# Topology: Sphere to plane

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:

Side View:

• What distinguishes "poor" from "better" ? Jul 27, 2017 at 17:30
• @MutantBob My ideal solution would be a transition made out of quads where the quads are as close to squares as possible. Jul 27, 2017 at 18:03
• 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. Jul 27, 2017 at 18:09

I guess this is one way to do it:

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

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

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

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.

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:

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

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:

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

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:

• Thanks. This was super helpful. I wish there was a way I could award more points without waiting 2 days for a bounty. Jul 27, 2017 at 19:04
• @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. Jul 27, 2017 at 19:22
• A suggestion: To fill the bottom use grid fill.
– user1853
Jul 27, 2017 at 20:09
• That's a big +1 - might take some finagling to get it symmetrical Jul 27, 2017 at 21:22

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.