This thread is reserved for assignments. I like to gather them in one thread so that later on this thread can be read as a sort of walk through of what we did/do in here. I'll post each assinment in a new post in here, and create a thread for each assignment in the main Island area for you all to post your work in and for me to comment on it.
So, what can you actually expect of me and this thread? As I already said, I will be teaching along the method we use at my study, Industrial Design Engineering at Delft UT. We use it to teach students a way to put their ideas on paper so they can communicate this to others. A lot of first years have never actually touched a pencil in years, so we start at the beginning of beginnings. This might mean that some of the things I tell in here are things you already know, but then again this might not be the case . Anyway, it is always good to repeat the basics.
It also means that the first few exercises aren't about spaceships or monster trucks. Far from it, in fact. However, getting these basics down is vital for the rest of the course, so hang tight. I am willing to spent some time on this every week, so I expect you to do the same. In everyday live, I get paid for doing this so I hope you realise what I'm offering here.
A small disclaimer: some of the things I'll say in here might seem contradictionairy to what you already might know or are short-cuts to get to a certain result. The reason for this is often speed or simplification, as ID drawings are sometimes more about getting the idea across than making the best rendering of it. If you've got any remarks, comments or questions about what I say, I encourage you to say it out loud. I'm not all-knowing, nor am I too proud to correct myself if proven wrong. Discussion is just another way of learning.
Below I added a list of the topics I want to go cover in these assignments. I am a little unsure yet what the exact order is in which we did this for the firsts years here in Delft, so this list isn't final and I might modify it when things develop, but for now it'll provide a quick overview so you can see where we'll end up.
Assignment 1: Straight lines and line wheight. Assignment 2: Perspective
Assignment 3: Cubes Assignment 4: Cubes as a guide for construction
Some theory 1: Drawing without a ruler and no eraser Some theory 2: Them markers and how to handle them
Assignment 5: Cilinders
Assignment 6: Shadow construction 1 Assignment 7: Shadow construction 2
Assignment 8: Constructing from life - Rietveld chair (if I can find a good example that is )
Assignment 9: Combining cubes and cilinders - Wooden Toys (again, if I can find some good reference for this) Assignment 10: Wooden Toy with side- and front view
Assignment 11: Central (1 point) perspective - a room
Assignment 12: Roundings Assignment 13: Toasters! Yay finally a product
Assignment 14: Cilinder constructions Assignment 15: Tubes and Pipes
There's more to come, I just need some more time to think it through.
As said, we'll start with the very basics. These first couple of exercises are very important though, as they form the start of what is to come.
The first thing I want you to do is start practising drawing straight lines without a ruler. I can immediately see when people start using a ruler, and although it is a very usefull tool at times I don't want to see it yet. Practising straight lines might sound dull, but it improves several things you might not immediately realise.
The most important thing is it simply trains your control over your own arm and wrist movements. The more you do it, the better your control will be. This will also improve the 'confidence' of your lines, something you;ll develop naturally after a while if all goes well. A third effect is that it will train the eye, as long straight lines are not always easy, getting them from a certain point A to a point B is even more difficult. Training is key, so I suggest you keep practising the following exercises for now.
Allright, now for the exercises. The first thing I want you to do is to take a page of A3 format paper and start by drawing two horizontal lines at the top of it, some 10 cm apart. Then, start drawing straight vertical lines between those lines, as much as fit on the width of your page. Your basic training in drawing long straigth lines.
Then, draw two horizontal lines again on the remainder of the page with as much space between them as is left, place a couple of dots on each line and start to connect them randomly. This is the A to B part of drawing straight lines, and you might find it helpful to first draw the line you want to put on the paper a couple of times in the air to get the direction.
Basically, the trick for drawing straight lines is to start using your whole arm when drawing instead of your wrist or elbow. Also, don't grab your pen or pencil to close to the point, as this will often make you press to hard on the paper and start drawing from the wrist again.
See the figure below for an example (on scale )
The second practicing example is to draw the following 'star'. Start by drawing one line, draw a second trough it at an angle and repeat this process until you have a star. Make sure all the lines pass through the same point, it trains your accuracy. The important thing is to do this without turning the paper, as you will find out some lines are more difficult to draw than others. For me, as a lefty, the line from A to B is the easiest and most natural to do while the line from C to D is way harder and goes often wrong. To counter this I turn the page a lot when drawing things, but for now I ask you not to do it because it makes this practice less effective.
Below are some things to consider when doing the above practices. The first is to show how to draw the lines and how not to. Draw lines in one go, even if this means you have to do it twice over. It'll often still read better than the line next to it, which is build up out of small pieces of lines. Especially if you need to make complicated constructions, which we will do later on, the second line will easily make your image full of thick lines that make it unreadable and crude.
The second image is to show what different line wheights you can get by simply changing the amount of pressure you put behind the strokes. For the real thin ones, my fineliner barely touched the page, while for the real thick ones I pressed harder to get more ink on the page. All those lines come from the same fineliner.
You don't have to put those exercises up here actually, as they are just practice for yourselves. You may if you want, but tomorrow I'll put up something I do want you to post here which will show me how well you took in the exercises from above anyway. I encourage you to do them regularly the first week or so, as it will prove very usefull later on if you got this down.
Next part is perspective. I assume most of the basics are known, but I will mention them nonetheless as these first assignments will be something for me to point at later on.
Perspective is basically right in front of your eyes. Look at anything and you'll see it. However, you might not realise what you actually are seeing, because the human brain doesn't think in such abstract rules as shown here. So, where to start. Well, one of the basics is the horizon. Together with vanishing points, these form the basis of perspective theory.
The first image on the top left shows where the horizon in most of the cases you'll encounter is in a photograph or drawing: at eye-height. I put it at 1,7 meters (I have no idea what it is in a non-metric system, I'm sorry) because that is about the average height of a human being. The vanishing point here is right in front of you. The closer an object is to you, the bigger it appears. Check the humans and lantern poles, they all have corresponding points on a line from the vanishing point towards the viewer. Something else that happens is foreshortening, which I will explain in a minute.
The second drawing on the top right shows actually the same, I just made a blockshape on the guidelines instead of a row of lantern posts. Also included a fence, human and some clouds and there you have a simple environment. This type of perspective is called 1-point perspective.
The third image on the bottom left is called 2-points perspective. The basic principle is the same, except that we are now looking at a block shape thats twisted so that we don't look at just the front anymore, but actually see three sides of it. Instead of using one vanishing point, two vanishing points are used. They're still on the horizon, but you're free to choose how far they are from each other and from the middle (except that one has to be to the right of the middle or in the middle, and the other has to be to the left of the middle or in the middle -both in the middle is 1-point perspective again ) This type of perspective is mostly used for ID drawings, as well as a whole range of other types of art. Realise though, that it still is a simplyfication of reality, as I'll show in the next image.
The last image on the bottom right shows perspective more close to reality. Instead of just two points on the horizon, there are also two other points of perpective on the vertical line through the middle of your eyesight. This might sound and look weird, because there is something happening where the vertical lines of the block above the horizon and the one below it connect with each other. Instead of a nice straight vertical line, these lines should actually be curves! Why don't we draw it like that you might wonder? Well, because our eyes are set in a horizontal line we tend to see the perspective in horizontal lines better than the perspective in vertical lines. While these lines should be curved, we represent them with vertical lines in 2d drawings because it simply looks better and more realistic (weird but true, this is one of those short-cuts). In photographs you can sometimes see these vertical lines become curved above and below the horizon, but nowadays most cameras have something to counter this effect.
Edit: Actually, there's a lot more to that last perspective than I tell here, check out this link: Perspective Tutorial
However, the name might already tell you something, we do sometimes use a 3-points perspective. This is best visible in photographs taken out of a helicopter above a big city, where the third vanishing point theory is very clearly visible. This is often used to make the product you draw appear to be really huge (large buildings etc) or to give it a bit more dynamic feel (often used in automotive drawings or anything with some speed). For now, we will not use this though.
Should you always draw a horizon and vanishing points for your drawing to be right? The answer is no, because quite often the object is quite small and doesn't look right if you draw it with much perspective. I put the above up so you have a reminder of the basic idea of perspective. The image below is what often works well enough.
As you can see, there is some perspective going on here while I didn't draw any vanishing points or horizon. As long as you imagine there being a vanishing point somewhere on the horizon and realize that all the lines have to converge to that point you should do fine without them. I used the a sort of mathematic annotation here (the arrows on the lines) to show which lines go to the same vanishing point. Note that I didn't use a third vanishing point, all vertical lines stay vertical. Also, I draw the block completely transparent, meaning you can actually see all the lines that make up the shape. This is very important, because it provides information for any further constuction lines.
I suggest you experiment a bit with these perspective drawings, so you get familiar with them. Draw a couple of those block shapes for example. I still have to put up a real assignment I'm afraid
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 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.
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.
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.
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.
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.
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.
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.
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 )
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:
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 ).
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).
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.
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:
The upper image here is a circle (or as much a circle as I could manage at the moment ). 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.
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.
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 ). 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.
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.
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 ). 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
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.
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.
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.
Alright time to move on to the next topic: shadows and shadow construction. This assignment will handle how to find out what the shadow of an object looks like and how to construct it in a quick and easy way.
The theory behind shadow construction is actually pretty simple and can be explained solely by the example below. Any shadow construction of a more complex form works in the same way, but of course there are tricks, shortcuts and pitfalls when it comes to drawing the shadows. I'll explain the most important ones further up in this assignment.
One note on beforehand, this assignment will deal with pretty basic settings. No difficult lighting schemes with multiple lights, nothing fancy on fading out and bounce light etc. For that sort of thing I suggest you do some study from life. This assignment deals with the very basis of shadow construction and how to get an effective shadow in a quick way.
Once again, a step by step on how to get a nice and controlled shadow. We take a simple example to start with: a vertical pole (or stick or line - check the schematic version below the actual pole).
Step 1: Start out by drawing the actual stick or fencepole or whatever you like that looks somewhat like the example above.
Step 2: Now, introduce a lightsource. In this case, pick a spotlight (meaning, a single point in space that emits light in all directions). Notice that by drawing only the lightsource there are still a lot of possibilities left open on where the bulb actually is in respect to our fencepost.
Step 3: To determine where the lightbuld is, draw a vertical line to the ground and a line through where the vertical hits the ground and through the base of the fencepost. This can be anywhere you want, in this case I chose one that'll give a nice shadow on the ground. Play around with it if you like to find out what works and what doesn't. The line on the ground is called the 'projected light direction', as it shows on the floorplane the direction of your lighting. The vertical is to show how high the lightsource is in respect to your product.
Step 4: Now add the lightbeams that hit the top and bottom of the fencepost. The bottom one in this case isn't really necessary, but comes in handy if the post was actually floating.
Step 5: Where the lightbeam the hit the top of the post crosses the projected lightdirection is where the shadow ends. I added the thickness of the shadow already as the fencepost isn't a real one dimensional thing in space but has shape and thickness as well. For clarity you might want to check out the example below it.
For the rest of the examples in this assignment, keep the lower construction of the above example in mind. The next one uses it in basically the same way, only now it is two of those fenceposts connected with each other so the whole forms a plane (I made it a fence out of wooden planks ).
Step 1: As with the fencepost, start out with drawing the actual object first. Whatever you want to make of it, keep it a simple plane like the lower case above.
Step 2: Again, introduce a lightsource.
Step 3: As with the fencepost, determine where you want your lightsource to be. In this case I opted for it to be in the center front of the plane, but you might want to play around with this a bit more.
Step 4: Draw in the projected light direction and the lightbeams the pass trought the topcorners of the plane. Connect the two points you find in this way (the two points where the lightbeams cross the projected light direction).
Step 5: Marker in the shadow. As you see, I did make it fade out a bit the further away it is from the object. You can try to do this with markering it already, but since we haven't really gone into markering techniques yet you can also try it with either a white or a black pencil.
So far, we've only used point lights. While they give a decent shadow, they also have certain drawbacks that can be avoided. The most important drawback is the fact that the shadow is always a bit warped with respect to its origine, because the projected light direction diverges from its source. This both makes the shadow look exagarated and larger than needed (in the examples above the shadow is almost as big as the actual object). The problems I just mentioned can be countered somewhat by placing the lightsource further away from the object or by putting it higher from the ground, but the best solution is to use parellel lightbeams (meaning, placing the lightsource an infinite distance away - basically sunlight )
In the example above, the first one on the left is point light while the second on the right uses a light source with parallel light beams. As you can see, the second one looks less messy and doesn't distract as much from the actual object as the first one. You no longer need to determine a lightsource and where it exactly is in respect to the object, all you need to choose is the angle of the light and the direction of the projected light direction. Again, this decision is up to you.
In all of the following examples I'll be using the parallel light beams to construct the shadow, as it saves some work and marker inkt. Now that we've had simple sticks and planes, let's try a 3 dimensional shape. The cube is a nice subject for this
Step 1: Nothing new, draw a cube to begin with. Note that I already played a bit with linewheight by making the lines which touch the ground a bit heavier.
Step 2: You can wait with this step until you marker the shadow as well, but as there's something to say about it already I put this step in second place. Why do we put shading on one side of the cube? The reason is that although you could opt for a light setting where each of the sides get an even amount of light, this doesn't help explain the shape. It's better to get as much difference in the different sides of an object as possible, as it will convey the shape stronger and makes it more readable for the viewer. Therefor, its best to have one side with shade. The little top view of the situation (image 2a) shows how the lighting works; the lower corner is closest to the eye while the light comes from 'over your shoulder').
Step 3: This step is basically four times the fencepost example: draw in the projected light direction for all four corners of the cube. Chose a direction the fits with the shading, in my example that is the light comes from the left.
Step 4: Now add the actual light direction on all the four corners of the top plane of the cube. It might be handy to mark where these lines cross the projected line direction as especially with complex objects it'll get messy real quick if you don't.
Step 5: Connect the dots and marker the shadow
Step 6: This is actually not a separate step, but an observation on the shadow you have drawn for the cube. If done well, you should see that the line AB of the shadow corresponds to the same vanishing point of line ab of the cube (they are parallel in perspective). The same goes for line BC of the shadow, which corresponds to the 2nd vanishing point of line cb of the cube. This is an important observation, as it allows you to draw the shadow much quicker: you don't even need to draw the actual light direction any more, you can go straight ahead and draw AB and CB by choosing their distance from the sides of the cube. Note that the projected light direction is the projection of the vertical ribs of the cube much like the fencepost example.
Okay, the next step is a floating cube. In essence, this isn't much different as you apply the same technique.
Step 1: Start out with the cube again. By now you should be able to get it more or less cube-like Note that the cube in step 1 can be either floating, hanging from a wall or standing firmly on the ground. As long as there is no cast shadow, this will remain unclear.
Step 2: For the cube to float, we need to know how high it actually is from the ground. To do so, extend the vertical ribs downwards like in the example. You can chose whatever height you want, but the higher you let the cube float the further away the shadow on the floor will be.
Step 3: The next steps are quite similar to what I showed earlier: add the projected light direction and the real light direction. Only this time, use the points on the ground rather then the real corners of the cube.
Step 4: The result in this step is a shadow of the top of the cube. Still missing are the sides and bottom...
Step 5: Repeat step 3 for the bottom surface of the cube. Note that you can use the same lines for the projected light direction as you already used for the top. Now that you have constructed the shadow of the top and bottom surface, the only thing left is to connect the two to make it a shadow of a solid object.
Step 6: Marker the shadow. It might be usefull to compare the shadow of the earlier example with the cube firmly on the ground with this one.
Again, you end up with a lot of construction for a 'simple' shadow. Later on I'll put up some quick and dirty example that give you the same effect with less work
The next example is about shadows on other objects. Having a nice open floor to put your object on is nice and easy, but often you'll have more complex shapes where the object has cast shadows not only on flat surfaces but also on vertical surfaces like walls.
Basically, step 1 to 3 are nothing different than what is shown in the earlier examples. However, a wall is added so that the shadow will partly fall on the wall instead of only the floor. Step 3 ends with the shadowconstuction as if the two objects are separate drawings.
Step 4: Mark where the projected light direction hits the wall. This is where the shadow stops being on the ground and start to go up on the wall. Since we're dealing with a vertical stick, the shadow on the wall will logically be vertical too.
Step 5: To determine where the shadow ends on the wall you need the light direction as already drawn in step 3. Draw a vertical line from the mark you put down in the previous step and go up until you cross the light direction.
Step 6: Tada! There you have your cast shadow. I also added a shadow of the wall on the ground, though this isn't really necessary.
Sticks are easy, now we try the same with a cube.
Note that I deliberately put the wall at an angle to the cube, so that the wall isn't parallel to the side of the cube. Feel free to try this yourself, but it's the easier version of the example above (also, I'm aware the wall seems slightly curved. Too lazy to fix it since it doesn't influence the construction for now )
Again, the first couple of steps are nothing new so I'll skip these.
Step 5: This is where it gets interesting. As you can see, I use the same technique as with the stick to find the top of shadow of the rib at the back of the cube on the wall.
Step 6 Connect the dots that make up the shadow and give it a marker tone and you're done.
The next examples are for you to try out. As you might have noticed, shadow construction is actually quite simple. However, it's easy to get lost in your own constructions.
The four objects shown above all have their own nasty tricks to confuse you, which is why I will not do them for you. The theory as explained above still applies to all of them, so you should be able to construct the shadows by now.
1: A box on the wall. Make sure the shadow of it falls partly on the wall and on partly the ground. Making it an open box is optional.
2: A hollow box with a given light direction. You can vary the direction a bit, as long as all the dark sides of the box are at the back of the box.
3: Same story as 2, only with a different light direction.
4: Two objects, where the cast shadow of the first falls on the box behind it.
Now that you are able to construct a shadow for (at least) basic objects, it's time to make things a bit easier again. You might have noticed that to construct the shadow precisely, you need an aweful amount of lines and constructions that clutter up your drawing. As shown with the cube example, you don't really need all the construction lines. The following image shows a very useful trick that does not only apply for just this cube, but for most shadows you'll have to draw.
The red line of the shadow has the same vanishing points as the corresponding red lines from the cube, the same counts for the green one. This is because they are both a projection of the 'horizontal' ribs of the cube. They also should have the same length as the lines they are the projection off (unless you're using a spotlight, but lets not go there for now). The only line that needs some thinking is line AB; this is the projected light direction as mentioned earlier. Choose this wise and your shadow stays simple
About that 'chosing your light wisely': here's another example. It shows three different light situations, each with their own uses and pitfalls.
Situation 1: This one is often preferable above the other two. The reason is that by adding the shade on the right side of the object, you immediately make it more readable. At first glance the shape already reads like the tetris-block it is Note the little cast shadow behind the cube on top.
Situation 2: By shading the other side of the shape, it becomes a little less clear already. Instead of one solid shaded side, the shade is broken up in basically two squares. Again, note the cast shadow on the object itself. For some drawings this shading might be prefferable, but for most of the drawings you will make in this mentor course it's better to use situation 1, as this conveys more information.
Situation 3: Though a combination of 1 and 2 might sound cool, it often is the least useful of the three shown here. Though it is possible to differentiate the shade on the sides (left sides are a bit darker than the front) it doesn't read as well as situation 1 or even 2, as it tends to look like a solid block most of the times. Then again, when handled well this could work to give a drawing something more dramatic by using a backlight and rimlighting.
There are a couple more variations as you might guess, but the important point in most industrial design sketches is to quickly convey as shape/design without having to spend too much time on it. Also, when presenting tons of ideas at one time it is usefull if they all read quickly and easily
To conclude this assignment, below are some example of what shadows can do to your object. Note that all those shadows are 'guessed'; no construction was used, just the same knowledge as in the above exercises.
1: Simple, you've already seen this above.
2: Now, by lifting the shape up a bit, suddenly the shadow is visibly at the front too. This really works well for small hand held products, but also for larger objects (check out some pictures for cars, they usually have a shadow like this underneath ). Important to watch for is the fact that the shadow on both sides should be different in width: the shadow up front is much thinner than on the side. If you make those the same width, the drawing becomes dull.
3: Analyse this one for a bit. By simply twisting the swadow a bit, the object suddenly stands at an angle to the floor. Note that the shape of the shadow doesn't change, except that it becomes a bit shorter (or longer, depending on where you put the light).
4: This is a more dramatic shadow, much like it would look if you place a spot right above your object. I must admit I never use this one myself, as it is a bit too far out there, but some designers like it. Note that there's still only one side of the object that gets shade, so the form still reads easily. Also, by diffusing the corners of the shadow at the left and the right you can create a reflection in the shadow. We'll get to reflections later on.
In the previous assignments we covered a lot of theory about basic shapes and construction. In this exercise we'll finally put it to some sort of use. We're going to draw wooden cars and anything made of wood that you can come up with. But first, a 'simple' exercise to warm up. This is actually an assignment where you get to design something, rather than me giving you an example to recreate
We'll start with some orthogonal views which we're going to translate to a perspective drawing. Orthogonal drawings are potentially a quick and easy way to design anything, as there is no perspective to take care. However, it is usefull to keep in mind that it needs to be translated into 3d once you're happy with it.
Below you see two examples of orthogonal views. Notice the difference between the two. The first one is pretty random, and while it still conveys almost the same information as the second one, it is a lot harder to put into a perspective drawing. The reason is the way its set up.
You'll notice that in the second one, the base of it is made up of squares. Squares, as you've seen in previous assignments, can easily be translated into perspective and become a cube. Cubes can be used to make sure the measurements of the ortho's stay that way into perspective so the proportions don't change. The squares are divided in sections that are more easily to find in a perspective drawing. Instead of drawing a random shape in there, the crossings of lines in there is used to built up the shape of the boat. Further down you'll see how this translates into a 3d drawing.
Now that we have a side- and front view of the object, we should be able to make a perspective drawing out of it.
Step 1: I started out by drawing the cubes first. In the sideview, the boat was two and a half square long, so I started out by setting up a sort of grid of two and a half cubes. It is easiest to divide it into halves and 1/4th pieces already, as you're going to need it later on to find certain points of the boat.
Step 2 to 4: This is basically just one step, only I thought it'd be good to show the process a bit. Use the side- and front view to find out the important points, and translate those into the 3d grid. The bow section of the boat is a good example of this.
Step 5: As you might have noticed, this drawing gets pretty complicated. All the construction lines can very easily obscure the actual boat itself, especially when you're not paying attention to line wheight . However, when the line drawing is finished and you didn't lose your way in the process this is the step where things become clear again. By applying shade to the boat it starts to come out of the linework of the cubes and construction again.
Step 6: To finish it off, there are several things you can do. In this case I added cast shadow on the boat itself to bring out the shape even more. Instead of adding a cast shadow on the floor though, I opted for a background. Since the lines of the cube and construction obscure the silhouette a bit and are not really needed anymore, this is a good way to get rid off them. Watch out for tangents and weird spots where the background connects with the boat. Also, if you draw the background too low it'll make you're design float
The assignment for now is for you to start out making the orthos as shown in the second example, then translate it to a perspective drawing like I did. The topic is to draw a boat. One warning, you might want to go all out and go wild with details and curved shapes: don't! Keep it flat surfaces, low on detail. It might not become the nicest design, but you'll find it's hard enough to translate allready.