Remaking the sphere.
Blender provides us with two flavours of sphere but they both contain triangles which cause significant problems for the subdivision surface modifier.
Eliminating the triangles from either of these sphere creates new problems with surface continuity and they cannot be satisfactorily fixed as subdivision surface models.
Let’s take a look at the problems before we create a good sphere.
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First of all we have the 'UV sphere', which makes a great sphere if you don’t want to a use subdivision surface modifier or change its shape, but we always want to use a subdivision surface modifier and we always want to change it’s shape!
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The problem is the poles at the top and bottom of the 'UV sphere'. The single vertex creates a megapole at the top connected to the first loop. This is creating a dense fan of triangles which create a pinching effect when a subdivision surface modifier is applied to it.
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Moving on we can look at the 'Ico sphere'. It is made entirely of triangles connected as 6 spoked poles across the entire mesh which immediately signals that this is going to be a problem. Triangles do not work well with the subdivision surface modifier and 6-spoked poles are only acceptable in very few circumstances. This is not one of them!.
The Blender UV Sphere
The Blender Ico Sphere
If we add a subdivision surface modifier to these spheres and use the zebra stripe matcap to display the results, we can see that the UV sphere has unnacceptable wrinkling and the Ico sphere is very lumpy where the modifier is struggling to display it properly.
Subdivided UV Sphere
Subdivided Ico Sphere
A better, but still incorrect, sphere used in subdivision surface modelling, is the quad sphere and bizarrely, blender doesn’t even provide one! There is an add on which can give you one in the add menu but that is not correct either.
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We will use one of the common methods of creating a quadsphere but we will go a few steps further to make a truly useful subdivision surface sphere.
01 | Create a quadsphere.
We can start, as so many modelling tasks do, by using the default cube. Delete it first and add a new one if you want - as is tradition!
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As with anything you create in blender, it should first be given a sensible name. Select your cube and hit “F2” to rename it “Quadsphere”. Hit “Enter” to confirm the new name.
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We could use an add-on to create a quadsphere but the one created by the add-on uses a cube subdivided without the Catmul-Clark algorithm and can’t be corrected later as a result. We need to add our own subdivisions to a regular cube using the subdivision surface modifier in order to have our vertices placed in positions we can alter predictably.
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We can create a ball out of this cube now by adding a subdivision surface modifier with 3 levels of subdivision. You can do this very quickly by hitting “Crtl-3” while it is selected.
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3 levels of subdivision usually works out to be the optimum for creating a good sphere. Any more and the geometry becomes unwieldy when modelling and any less doesn’t give us many options for changing the shape.
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Immediately apply this modifier by hovering over its properties in the modifier properties window and pressing “Ctrl-A”.
This is now just a regular mesh which we can be edited like any other.
Subdivision Surface Modifier
It is now ball like but not actually a good sphere yet. We need to change the positions of all of the vertices using either the cast modifier or the 'To-Sphere' operation.
As we don’t need the continued influence of the cast modifier, we will use the 'To-sphere' operation this time.
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There are better reasons to use the cast modifier which we will explore when we make the pawn for our chess set.
The Subdivided Cube
Go to edit mode by hitting “Tab” and with all of the points selected (hit “Ctrl-A”), use the 'To-sphere' operation by pressing “Ctrl-Alt-s” then dragging the mouse to the right until it looks like a sphere.
The number in the top right hand corner of the viewport should read "1.0000".
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This is where a lot of people would stop and decide that this is a sphere but it is still not quite good enough.
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02 | Improving The Quadsphere.
One of the problem vertices
When rendered or displayed in any shaded mode, there are actually 8 dimples on the surface where the corners of the original cube were. If a reflective surface of any kind is applied to the sphere they will be visible.
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The problems are the vertices with only three connecting edges (and the vertices surrounding them!). There are eight of them and the 'To-sphere' operation does not account for the missing edges and as a result leaves them in incorrect positions.
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To fix them go to edit mode and select any one of them. They should be easy to locate!
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In the 'select menu' choose 'select similar' and then 'Amount of Connecting Edges'.
This will select our 8 offending points. They are in the wrong place. They need to be moved in toward the centre of the sphere. The numbers I suggest here are not perfect but they do make a huge difference.
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Now press “s” to scale them and immediately type “0.9946” - We are not scaling them by much!
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Selecting all of the problem vertices
It turns out that the second row of vertices is also adding some influence to the effect and these need to be moved too.
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Still in edit mode again, press “Ctrl-+” on the numpad to expand the selection out. You can now see we have these 8 islands of vertices selected.
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This time press “s” to scale them and immediately type “0.9983” - An even smaller amount!
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This is now a good subdivision surface sphere. Add a modifier by hitting “Ctrl-3” in object mode.
Change the shading of the object to “smooth” by right clicking and selecting 'smooth' in the pop up menu which appears.
The Expanded Selection
Now if you look at your sphere with the very unforgiving Zebra stripe matcap and move the camera around your sphere, you will see that we have the best quadsphere we can make in blender.
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We will be using this method a lot in later tutorials because the other spheres are not suitable for use in subdivision surface modelling.
The Final Quadsphere with Zebra Matcap
03 | A quick recap of the steps
The quadsphere can be made in under a minute using these steps. Only steps 1 to 10 are actually required!
1. Press “Shift-a” and add a mesh cube.
2. Press “F2” and rename the cube to “Quadsphere”.
3. Press “Ctrl-3” to add a subdivision surface modifier.
4. Press “Ctrl-a” while hovering over the modifier to apply it.
5. Press “Tab” to go to edit mode.
6. Press “Ctrl-Alt-s” and drag the mouse to the right to make a sphere.
7. Select any vertex with only 3 edges connected to it.
8. In the 'select menu' choose 'select similar' and then 'Amount of Connecting Edges'
8. Press “s” and type “0.9946”. Hit “Enter”.
9 Press “Ctrl-+” on the numpad to expand the selection.
10. Press “s” and type “0.9983”. Hit “Enter”.
11. Press “Tab” to go to object mode.
12. Right click and select 'smooth shading'.
13. Press “Ctrl-3” to add a subdivision surface modifier.