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I work mostly on the scripting/texturing side of CG and am trying to improve my topology skills in Blender. I have tried three different of connecting a sphere to a 90 degree plane, but the ways I've tried end with poor results. What is a better way to make this edge transition?

The three ways I've tried: enter image description here

Side View: enter image description here

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    $\begingroup$ What distinguishes "poor" from "better" ? $\endgroup$ – Mutant Bob Jul 27 '17 at 17:30
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    $\begingroup$ @MutantBob My ideal solution would be a transition made out of quads where the quads are as close to squares as possible. $\endgroup$ – Aoradon Jul 27 '17 at 18:03
  • $\begingroup$ Interactively, you could probably accomplish that using the knife tool to connect vertices from the sphere's surface to the radial edges. Algorithmically it is also possible, but you would have to take care to get the topology right when some vertices of squares are inside the sphere and others are outside. $\endgroup$ – Mutant Bob Jul 27 '17 at 18:09
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I guess this is one way to do it:

Delete the top center vertex and extrude out the sides. Remove Doubles:

enter image description here

Select the horizontal edges only on the faces you just created and Subdivide them twice:

enter image description here

Use Proportional Editing to bring the subdivided loops toward the corner a little more:

enter image description here

Now select the only the edges shown and subdivide those as well. This will make the odd number of loops that we need to complete the Quad structure on the top and bottom.

enter image description here

Next, create the edges shown below and subdivide the edges once. Press GG to slide the new vertices toward each other and merge them at the center. Subdivide the remaining edges twice more (Note: I have a the number keys 1-3 mapped to Vertex, Edge, and Face selection). You can use the F2 Add-on to make face creation faster:

enter image description here

Continue that process until you get to the end and simply extrude out the remaining vertices to create the final quads:

enter image description here

Repeat the same process above for the top as well. Since we cheated at the beginning by deleting the center vertex, you can use Proportional Editing to add a little smoother termination. Hide the geometry below so that it's unaffected:

enter image description here

Here's the final. It may not be the best way, but it's one way to do it:

enter image description here

EDIT: A quick and dirty way to do it, building on @Marcus' answer, is to take the subdivided cube and make "projections" for X, Y, and Z. You can then dissolve unnecessary edge loops. It doesn't really teach much about modeling, but it is does make an eighth of a sphere out of quads:

enter image description here enter image description here

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  • $\begingroup$ Thanks. This was super helpful. I wish there was a way I could award more points without waiting 2 days for a bounty. $\endgroup$ – Aoradon Jul 27 '17 at 19:04
  • $\begingroup$ @Aoradon - Ha! No problem at all. I was worried maybe I misunderstood your question so I deleted it. Then I undeleted it just in case it would help you. Glad it helps. $\endgroup$ – bertmoog Jul 27 '17 at 19:22
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    $\begingroup$ A suggestion: To fill the bottom use grid fill. $\endgroup$ – cegaton Jul 27 '17 at 20:09
  • $\begingroup$ That's a big +1 - might take some finagling to get it symmetrical $\endgroup$ – bertmoog Jul 27 '17 at 21:22
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You can also:

  1. Subdivide three sides of a cube using two cuts.
  2. Use a cast (to sphere) modifier.
  3. Apply modifier.
  4. Draw missing faces. enter image description here enter image description here enter image description here
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