square. The horizon I drew is actually a little too low to get the best result here. The idea is that you now rotate the flat surface on the axis AB until it becomes a horizontal plane in perspective.
Step 3: This is where the construction becomes a bit tricky. You'll have to guess where the horizontal line comes that represents the front of the plane. The easiest way to this is by starting out to draw the small vertical squares on either side of the planes, as these are easier to judge. This is often where the construction goes wrong, especially if you're using a low horizon.
Step 4: Now complete the horizontal plane by using the diagonals to find the edge at the rear. Again, some precision is required, as these diagonals come in handy in the next step.
Step 5: In this step you need to find some points through which the ellipse that represents the circle on the horizontal plane goes. Four of the points that the initial circle shares with the square are easiliy found on the new plane. These are the midpoints of four lines that make up the square. To find some more, use the diagonals (remember, the small 1/3th part or 1/4 of the diagonal). To construct these properly though, drop a line from those points on the original circle down to line AB and use the line from the vanishing point trough the crossing of the previous vertical line and line AB. Sound complicated, but it is quite easy. Again, keep it as precise as you can.
Step 6: Now that we have more points that make up the ellipse, draw it. Make as much use of the points you found earlier as you can.
As you can see in the example above, several interesting things happen. The easiest thing to spot is that the ellips is wider than the initial circle! The explanation is simple though: things up front appear to be bigger than further away. The same happens here. The vertical circle is further away than the front of the ellipse, so it appear to be bigger. Note that it still is tangent to the edges of the horizantal plane at points A and B.
The other thing you may notice now is that the major axis is below the actual line AB. This means that the midpoint of the circle in perspective (the ellips) is not the same as where the major and minor axis cross each other. Again this is explained by the fact that in perspective things up front appear bigger than things further away. This means the front halve of the circle in perspective should be larger than the back part. See the pizza above, the same happens there.
(Note: the above construction rarely will be perfect. Mine has multiple little mistakes, but that doesn't change the point it tries to get across. If you'd make the same image with a CAD program you'll get the same result: the midpoint is above the major axis of the ellips -unless you look from beneath in which case it is below it )
To get back to the toilet paper exercise, what would the above mean for drawing it? Well, the most important lesson is that the inner ellips doesn't share the same major axis as the outter ellipse. Rather, the major axis of inner ellips is somewhere in between the real midpoint of the circle in perspective and the major axis of the bigger ellips. Also, the total height of the cilinder is still easier to set out with the two major axis as both the upper and lower ellips have the same displacement for the real midpoint.
I added some more information here that has little to do with the above but is still good to notice. The ratio of the width and height of the ellipse of the hole should be the same as the ratio of the bigger ellipse around it. Otherwise you'll end up with an oval-shaped hole in a cilinder like what happened a little in the lower ellips of my roll of toilet paper
The second part of the toilet paper roll exercise was to draw one lying on its side. Although there are several differences with a standing cilinder, some guidelines stay the same. The first thing is that it isn't necessary to first draw a square or block shape to find the ellipse inside it. I noticed a tendency to do so by students, and saw some of those as well in the last exercise. Apart from the fact that it only takes more time to set up, it also makes the drawing less accurate most of the times. This is because constructing a square in perspective is not a precise science to start with.
One of the things a cilinder on its side shares with the standing cilinder is the major and minor axis of the ellipse. The examples below show them in a in a couple of pipes and tubes.
The following steps explain how to create these on paper:
Step 1: Start out just like with the cilinder from assignment 5, only now make sure the central axis is at a angle with the horizon (for now, I suggest you keep the angle smaller than 45 degrees like my example. I'll explain some more about it later on). Add the major axis. Make sure this axis is perpendicular to the central axis. Unsurprisingly, the rules for a good ellips still apply: you should be able to mirror it in the two lines you just drew. Set out the points on the axis through which the ellipse should go.
Step 2: Draw the ellipse. If you're having trouble getting it right, remember to first draw it a couple of times in the air above your points to get your bearings before you put down your pen (while continueing the motion).
Step 3: Set out where you want the back of the cilinder to be. Draw the axis and points to guide the ellipse. Also, it might be easy to already draw the outlines of the cilinder as well, so you got some extra boundaries for the ellipse. Make sure to give the outline some perspective (they should go to the same vanishing point somewhere off the page). Also, the back ellipse should be a little wider than the front one. Much like horizontal ellipses which become flatter the closer to the horizon they are, the ellipses in this example 'turn away' from you and become more like a circle. Check the example below.
Step 4: Draw in the ellipse at the rear. Now you should have a drawing that already reads like a cilinder on its side. Note that it is still somewhat messy and not definit yet. The next two steps are to tighten it all up a bit.
Step 5: Get out your marker and start laying in some shade. For now, keep it below the central axis and do it just like the standing cilinder. When we get to shadow construction and all I'll explain some more about it. As you can see, here and there I choose to ignore my earlier sketchy lines to define the cilinder a bit tighter. This requires you to look sharply at your sketch to check which parts seem off.
Step 6: The last step is to make some lines heavier than others. It is better to do this at the end, as the marker sometimes messes with the fineliner ink if you made your lines to thick at the beginning. If I was to put some color on it as well, I'd save this step until after that as well.
There are several things you may have noticed which I did not cover yet. The most important part is how 'round' the ellips should actually be. During the lessons at my faculty I noticed one of the most common things to go wrong is that the ellipse either becomes too flat or too circular. The 'roundness' of the ellipse has got everything to do with the point of view. In the example below I attempted to show several different ways in which you can depict the cilinder.
In an earlier exercise I already talked about how we view objects in a more or less neutral manner. Instead of drawing situation 1 or 3 in the left image, it's better to take a point of view like that of 2. The reason for this is that it is often more informative than the other two options. Option 1 only shows at most 2 sides of the object, and if you show it head on it'll only show one side. 2 and 3 both show a maximum of 3 sides (front, side, top), but in option 3 the front side appears really flat again because you look at it from above (3rd vanishing point).
Since we opted for the 2nd position for clarity, the roundness of the ellips has a relation to the angle the central axis makes with the horizontal plane. In the left image, take a look at row 2. If we see it head on, the central axis is vertical and the ellips is almost a circle. The more we turn it to the left, the smaller the angle between the central axis and the horizontal plane becomes and subsequently the ellips becomes 'flatter'.
In the image above on the right I also put up an example why the ellipse at the back is more round than the one up front. Since the plane in which the ellipse is situated 'turns away' from us the more it is on the right or left from the center of our vision, the square actually becomes wider than the one up front because we see it more like a real square instead of in perspective. The same happens to the ellipse of course. Take care though, as this effect is countered by the fact that things become smaller further away. With an extreme perspective as in the example image, this makes the ellipse simply smaller rather than more round. In our case though, where we often choose not to have such an extreme perspective, the effect starts to play a bigger role.
After this new pile of dull theory it's time to get some practice in I suggest you try to get a couple of these cilinder on paper to get a feeling for them while I work on the real assignment for this week.
Last edited by yoitisi; February 23rd, 2008 at 08:42 AM.
Assignment 7: Cilinders and squares
Part of the assignment for this week will be to pushing the cube-construction to find the ellipse to its limits. The steps below explain how to begin with it, it's up to you to finish the construction. Don't panic if you get lost in your drawing because of the many lines or because the ellipses don't fit or whatever, that is the idea behind this construction anyway
Step 1: Start out by drawing a cube. Do this at a reasonable size, say 10-15 cm heigh. Also, try to get it as near as perfect as you can. Starting out with a shabby cube here will pose all kinds of problems later on in the construction you'd rather not face. Don't get stuck though trying to get a $100.000 cube, part of this construction is that you see what happens if your cube is a little off.
Step 2: In this example I'll only explain how to put a cilinder on one side, in this case the 'front' of the cube. Start out by drawing the diagonals to find the middle of this surface, as that is what will be the middle of the circle in that surface as well. Do the same on the surface at the opposit side of the cube, as you need this in the step 4.
Step 3: Draw in the points through which you know the ellipse will go. In this case, those are the A, B, C and D and the points on the diagonals as explained in assignment 5 (the points on the diagonalline from the middle to one of the corners, between 2/3rd and 3/4th of its length). I used a little trick here to show that if you got one of those points, you can draw the vertical lines and the lines following the perspective in this plane to find the other three. You could also try to measure them on the diagonals, which works just as well.
Step 4: Although with the points we found it is possible to draw the ellipse already. However, to find the direction or angle of the ellipse draw in the central axis of the imaginairy cilinder inside the cube and the major axis as well. For the major axis, remember that this line will be slightly in front of the exact middle of the square in perspective because of foreshortening.
Step 5: Draw in the ellipse. You can do this by building it up from connecting the points you found earlier, but I prefer it if you'd do it by keeping an eye on both the axis you laid in and the points through which it should pass. Draw it in the air a few times before putting down your pen, keep you're lines as thin as you manage and above all correct yourself while drawing the ellipses. It might seem like juggling with too many balls, but this is simply where drawing ellipses gets a bit harder because its position is already predefined by many points and guides. Aiming an ellipse is what requires training.
Step 6: I now added the outlines of the cilinder as well as a new major axis on the central axis closer to the viewer. As you can see in the next step, I mislaid the lower outline by drawing it a bit too low. Correcting while working on a drawing is very important, as is drawing with thin lines.
Step 7: After correcting the outline, I simply drew in the ellipse. I also made a couple of lines a bit thicker to make the final form a bit more clear. After this step, you could shade it with marker as the cilinders above if you like.
Now, after the last step, repeat the whole process for every side of the cube. That means you will have to draw six cilinders in total. The cilinders at the back and bottom might not be as visible, but draw them out completely as if the cube is transparent anyway. Applying some shade with the marker will show what is visible and what is not.
You've probably seen by now that not every ellipse in your cube fits perfectly. Sometimes however, you will need parts of the construction above to find certain shapes. There is an easier way to find this though. Remember the cube dividing method and the cube multiplying method? The next method is likewise. Instead of starting out with the outside construction and working our way in, here we start with the inside (the ellipse) and work towards the square around it.
To explain some of the ideas below, take a look at the circle on the left first. Since this is a circle in simple front view, drawing a square around it is easy. The sides of the square should be equal, the lines are perpendicular, the middle of each side should connect with the circle and the middle of both coincide. Easy. To translate this to a perspective view though is a bit harder. For one, the lines of the cube will no longer appear perpendicular, and the middle of the ellipse (the mathematical ellipse mind you) isn't in the middle of the square surface anymore. An important aspect that remains unchanged is the fact that the ribs of the square are still tangent to the circle (or ellipse). This is what we will use in the following steps to find a square around the ellipse.
Step 1: Start out with a horizontal ellipse. Make sure it follows the rules as explained in assignment 5 for drawing ellipses.
Step 2: Choose a direction. This can be anything, but remember to let it pass through the real middle of the circle in perspective and not through the crossing of the major and minor axis. Notice that the line you just drew is actually 1-3 or the line 2-4 in the example on the left. The choice you make here defines the perspective of your square around the ellipse.
Step 3: There are actually two ways to go about this, I'll explain the second in the next step-by-step example. Draw the line perspectively parallel to your first direction, but now on the spot where it will be tangent to the ellipse. Basically, keep the direction of the first line in mind and try to find where it'll touch the ellipse on the edge.
Step 4: Now do the same on the other side. Keep in mind that there should be some perspective in those lines, they should go to the same vanishing point somewhere off the page.
Step 5: Mark the spots where both the lines of the last two steps touch the ellipse and connect them. If you find one of the to be off (because your line doesn't pass through the middle) correct this.
Step 6: No do the same as in step 3 and 4 but now for the other sides of the square. Note that the direction you choose in step 2 determines the whole of the rest of the square you draw. You can draw any square around it you like by choosing a different direction.
The next assignment is to put the above theory in practice. We're going to divide a standing cilinder and a cilinder on its side into four quarters using the tangent lines (that is, I give an example of the first one and you draw them both ).
Step 1: Start out by drawing a standing cilinder. My apologies for the light lines, my scanner doesn't pick them up very well I'm afraid. Don't play around with linewheight too much just yet though, as that is something for the last step. The reason for the cup of coffee next to it is that you could of course divide the cilinder in four parts by using the central axis and a horizontal line trhought the middle of the circle in perspective on top. However, this becomes a central perspective drawing and doesn't convey as much information as a proper perspective drawing.
Step 2: Again, choose a direction by drawing a line throught the middle (which is a bit heigher than the horizontal major axis...).
Step 3: As we're going to separate the whole cilinder in four parts, it is easiest to start by cutting it in half already. Draw from the points where the directional line crosses the ellipse two vertical lines downwards and add the directional line in the bottom ellipse. As the vertical lines are probable somewhat inaccurate, keep an eye on the upper directional line while doing so to keep them in the same perspective.
Step 4: This is were we deviate a bit from the earlier example. Instead of taking the tangent lines in the same direction as the first line, use the point where the directional line crosses the ellipse. Through this point, draw the tangent line to the ellipse in that spot. It can be a bit more difficult than the earlier example, but in the end I think they're both as accurate. I personally prefer this method because it is a bit quicker, but find out for yourself what you like best
Step 5: Now you're ready to draw the second line that separates the upper ellipse in four equal parts. From here, the rest is easy.
Step 6: Repeat the process for the bottom ellipse. You coulde either first draw the vertical lines downwards and connect them or draw a new tangent line in the bottom ellipse to find the second directional line there. Basically, you've now divided the cilinder in four parts.
Step 7: To make the drawing a bit clearer, play around with the linewheight.
Step 8: The last step is to apply some marker tones to the whole. Not only did I add some tone to one side of the cut up cilinder but I also added some cast shadow to it. Feel free to copy it from my example, as we go into that in a later assignment.
Now for the next assignment of this week, I want you find out for yourself how to divide a cilinder that on its side into four equal parts. The theory is basically the same though. Take a look at the frontview below to see what it should like like when looked at from the front. The shaded area is the ground.
As an addition, design and draw me a coffee cup with a handle in perspective. That means not like the little 'blah cup' I drew, but with the handle turned towards or away from the viewer. Don't overstretch yourself on the design, keep it basic. You'll find you need the tangent line construction here.
So, for this week you have basically three assignments: draw the cube with the cilinders sticking out of it, draw the two cilinders and divide them into four equal quarters and draw a coffee cup with handle in perspective. Good luck, if you've got any questions feel free to ask.
Deadline: Saturday March 1
Last edited by yoitisi; March 1st, 2008 at 06:32 AM.
Ha well, uhm, I've been trying to get to work on the examples for the last exercise, but something else came in between I'm afraid. I will put it up this evening if all goes well, so stay tuned.
In the meantime, don't be afraid to show some of your practices in here already
Thanks for putting your time into making these assignments, must have been quite a work.
I don't quite understand step 5 so I did a bit of a guessing there.
Added the last part to the assignment for this week...finally. It's in the second post as it got too long to fit into one. The next assignment will be either shadow construction or designing and drawing wooden toys, have to think on that for a while
Enrigo: Your guessing of the points on the diagonals is correct I think, the only thing I'm really missing is step 6. You missed both points on the diagonals up front in the horizontal plane, which causes your ellispe to be a bit too slim. It should be wider. More importantly though, I miss the horizontal major axis of the ellipse which has nothing (or at least not much) to do with line AB.
I did finish the steps and when I read further I just noticed you mention that the ellipse should be wider that the circle.
I'll try it again a few times and look out for that.
I did try it a number of times but I always screw up badly half way down from inaccurate stroke.
These are the better ones I got, I don't know if the ellipse is actually too wide or not.
Should I continue with these exercises or stop for now and go back to the first line practices ?
Enrigo: This construction is mainly to get the point across that the middle of the ellipse is not the middle of the circle in perspective, and is quite hard to get perfect as I already said. I'd say continue with the rest of the assignment before going back to it. Some comments though: remember to keep the ellipse in the horizontal square Also, in both you made that square a bit too long (as in, the front horizontal should be a bit closer to the horizon. Accuracy is something I hope you pick up along the way, it simply takes some practice. If you feel that doing the first couple of exercizes will help, do them again yes. It might be helpful to practice some more ellipses as well. Anyway, don't forget to do the rest of the assignment for this week
I'm a little lost on how to find the guideline points for the protruding ellipse of the cube-cylinder one. I think the explanation on major-axis/central-axis gets a bit confusing
Done a few attempts at the first excerise and a few at the second but I wasn't at my computer for them so I might have followed the process wrong.
Try to get rid of that scribbley nature of my drawings, I think I lack the confidence in my lines - not had much luck as the circles that don't have scribbley lines have a poor form.
Edit - added missed off images.
Edit 05.03.08 - final images put up.
Last edited by D-Holme; March 5th, 2008 at 05:25 AM.
I'm up to the point where I need to replicate cylinders out for the other five sides of my cube. I know I'll have everything done by Saturday morning California time. I'm just noting here that Saturday is the 1st rather than the 2nd of March. Hope Saturday morning Pacific time will be OK.
And thanks for what must have been an enormous effort to make the assignment. My pitiful cylinders are shameful by comparison. You'll see.
Arttorney: Yep my bad, I forgot February had an extra day this year.
By the way, should I extend the deadline a bit? I realise the amount of work for this assignment might be a bit too much for a week, and seeing only three people actively involved at the moment I guess not everyone is finished yet.
Here is my training. I'll probably do some more excersizes. Having huge problems with my circles.
Had a lot to do at work this week so I hade not so much time to practice. I have a pad and pens att my desk at work. A customer wondered why I drew boxes all the time(I'm a coder) .
Opps... I am afraid that I would have to hand it late today due to my absent-mind. And also hope that there is scanner available in school, otherwise I will get it done tomorrow surely.
I think I'll leave it open for a couple more days, as I'm kind of bogged down myself at the moment. Still some people missing in here as well.
A general note, I think I'll put up some more to explain certain aspect in this weeks assignment, as I see not everyone picks it up as easily as I hoped Nothing to worry about, a lot of students here at the university never seem to get it even after three years of drawing classes so I didn't expect perfect results the first time around. However, since this is really imporant stuff for future drawings I think it's good that you all get them eventually.
Here's what I have so far. Drawing these complicate stuff is frustrating.
All right, sorry for the late submission.
I practiced a bit for a better result in drawing six cylinders with the cube, cause I guessed it would be a mess anyway.
I couldn't find the centres of ellipses in the back and button side cause all lines just got cross with each other... . And I found the end side of cylinder(away from the cube) is a bit difficult to define its guide line as well.
The coffee cup and the handle don't seem to go together, I think I messed up the perspective a bit.
Alright there seems to be some more work coming in I'll have some time tomorrow to put up some comments so stay tuned.
ok , all done!
the cup turned out a lot better than what i expected.
Last edited by pomegranate; March 5th, 2008 at 06:49 PM.
Just to comfort you all a bit: so far I haven't seen anything to really worry about at this point. Several errors occured by most of you, but that was to be expected and is, in fact, the reason I made you do these constructions. I wouldn't think you will ever have to do these ever again in your life but they hopefully give you some insight in the theory. This assignment should probably have the words 'Don't Panic' printed in bold letters on the back
As said, I should have some time tomorrow to comment and put up additional info on the construction methods.
Legato: Not a problem I know you're going through a busy period so take it easy.
Apologies to all for taking so long to comment in here and putting up a new assingment, I should get a bit better organized I guess. Check back in a couple of hours for something new
Great precision with the last few cylinders, pomegranate.
Any tips on drawing those ellipses.
Okay, high time for some crits in here. I'll start out with some general information, so I can point and grunt when talking about each of your efforts these two weeks
I'll start with a simple method that can help yourself to evaluate your ellipses in the future. This is by no means a way to go around in your drawings and draw it in, but try to keep it in mind when drawing and checking your drawings afterwards.
If you'd draw a perfect circle in a square, you'll see that the areas I shaded in the first drawing all have the same square surface. If this is not true, the drawing is either not a circle or the square isn't drawn right around the circle. This rule is very useful when evaluating your ellipses, as it still holds up in a foreshortened surface. The foreshortening does have a small influence, but not as big as it has on the depth/length of the square.
When drawing the tangent lines to the ellipse, and forming a square in perspective with them, you can check the whole by looking at those areas. If there are major differences in square surface you either misjudged the ellipse or you misjudged one or more of the tangentlines.
The following example is another rather common mistake:
Some of you mentioned to have problems with the whole axis-business. I hope this explains at least some of it.
When drawing ellipses on a square/blocky object, suddenly some of you start to use either the verticals of this block as a guide for the ellips. The result is that the cilinder looks like a variant of the little sideview I added.
What goes wrong is that the idea of Major and Minor axis has very little to do with the actual perspective of your drawing. Yes, the minor axis (which is the same as the central axis of the whole cilinder...yes I hate terminology as well) lines up with either the vertical of a standing cilinder or the perspective direction for a cilinder on its side. However, the Major and Minor axis stem from the whole mathematical explanation of what an ellips is.
This is actually the same as the previous problem, except it is a bit more common. Instead of keeping the Major axis vertical, as is always the case for a cilinder standing upright, suddenly the direction of perspective becomes the Major Axis and you end up with a pretty weird ciliner. In fact, it becomes an elliptical pillar instead of a cilinder (see the little top view).
In the last two examples above, the funny thing is that all of you are able to draw a good cilinder standing up and on its side, but when you're confronted with a combination of these cilinder with a cube you get confused. To gain some insight in your own drawings, it might be helpful to compare the drawings from the beginning of this assignment and the previous one with the drawings of the cube.
I hope the example drawings are clear enough, it's actually pretty hard to draw something the wrong way on purpose