## Tuesday, January 19, 2010

### Angles of Light and Shadow: How to Draw the Shadow of an Angled Object

Supplies needed for this lesson:
Protractor
Straight ruler
Rolling Ruler (if you have one)
8” x 10” piece of paper
Eraser
2B Pencil
HB Pencil

Yesterday’s lesson covered the very bare basics of shadows. Today, we’re going to tackle the problem of What if the sun hits an object on its corner? How do we know how to draw the shadow and how long to make it? So, take out your supplies and let's get to it!

If you have never used a protractor before, now is the time to give you a brief lesson on how. Look at fig. 1. You will see a line drawn horizontally, and another line perpendicular to that line. Where the two lines meet you will see a circle. That circle is where you want to line up the little circle in your protractor. See fig. 2 to see what I mean.

Fig. 1

Fig 2

To figure out the angle of the light, first decide how steep or shallow an angle you want the light to reach your object. In today’s lesson we will be using a 45 degree angle for the light. Look to the left side of your protractor and look for 40, then count five more bars up and that will be 45. Then, to draw a straight line, you can place a small straight ruler over the protractor (make sure you hold onto the protractor tightly so you don’t accidentally move it), and line the right end of the straight ruler up at the location where the two lines meet, and the other end should line up with 45 degree angle. You can then make a short line along your straight ruler. Lift the ruler and protractor up. You have now drawn a line at a 45 degree angle to your square!

Okay, now that you know how to use a protractor, let’s draw our object, which is a square turned so that the point of the square is facing you. A one or two inch square should be big enough, but you can go bigger if you want. Just remember, you will be drawing lines and a shadow outside of the square too, so you will need a good deal of room surrounding your square.

To help you see just how to draw a square with its corner facing you, look at Fig. 3. Remember when drawing your square, all angles and all sides should be exactly the same! You will also notice that I have drawn in the angle of your light source as well. Use your HB pencil lightly so if you have to erase you can do so without leaving a lot of marks on the paper. I erase a lot since I tend to be a perfectionist, so I draw lightly at first, then when I am sure I have the object exactly the way I want it I will go over the lines with my 2B pencil (using the straight ruler of course).

Fig. 3

Now that you have a 3-d square, we need to finish it off by indicating where the back corner and bottom sections of the square are located. These, of course, would be invisible to your eyes, but are necessary to help you measure where the shadow falls from the object. So, take your HB pencil and, using your straight ruler, lightly draw dotted lines where those invisible sections are located, use Fig 4 as a guide. Ignore the lines in fig. 4 that are drawn outside the square at this time.

Fig, 4

Once you have drawn those “invisible” sections, you will want to draw in some ref points outside your object as well. You will notice the line at the front part and to the right of the object is not exactly parallel to the base line you drew. That’s the way it is supposed to be. You want that line to be just a little bit off of parallel, and you want it to be dotted. Then, from the right corner of the square, draw a dotted line parallel to the dotted line you just drew. Finally, you want to draw one more dotted line from the back corner of the square parallel to the previous two lines you drew. These lines are used to tell you just how long the shadow is going to be.

Before you can continue on, if you have not done so already you will need to draw in the angle of light you want to use. We are using with a 45 degree angle for this lesson. Place the angle of light in the same location I put mine in Fig 4.

If you have a rolling ruler, you'll want to pull it out to use for the next part. The lines indicating the angle of the shadow must be the same as the angle of light. Line up your rolling ruler with the line for the angle of light, then roll it over to the top corner in front of the square and lightly draw a solid line from that corner down to the first dotted line you drew. Do the same to the next two corners on the top of the square going to the right, lining them up with their respective dotted lines. If you’re not quite sure what I’m talking about, take another look at Fig. 4. I circled the points at which the dotted lines and the angle of the shadow intersect.

Now I want you to draw in the lines of your shadow. To do this you will connect the lines from where the solid and dotted lines you just drew meet. Look at Fig. 4 again and see the small circles I drew where those lines meet. Just connect the dots, so to speak. For more help, take a look at Fig. 5.

Fig.5

Fig.6

Now you can erase your dotted lines inside the square and add shading and highlights to your square and you will have a 3-d square with an accurate shadow. Congratulations on completing your first lesson on angles of light and shadow!

The next lesson will cover how to draw the shadow of a pyramid and how to draw a shadow cast against a wall.