Materials, Part 4. UV Mappers. Section Two: A Little Deeper

(version September 16, 2007)

We continue the work started in UV Mappers. Section One in this article. We take a closer look at definitions and try out some more examples. We also take a look at unfolding.

A Working Definition of (u,v) Coordinates

UV mapping concerns itself with associating the surface or “skin” of a three-dimensional object with a two-dimensional picture. Said a more mathematical way, a three-dimensional object is mapped onto a two-dimensional plane. The (u,v) coordinates are points on the two-dimensional surface that the three-dimensional object gets mapped to. They are not called simply (x,y) coordinates as is customary in two-dimensional geometry. Rather, to underscore their unusual nature, they are referred to in a different way as the (u,v) coordinates. The most important aspects of this convention are the following points:

  1. A three-dimensional object is mapped onto a two-dimensional surface.
  2. The (u,v) coordinates are points on a two-dimensional surface (= plane in a mathematician’s language).
  3. There are multiple ways to map a three-dimensional object onto a two-dimensional surface. The mappings are not unique. Some objects have a “traditional” mapping.
  4. (u,v) coordinates are a pair of numbers. The numbers are coordinates on a plane, the flat image file. Every point on the 3D object has a point on the image that it corresponds to.
  5. There are multiple choices of tools for UV Mapping. Get to know a number of them and you are likely never to be stuck with a problem. If a problem happens, go to the other tools you know.
  6. You can edit the flat image file. Our image editing programs generally work only on flat image files anyway. Once you have edited the file, you can re-wrap it on the original object and see your changes on the model.
  7. Generating image maps is sometimes best handled in the original modeling software. We'll take a look at a Poser 7 example to make this clear.

We will explore these points some more, but let’s first look a few more examples. After looking at some more unwrapping we will then look at unfolding. We will go into more detail with Ultimate Unwrap as well.

 

Another Example of a Different Kind

We are using Ultimate Unwrap here for our work.

In the previous article, UV Mappers. Section One, we worked with two very familiar objects, a box (cube) and a ball (sphere). The object above is called a torus, or just a doughnut by some. It has 16 segments around the entire large circle and the smaller circle (diameter) also has 16 segments. That is 16x16 segments in all, or 256 "rectangles" (also called polygons by the mathematicians and 3D artists/animators alike). In the above diagram you see to the lower left a rectangle with 256 subdivisions or smaller rectangles. This is the UV unwrap of the torus shown. Each of the 256 rectangles in the lower left corresponds to the one of the rectangles in the doughnut at the top right. If I wished to, I could make each one of the rectangles in the lower left a different color, then re-wrap the map back onto the doughnut, obtaining a doughnut with 256 different colors over its surface. For some more complex objects such as the doughnut or the sphere, the UV map is still very simple in nature. It starts to change, though, as our objects get more complex.

UV Unwrap Example with a 3D Font

In the example below we are working with a 3D font of the name Texas. Notice how the letters are broken up into multiple triangles (also called polygons by 3D artists and animators). That's in the top right. In the lower left you see the unwrapping of the letters. One triangle is highlighted red in the lower left and its corresponding polygon in the 3D text is highlighted (see the letter T).

The steps we are looking at here have their counterparts in 3D software. Almost every major program makes use of UV mapping. By looking at UV Mappers outside of a particular 3D product you are learning that this operation has nothing to do with a specific piece of 3D software. This is something that is generally used and found in most 3D products in some form. We are focusing on UV Mappers outside of 3D program so that you will build a more general understanding of how things work. The other thing this will help you with is working with the right program for the right solution, and not just using one program to do everything. Multipurpose software may in some respects be like multipurpose kitchen appliances: they can't do everything equally well, and they are quick to break.

 

Unfolding

Now we will take a look at the concept of unfolding. Unfolding is a way of addressing the problem of distortion that you get when your object is not perfectly cubical, spherical or cylindrical. These are the more common types of "projections" of 3D objects. Go back to the example in UV Mappers. Section One where we used a sphere. What we did with the sphere was to project it onto the flat surface, which is how we got our 64 sections. Down below, instead of unwrapping, we unfold the sphere. There are still 64 sections in the map, but the layout has changed. We still have the same resulting shapes of the individual rectangles as before. (This step in Ultimate Unwrap was crated using: 1. Create Sphere. 2. Control-A to select all. 3. From the menu 2D Tools | Unfold Faces. On the options select Type: Ruling Lines; Separate by: None.)

For the same sphere in the above example we can select groups of faces and assign them to a name we create. These groups can be unfolded then separately. In the example below the top 64 faces were assigned to one group and the bottom 64 faces were assigned to a second group. In the resulting unfolding we have two separate groups showing. This simplifies applying our textures, which can be put onto any one of the groups at a time.

This is the end of Section Two on UV Mappers. We'll look at a Poser object in Section Three.

 

Additional articles will appear in this section.

 

Topics for further exploration and reading on your own


1. Using the trial version of Ultimate Unwrap (download, install) and experiment with creating other objects and unwrapping them. We have so far done unwraps for a cube, sphere, torus, and 3D text. Try some of the other options (using Create from the menu). Choose, for example, cylinder, frame or ellipsoid. When prompted for the number of sides or segments on the create command, initially accept the default and see what you get. You can then repeated the Create command with other settings.
2. Once again work with Ultimate Unwrap. Look at the Create menu objects. Do you know what all these objects are (Can you recognize them if you see them?. Can you draw them by yourself without clicking on the menu object? You need to learn these in order to succeed in 3D. These are basic objects sometimes called primitives. Almost all of them are in every 3D program you will ever touch. Get to know each of them, be able to draw them freehand by yourself without looking at the display.
3. Summarize in a general way what happens to the objects you get when using the Create command in Ultimate Unwrap and increase the number of segments. Give a general statement to explain what happens, in general.
4. Tell a friend what you learned by reading this article. Show him or her some examples. You will increase your understanding of the topics presented here when you present them to someone else.

We enjoy hearing from you. Some of the questions listed above will appear in future "Topics in 3D" articles. Please send your comments about this article to