Interstellar dust grains cause extinction (absorption and scattering) of light from background astronomical sources. The spectral shape of the extinction curve depends on the dust composition. We used low-resolution optical spectra to measure the extinction curve of 130 million stars. By inverting these data, we mapped the extinction curve parameter R ( V ) within the Milky Way in three dimensions and within the Magellanic Clouds in two dimensions. These maps provide improved extinction corrections for astronomical observations. We find that R ( V ) varies with extinction, consistent with dust grains growing by accretion in low-extinction regions and by coagulation in higher-extinction regions. Star-forming regions have high R ( V ) values, indicating either preferential destruction of small dust grains or additional supply of large dust grains in those regions.