### Construction of the pyramid

Construction of **basic forms** in perspective

Now that you know how to construct a square in perspective, you can also build up all sorts of simple forms which will come in very useful.

Let’s start with the pyramid.

Fig. 1 A pyramid is constructed on the base of a square or a rectangle placed on the ground. This quadrilateral must first of all be put into perspective. For the sake of simplicity, I’m going to show you this with a square but it works just as well with a rectangle.

Begin by drawing the diagonals of the quadrilateral in order to define the centre. Fig. 2 Prolong one of the diagonals towards the horizon line and materialise the vanishing point of this diagonal.

Fig. 3 Now draw a vertical at the intersection of the diagonals. This is the centre of the square, seen in perspective. Next, we need to define the height of the apex of the pyramid on this vertical axis. Imagine that this pyramid fits exactly in a cube. In this case, the height of the apex will be equal to the length of a side of a square. But the apex is not in the same plane. It’s further away and will therefore be smaller. But how are you to find its height in perspective? You are going to use a side of the square to find the solution. The side nearest to you is free from all perspective deformation so this is the one to choose. After that it’s plain sailing in this case since you are in frontal perspective.

Fig. 4 Raise a vertical line in the angle on the left. Use a compass to copy this measurement on an angle or measure it yourself. This gives you a new point.

Fig. 5 Trace the vanishing line running from this point to the vanishing point of the diagonals. This line bisects the vertical leading to the perspective centre of the square at a point which will be the apex of the pyramid, seen in perspective.

Fig. 6 Now all you have to do to finish off the construction is to join up this apex with the angles of the square.

You notice that if the base square was a circle it would be quite easy to draw a cylinder and of course a cone.