We consider proper subdomains G of Rn" style="position: relative;" tabindex="0" id="MathJax-Element-3-Frame" class="MathJax">ℝn and their images G′=f(G)" style="position: relative;" tabindex="0" id="MathJax-Element-4-Frame" class="MathJax">G′=f(G) under quasiconformal mappings f of Rn" style="position: relative;" tabindex="0" id="MathJax-Element-5-Frame" class="MathJax">ℝn. We compare the distance ratio metrics of G and G′" style="position: relative;" tabindex="0" id="MathJax-Element-6-Frame" class="MathJax">G′; as an application we show that φ" style="position: relative;" tabindex="0" id="MathJax-Element-7-Frame" class="MathJax">φ-uniform domains are preserved under quasiconformal mappings of Rn" style="position: relative;" tabindex="0" id="MathJax-Element-8-Frame" class="MathJax">ℝn. A sufficient condition for φ" style="position: relative;" tabindex="0" id="MathJax-Element-9-Frame" class="MathJax">φ-uniformity is obtained in terms of the quasi-symmetry condition. We give a geometric condition for uniformity: If G⊂Rn" style="position: relative;" tabindex="0" id="MathJax-Element-10-Frame" class="MathJax">G⊂ℝn is φ" style="position: relative;" tabindex="0" id="MathJax-Element-11-Frame" class="MathJax">φ-uniform and satisfies the twisted cone condition, then it is uniform. We also construct a planar φ" style="position: relative;" tabindex="0" id="MathJax-Element-12-Frame" class="MathJax">φ-uniform domain whose complement is not ψ" style="position: relative;" tabindex="0" id="MathJax-Element-13-Frame" class="MathJax">ψ-uniform for any ψ" style="position: relative;" tabindex="0" id="MathJax-Element-14-Frame" class="MathJax">ψ.