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Description
So far, we've drawn a nifty grid. Now, we will do something with it- including the promised Checkered Floor!

Step 4: Color in the squares on the floor, being sure to alternate them, as shown. You do not have to, say, make the square on the lower left dark, but then the one to its right must be dark. It's up to you.

There you go- a genuine Checkered Floor!

Great!

Previous page:

[link]

BUT- you can do more, and since I have the extra space, why not?

From the lower left corner, draw a vertical line. For this example, make sure it ends somewhere above the vanishing point. Connect the top of that line to the vanishing point.

Extend the bottom horizontal line out to the left a little. Draw a vertical line up from there, and make it just as high as the other one. Connect their tops, as shown...

O.K., from the upper left corner, draw a vertical line until it reaches the line going to the vanishing point.

And you have...a wall!

Since the top of the wall is ABOVE the vanishing point, you cannot see it (unless the wall is transparent). Remember, the vanishing point in these cases usually at the horizon; the level you are looking at.

For the other side do the same thing, except the vertical lines from the corner must end BELOW the vanishing point. Connect those vertical lines, and see what happened?

You can draw not one, but TWO lines to the vanishing point. Why? Since the wall is below the horizon (your line of vision), you can see it. The opposite of the left wall in that way, too!

Draw those two lines to the vanishing point.

From the upper right corner, draw a vertical line until it touches the line as shown.

From that point, draw the little-short line to the other line going to the vanishing point.

You have the other wall. Study it for a moment, see how it worked. Step 4 is done.

It's what you see all the time in real life; now you've seen a way to draw it, too.

Now you can draw something that is the cornerstone to so much involving basic perspective. Since the squares are all the same size, for example, you can equally space objects on that floor- anything two squares above something is the same distance away as something two squares to the left, for example.

What, am I going to leave all that white space? Never!

For Extra 1 (why not?), everything was done the same way as Steps 1, 2, and 3, with one exception: I moved what was Point A a ways to the right, to about 5 cm.

Look at the result: rectangles, "upright," and the Point C angle is 54 degrees, not 45. One look at that long diagonal line to the 5 cm point shows why.

Also notice how the horizontal lines are higher than before?

Try moving Point A to the left. You'll get rectangles, but "on their sides," squat. And the horizontal lines will be lower than before, too.

You can control what kind of shapes you get just by moving that one point! It's that easy, and shows that you should never be afraid to experiment with these things; the results can teach plenty!

For Extra 2 (imaginative, aye?), I moved all of the points on the bottom horizontal line 1 cm to the right (moving them all 2 cm to the left would do the same thing). Otherwise it was all done as in Steps 1, 2, and 3.

Notice how everything has been "shifted over." Also notice- very important!- that the horizontal lines are all at the same levels as before.

Also notice the 41 degree angle, and where it starts from? Point C is not used here this time.

This would be useful for animation, too, if a character was walking by such a floor.

Well, that's it! Now you have even more than a mere floor!

And if that last line didn't make you want to leave, well, then- on to more in the world of the Single Vanishing Point!

Description
So far, we've drawn a nifty grid. Now, we will do something with it- including the promised Checkered Floor!

Step 4: Color in the squares on the floor, being sure to alternate them, as shown. You do not have to, say, make the square on the lower left dark, but then the one to its right must be dark. It's up to you.

There you go- a genuine Checkered Floor!

Great!

Previous page:

[link]

BUT- you can do more, and since I have the extra space, why not?

From the lower left corner, draw a vertical line. For this example, make sure it ends somewhere above the vanishing point. Connect the top of that line to the vanishing point.

Extend the bottom horizontal line out to the left a little. Draw a vertical line up from there, and make it just as high as the other one. Connect their tops, as shown...

O.K., from the upper left corner, draw a vertical line until it reaches the line going to the vanishing point.

And you have...a wall!

Since the top of the wall is ABOVE the vanishing point, you cannot see it (unless the wall is transparent). Remember, the vanishing point in these cases usually at the horizon; the level you are looking at.

For the other side do the same thing, except the vertical lines from the corner must end BELOW the vanishing point. Connect those vertical lines, and see what happened?

You can draw not one, but TWO lines to the vanishing point. Why? Since the wall is below the horizon (your line of vision), you can see it. The opposite of the left wall in that way, too!

Draw those two lines to the vanishing point.

From the upper right corner, draw a vertical line until it touches the line as shown.

From that point, draw the little-short line to the other line going to the vanishing point.

You have the other wall. Study it for a moment, see how it worked. Step 4 is done.

It's what you see all the time in real life; now you've seen a way to draw it, too.

Now you can draw something that is the cornerstone to so much involving basic perspective. Since the squares are all the same size, for example, you can equally space objects on that floor- anything two squares above something is the same distance away as something two squares to the left, for example.

What, am I going to leave all that white space? Never!

For Extra 1 (why not?), everything was done the same way as Steps 1, 2, and 3, with one exception: I moved what was Point A a ways to the right, to about 5 cm.

Look at the result: rectangles, "upright," and the Point C angle is 54 degrees, not 45. One look at that long diagonal line to the 5 cm point shows why.

Also notice how the horizontal lines are higher than before?

Try moving Point A to the left. You'll get rectangles, but "on their sides," squat. And the horizontal lines will be lower than before, too.

You can control what kind of shapes you get just by moving that one point! It's that easy, and shows that you should never be afraid to experiment with these things; the results can teach plenty!

For Extra 2 (imaginative, aye?), I moved all of the points on the bottom horizontal line 1 cm to the right (moving them all 2 cm to the left would do the same thing). Otherwise it was all done as in Steps 1, 2, and 3.

Notice how everything has been "shifted over." Also notice- very important!- that the horizontal lines are all at the same levels as before.

Also notice the 41 degree angle, and where it starts from? Point C is not used here this time.

This would be useful for animation, too, if a character was walking by such a floor.

Well, that's it! Now you have even more than a mere floor!

And if that last line didn't make you want to leave, well, then- on to more in the world of the Single Vanishing Point!