Recently I read that the next B segment Toyota (4th gen Yaris I suppose) will be based on the Mazda2, as the Yaris is, well, not well received by reviewers and potential customers. It is not good enough, even though the 3rd gen is already a big improvement over the 2nd gen.

The current Vios is based on the 2nd gen Yaris, the new Vios may be based on the 3rd gen one. Though someone said the pics of the new Vios show a shape closer to the 2nd gen Yaris. Didn't take a close look.

The 3rd gen Yaris is a relatively safe car too, IIRC.

What I meant is the basic shape. For example look at the Kangoo II, the Kangoo II Phase 2 (facelift coming soon) and the Mercedes Citan. They can only change certain parts from the basic vehicle, but between A and C pillar it is the same car. Maybe doors can be changed, but the basic shape remains the same. Or the Peugeot 206 vs the 206+ and Malaysian 207, and the Chinese Citroen C3. You can see that they are the same car. Also one of the earlier Fiestas where they introduced that oval design. That might be the most striking example, because it really didn't work.

Body panels can be changed, but things like the A pillar can't, perhaps to a very small degree by layering on top of the actual structure, but there it ends. If those parts are more 2nd gen Yaris than 3rd gen Yaris...

That pic is not the new Vios. In China, they would re-use phased out model in joint venture to re-introduce as new cheaper model.

So don't even say that is the new Vios. The new Vios 2013 chassis can be seen clearly as totally new body.