Perspective: Seeing where you stand
Carrying on from Part One
A circle is a good example. Usually, if you want to draw a perfect circle you use a pair of compasses. But how do you draw one in perspective, so that it looks as if it is lying down? Compasses won't help you because the shape will be a squashed circle: an ellipse. Try this:
10. On a new piece of paper, or a new file, carefully draw another 10 x 10 grid. It helps to put in all the diagonals too (just like in the grid lying down in your picture). This grid will be your plan.
11. Now take a pair of compasses and draw a circle in the middle of it, the same diameter as your grid.
Can you see that your circle crosses lots of your grid lines at different points as it curves round? Each of these points might be about halfway, or a quarter of the way along a segment of a line in your grid, and that bit of line might be 2 squares in from the top and 3 along from the left.
12. Each time your circle crosses a line in your plan, look where it crosses and make a dot in the same place on the grid lying down in your picture.
Now all you have to do is join up the dots carefully! There: a circle in perspective!
You can follow the same rules to make any shape you like, just remember: first you have to draw this shape on your plan.
What if you want to make shapes in vertical planes?
First you have to make a vertical grid. You already have most of the information you need to do this. Look at your drawing.
13. Just in the same way as you started your horizontal grid, draw lines from the side of the frontal grid (the red one) back to the vanishing point. But this time make sure you are drawing these lines from the left hand vertical of your frontal grid.
14. Look at your drawing again. Can you see where the parallel lines end on the left side of your 1st projected grid? (Where the black dots are.) Draw a vertical line up from each point where these lines end, to the top receding line. You should now have a vertical grid projected into the perspective of your picture.
15. You can now draw in the diagonals in the same way as you did in steps 8 and 9.
16. To project a shape into this grid, follow the same procedure you used in drawing the first one, using the same gridded plan and coordinates, but plotting the dots onto the vertical grid. (Steps 10, 11, 12)
What if you want to make something more solid? An object with volume, like a sphere?
(This gets a bit more technical, and you will end up with hundreds of lines but it does work. This is why you need to be working on a large piece of paper, or a large computer file; that way the lines won't merge into each other so much. If you are working in a program like Adobe Photoshop, you can put all the different grids in different layers and only have the one you are working on switched on.)
First of all you have to make a lot more grids, but by now you should know how to do this. The easiest way to do this is to draw in all the outside grids first.
17. Start with the top horizontal one following steps 4 & 5, but drawing the lines to the vanishing point down from the top. In step 5 you will still draw the line to the same distance point, but, of course, this line will also go down.
18. All the other horizontal grids are made using the same principle of taking a new line from the frontal grid back to the same distance point, but each new plane starts with a different horizontal line on the frontal grid. Otherwise repeat steps 4 & 5.
19. Then make the vertical grid on the right hand side following step 13, 14 & 15 but instead of drawing your parallel lines up from the left side of the 1st grid, draw them up from the right.
20. All the other vertical grids are projected up from the bottom grid to the top grid, but using points that cross (intersect with) points between different receding lines and the same parallel lines. They all also start from the front on different vertical lines of the frontal grid.
You will now have a drawing teeming with grids!
Tip: when you get to the vertical and horizontal rows that cross the vanishing point, you won't have grids here because they are being looked at end-on: they will just be lines.
If you have managed to follow the above points, then you are ready to try something that looks really complicated. The following principles apply to any solid shape. You can draw anything you want, if you have the patience.
Now to make a sphere