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.