## Geometric shapes

A lot of subjects can be simplified to geometric shapes, such as boxes, pyramids, cylinders, and spheres. Instead of starting with the large shapes on paper, you simplify your subject in 3-D.

This section is also a crash course in perspective drawing. You'll need this to draw the basic shapes, but it is also a useful tool in case you don't have a reference for something, or if you don't want to make a perfect copy. As long as you work according to the rules, it will look good.

We'll look at perspective in more detail in chapter 9. All you need to remember for now is that lines that are parallel in the real world, will converge to a single point in your drawing. Such points are called vanishing points.

First, the cube. Here you can see how parallel lines intersect at a common point: The cube is transparent, so you can see all its edges. There are four parallel edges with the vanishing point on the left, another four with the vanishing point on the right, and four edges that we are looking at straight on. (Their vanishing point is so far away we can ignore it, and draw the lines vertical.)

By placing the vanishing points more to the left or to the right, we can rotate the cube. Figure 1.9. Drawing the cube from different angles

If we tilt the cube with the top towards the viewer, the third vanishing point (the one that was too far away at first) comes into view. Figure 1.10. A cube and three vanishing points

The center of one of the sides of a box can be found by drawing a cross between the corners. If we know the exact middle of the top side of a cube, we can use this point as the tip of a pyramid: Figure 1.11. Finding the middle of a face, and constructing a pyramid

By adding two more lines through the center, you can divide a side into 4 smaller squares. You can use this as a guide for drawing a circle in perspective. The circle will always touch the edges of the square in the middle, at the point where we have drawn the extra two guidelines. And it will cross the diagonals at a little less than three quarters from the center. Figure 1.12. Constructing a circle from a square, and a cylinder from a cube

The cube is drawn transparently here to make it clearer how both the top and the bottom face are turned into a circle in correct perspective. Note that the straight sides of the cylinder are parallel to the upright edges of the cube, and therefor have the same vanishing point.

Cylinders of various lengths are often used to draw a character's body. So practice a bit with drawing them at different angles, this will help you with foreshortening later on.

### Figure 1.13. Long cylinders at different angles

Here you can see a longer, thinner cylinder drawn at three different angles. Two are exactly perpendicular, so they use the same two vanishing points (which are located outside the drawing). The one that we are viewing lengthwise has its own vantage point.

Now let's draw something! Man-made objects are great subjects to simplify to geometric shapes: Figure 1.14. Photo with strong perspective distortion

This photo has been taken from up close with a wide angle, to exaggerate the effect of perspective. Don't put your vanishing points this close together in your own drawings, unless you're using the exaggeration for some effect.

The edges of the table and the base of the laptop share the same two vantage points. They are outside the paper, to the top left and the top right. There's also a third vantage point for all vertical edges (such as the leg of the table and the sides of the bottle), far down.

Start with the basic shapes: a flat box for the table, another one for the base of the laptop. And just like Juan Gris, we're going to make a bottle out of a cylinder. Some construction lines end in an arrow; if the drawing were bigger, these lines would be longer and meet at the vanishing point.

Figure 1.15. Blocking in the shapes using simple boxes Figure 1.16. Extended lines meet at the vanishing points

I've drawn crosses on the laptop base and screen to find the line that runs right through the middle. I use this line to place the latch, and to determine where the curve at the top of the screen reaches its highest point. More guidelines towards the vantage points are used to draw the keyboard and the trackpad. Figure 1.17. Refining the shapes

The top of the water bottle was added using the center line as a guide. The center line runs through the middle of the top and the middle of the bottom, and we already found those by drawing crosses.

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