Author Topic: PER103: Dividing Planes  (Read 7306 times)

Mother Roshiya

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PER103: Dividing Planes
« on: March 30, 2015, 07:38:34 AM »
Hello again and welcome to the next step on your way to conquering perspective drawing! So far we have covered the terminology of perspective drawing and learned how to draw the basic box using one point perspective; if you haven't yet had a chance to read those tutorials, I do suggest giving them a look before continuing this lesson.

Now that you know how to create a plane in one point perspective, I want to take a moment to teach you an immensely important fundamental skill that we will apply to creating complex shapes in future lessons: how to divide a plane.

It is vital that a comic artist knows how to divide up a plane evenly, not just on a facing plane where the width and height lines are parallel and hence easy to divide using a ruler, but also on planes shaped by orthogonal lines that are distorted by distance into looking smaller and hence less deeper the closer they are to the sphere of disappearance. If we were to use the same measurement for the depth of a box the entire length of the orthogonal lines, it would appear as though the boxes were getting deeper and deeper the farther away they were. Seeing as we don't want that, we use two simple methods to divide the space: halving and what I like to refer to as sliding. Let's get to it:

Step 0: Draw a Plane
Before we can divide a plane using either method, we first need a plane to divide. Seeing as we're just learning this technique, let's pick a nice facing plane with parallel width and height lines, like so.


The Halving Method
The halving method is your most used method of dividing a plane, and the foundation that the sliding method depends upon, so we will start with it first.

Step 1: Find Center by Connecting the Corners
Your first critical task in the halving method is finding the center of the plane. To do this, we draw two lines that connect the corners of the plane to make a big "X" that marks the spot!



Step 2: Divide at Center
Using your ruler to create the appropriate angle, draw a dividing line that crosses the "X" intersection in the direction you want to divide in. For this example, I only divided the plane vertically, but you can divide the plane horizontally as well at the same spot.


And that's it to the Halving method. If you were to erase the diagonal guidelines you would have a plane perfectly divided into two halves:


The Sliding Method
The sliding method relies on the 1/2 diagonal guideline to "slide" the dividing line over in order to add one more "piece" or division. This is almost exclusively used to divide your plane by a prime number, i.e. you slide 1/2 to 1/3, 1/4 to 1/5, 1/6 to 1/7, 1/10 to 1/11, etc. Let's try it.

Example 1: Sliding to Thirds

Step 1: Divide to your Starting Number
As we are only sliding to thirds, we'll take our halved plane from above for our starting number.


Step 2: Slide your Diagonals
Draw a line from the top of the halving line to the opposite bottom corner, left or right, as if you were going to halve again, but stop at just one guideline. You'll notice that it crosses the diagonal line already on the plane to make an "X".


Repeat with the other half


Step 3: Identify your Crossing Points
Identify where the sliding diagonals cross over the 1/2 diagonal lines. Important: Which 1/2 diagonal line to look at depends on which direction you drew the sliding diagonal lines. If you drew your sliding lines from top left to bottom right, you will need to look where it intersects the right diagonal line. If you drew your sliding lines from the top right to bottom left, you will need to look where it intersects the left diagonal line. You will have a correct and even division no matter which way you do it, so long as you are looking at the correct 1/2 diagonal line.


Step 4: Divide your Plane
Draw your dividing lines so that they intersect your crossing points to finish.


Step 5: Clean up the Guidelines
If this is your stopping point, go ahead and erase the extra guidelines and admire your perfect thirds.


And there you have it. Let's slide 1/4 to 1/5 just to make sure you have this technique down.

Example 2: Sliding to Fifths

Step 1: Divide to your Starting Number
Seeing as we have to start with fourths, we halve the plane twice, once for halves, and then again for fourths:


Step 2: Slide your Diagonals
You can see that our guidelines are starting to get a bit crowded with these larger numbers. To make it a bit easier to keep track of, draw all of your Slider Diagonals going in the same direction.


Step 3: Identify your Crossing Points
Identify where your Slider Diagonals are meeting up with the 1/2 diagonal line. I've made the lines red here so you can better see them among all of the other guidelines.


Step 4: Divide your Plane
Draw your dividing lines so they intersect the crossing points.


Step 5: Clean it Up
If this is your final destination, go ahead and remove those guideline now.


And there you have it!

Now you'll notice that I said "if this is your final destination" a lot. This is because you can use these techniques to divide your plane into however many pieces you want, depending on how you order your halving and sliding steps.

Example 3: Layering the Halving and Sliding Methods to get Twenty-secondths

Instead of doing a bunch of step-by-step photos, I color coded each step in this image, so see if you can spot the following:
Red: Halving the plane to Halves
Orange: Halving to Fourths
Yellow: Sliding to Fifths
Green: Halving to Tenths
Blue: Sliding to Elevenths
Purple: Halving to Twenty-secondths


And so you can see the final result without all of the confusion:


Congratulations! You are now a Plane Dividing Expert! Go forth and practice the Halving and Sliding methods to as high a number as you want. Remember to layer for those higher numbers, and go ahead and erase the non-essential guidelines if they get too overwhelming. Hopefully I'll be able to see your work up on the WIP or Completed Works boards soon! And once you've practiced to your hearts content, move on to PER104: Orthogonal Cutouts to continue your perspective journey!
« Last Edit: June 19, 2015, 11:30:03 PM by Mother Roshiya »

caleb

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Re: PER103: Dividing Planes
« Reply #1 on: March 30, 2015, 06:10:12 PM »
Great tutorial, thanks! I never knew most of that stuff