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Dividing an ellipse

From: Digital Matte Painting Essentials 2: Perspective

Video: Dividing an ellipse

With our ellipses completed, I want to talk about how you divide up a rounded surface in perspective. Let's take a look at this dome. It's divided up into 16 sections all the way around in the concept painting. But, how do you figure out how those divisions will look in perspective? Then make a new layer and sketch in roughly how it would look. I'm going to use bright green so you can see what I'm doing. This section that is facing right towards us will be the largest.

Dividing an ellipse

With our ellipses completed, I want to talk about how you divide up a rounded surface in perspective. Let's take a look at this dome. It's divided up into 16 sections all the way around in the concept painting. But, how do you figure out how those divisions will look in perspective? Then make a new layer and sketch in roughly how it would look. I'm going to use bright green so you can see what I'm doing. This section that is facing right towards us will be the largest.

The next one over will appear smaller since as the surface curves away from us, we see it at an angle. The next section will appear smaller still and the section right on the edge of the dome will be just a sliver. Drawing this freehand is really tricky, so let me show you how to draw it accurately in perspective. Let me delete these freehand lines. To divide up this ellipse in perspective we are once again going to take advantage of the fact that an ellipse is a circle viewed from an angle.

We're going to draw a circle the same size as our ellipse, divide it up, and then project down those divisions. We need more work space at the top so that our projection isn't right on top of our castle. Select the hill background layer with the sky on it. Go up to the top menu to Image, Canvas Size and add an extra 300 pixels only at the top of the canvas by clicking this down arrow in the anchor section. Now you have this checkerboard transparency that will be hard to work over.

So rectangular marquee select a tiny bit of the sky, press Cmd or Ctrl+J to copy it out, and transform it up to cover the empty area. It isn't beautiful, but it's good enough for a work area. I'm going back to that layer I used to rough in the ellipse divisions and selecting it and name it division guides. You may need a new layer here. Zoom in on the tower and select the Elliptical Marque tool. And holding down the Shift key to constrain it draw a circle the same size as the ellipse you want to divide up.

If you don't get it exactly right the first time you can go up to Select, Transform Selection, and transform the circle so that it precisely matches the edges of your ellipse. Hold down the Shift key so you can constrain the movement vertically and raise it up to get it out of the way of the castle. Go up to Edit Stroke and stroke it with a three pixel width. Deselect the selection and draw a square around the circle.

Carefully intersecting the edges on all four sides. Draw an x from corner to corner in the square to find the center of the circle. Not only have you found the center but you divided the circle into four. Draw horizontal and vertical lines through the center to divide that circle into eights. Draw a circular marquee that matches your original circle and press Cmd or Ctrl+J to copy the divisions onto a new layer.

Since a quarter of a circle is 90 degrees, an eighth of a circle would be 45 degrees. If you want to divide the circle into 16ths, you need to rotate the duplicate lines half of 45 degrees or 22.5 degrees. You can see your exact degree of rotation in the upper menu for the Transform tool. You have divided this circle up into 16ths. All you need to do is draw a line straight down to your ellipse, and project the divisions onto it.

Merge all the divisions together onto the Divisions Guide layer. Then create a new layer for your guidelines called Projections. We have a lot of lines here. So I'm going to switch to green to draw the projections. Set the opacity of the brush to 50% so it isn't overwhelming. Then holding down on the Shift key to constrain the line. Draw straight down from each of the divisions to the ellipse on the dome. Since the circle is the same size as the ellipse, we can project down the divisions from the circle on to the ellipse.

Where these guys intersect the ellipse, it's divided up into 16ths. I've got this dome divided up from top to bottom, and it's going to be hard to draw these divisions smoothly with only this one guide, so let's add some more to aid us in drawing the sections. Make a new layer, and call this layer Ticks. Set the color to white and the brush opacity to 100%. Zoom in on the dome so we can see where the guides have landed on the ellipse, and add a mark or a tick on each point.

Add a tick here, tick here Again here, here, here, here and here. To draw the section smoothly, you need more guide so lasso around all of the ticks, and drag copy at higher up on the dome. Press Cmd or Ctrl+T, and transform these down so that they fit that point on the dome. Zoom in so you can see it accurately, and here is your second set of guides.

Grab that same set again and drag duplicate them higher and transform it to match the top of the dome. Press Return twice to accept the transformation. In the process of transforming these ticks they've gotten very faint but you can beef them up by pressing Cmd or Option or Ctrl+Alt and right or left arrow key. Lasso around that first set of ticks and move it lower down on the dome.

And again scale it to match the dome with that position. And then one more at the bottom of the dome. Now, we've got one two three four five guides. That should be enough. Make a new layer. And call it Dome Divisions. You'll want to draw these as smoothly as you can. Luckily this first one is easy.

Just draw a straight line down through the ticks. For the next one hold down the Shift key and draw on short segments carefully looking forward to then next guide markers as you draw. So go through and delineate each of the sections. The more guides you add, the easier this will be. But, I'm getting reasonably smooth lines here with this set.

Take your time and keep your hand on the Undo button as you work. So, if you go off track. You can quickly fix it. And that finishes it up. Before we move on, let me show you one other thing. These division guides are reusable. Let's say I want to divide up this tower right here into the same number of divisions 16.

I'm going to turn off the Ticks layer and merge all of the guides for the circle division together. Then duplicate it and turn off one copy. Now, scale down this guide with the circle divided up to match the scale of the tower. Once again, since this guide is made of pixels, as we scale it way down, it'll start to get very faint.

And we'll have to use that same trick again of Cmd+Opt or Ctrl+Alt+Left or Right arrow key. To beef it up so we can see it more clearly. Go through and add tick marks on the ellipse and you've divided it up into 16 sections using the same guide. Note that this will only work if you want the same number of divisions. If you want a different breakup like 12 divisions or 18 divisions. You need to go through this process of dividing up a circle to give you the correct number of sections.

And then project them down onto the ellipse you want to break up. Next, we'll add more detail to our prospective drawing as we approach the finish.

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Digital Matte Painting Essentials 2: Perspective

30 video lessons · 3140 viewers

David Mattingly
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