Aims. Our goal is to identify bipolar H ii regions and to understand their morphology, their evolution, and the role they play in the formation of new generations of stars. Methods. We use the Spitzer-GLIMPSE, -MIPSGAL, and Herschel-Hi-GAL surveys to identify bipolar H ii regions, looking for (ionized) lobes extending perpendicular to dense filamentary structures. We search for their exciting star(s) and estimate their distances using near-IR data from the 2MASS or UKIDSS surveys. Dense molecular clumps are detected using Herschel-SPIRE data, and we estimate their temperature, column density, mass, and density. MALT90 observations allow us to ascertain their association with the central H ii region (association based on similar velocities). We identify Class 0/I young stellar objects (YSOs) using their Spitzer and Herschel-PACS emissions. These methods will be applied to the entire sample of candidate bipolar H ii regions to be presented in a forthcoming paper. Results. This paper focuses on two bipolar H ii regions, one that is especially interesting in terms of its morphology, G319.88+00.79, and one in terms of its star formation, G010.32−00.15. Their exciting clusters are identified and their photometric distances estimated to be 2.6 kpc and 1.75 kpc, respectively; thus G010.32−00.15 (known as W31 north) lies much closer than previously assumed. We suggest that these regions formed in dense and flat structures that contain filaments. They have a central ionized region and ionized lobes extending perpendicular to the parental cloud. The remains of the parental cloud appear as dense (more than 104 cm-3) and cold (14–17 K) condensations. The dust in the photodissociation regions (in regions adjacent to the ionized gas) is warm (19–25 K). Dense massive clumps are present around the central ionized region. G010.32-00.14 is especially remarkable because five clumps of several hundred solar masses surround the central H ii region; their peak column density is a few 1023 cm-2, and the mean density in their central regions reaches several 105 cm-3. Four of them contain at least one massive YSO (including an ultracompact H ii region and a high-luminosity Class I YSO); these clumps also contain extended green objects (EGOs) and Class II methanol masers. This morphology suggests that the formation of a second generation of massive stars has been triggered by the central bipolar H ii region. It occurs in the compressed material of the parental cloud.

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