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As a picture often speaks better than words, here are the two images of my problem. I'm trying to get a smooth render on this object. I tried many options but no way I always have these artifacts. Is it possible to have a smooth rendering with a convex surface? enter image description here

enter image description here

Here what I'm trying to model enter image description here

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The Subsurf Modifier doesn't work well with Triangles.

Ideal topology consists of mainly quads (faces with four vertices) and each vertex is connected with exactly four edges.

I created the following quarter sphere by smooth subdiving a cube (edit mode: w > u), shaped it to a sphere (edit mode: Shift + Alt + s) and deleted the excess vertices.

spherically curved surface with quads

EDIT: After requests and additional info in the question, I will provide a step by step workflow.

  1. Create a cube Shift + A > C, then go into edit mode (Tab). Make sure the pivot stays in the center of the cube. cube in edit mode
  2. Do a smooth subdivision operation three times. (W + U) smooth subdivided cube
  3. Select and delete the unnecessary vertices. select vertices on a spherical cube
  4. Select the outer edge loop (Alt + rightbuttonclick) and scale it to zero along the Y - axis. (S > Y > 0). Make sure to enable proportional editing for this step, so the topology stays even. scale to zero along y
  5. With the edge loop still selected, do the to sphere operation.(Shift + Alt + S > 1 > Enter) edge loop to sphere
  6. Select all vertices A, enable 2D Cursor as Pivot . and do the to sphere operation.(Shift + Alt + S > 1 > Enter), the last edge loop will still be on two axis. curved surface with straight end
  7. Delete the additional vertices, then select the lower edge loop. enter image description here
  8. Extrude, scale according to the reference, insert edge loop to make the edges clearer. enter image description here
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  • $\begingroup$ Thanks Leander but I tried unsuccessfully your method. I can't medel your shape. You use the "subdivide option first"? $\endgroup$
    – Grobby
    Commented Sep 29, 2016 at 6:35
  • $\begingroup$ Thanks Leander but I tried unsuccessfully your method. I can't model your shape. You use the "subdivide option first"? $\endgroup$
    – Grobby
    Commented Sep 29, 2016 at 7:26
  • $\begingroup$ I updated my post. I finally understood how to transform a cube into a sphere but the geometry doesn't match to what I'm trying to model (cf image). $\endgroup$
    – Grobby
    Commented Sep 29, 2016 at 9:49
  • $\begingroup$ @Grobby I extended my answer with a step by step explanation. $\endgroup$
    – Leander
    Commented Sep 29, 2016 at 11:28
  • $\begingroup$ Thanks Leander for your full tutorial. I don't know why (I enable the proportional editing) but at the step 4 only the edge loop turn into a circle shape and I don't have the protuberance on the back like you. $\endgroup$
    – Grobby
    Commented Sep 29, 2016 at 12:29

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