Vocal-tract area function is a one-dimensional representation of the vocal tract, in which speech signals are interpreted according to their place vs. area patterns. Recent work on deriving vocal-tract area functions from volumetric vocal-tract data is successful for the main tract part, whereas the region near the tract ends lacks accuracy due to the use of a planar grid system on the wedge-shaped tract opening. This study employs a special treatment on the anterior tract part using curved grid planes with a gradual evolution of convexity, which is applied to cross-sectioning the anterior tract regions including the post-incisor cavity, inter-dental channel, and lip tube. With the method, volumetric MRI data for vowels /a/ and /i/ were processed to describe the articulatory configuration in those regions. The results revealed that the anterior tract regions are observed as identifiable tract segments with a natural-shaped final opening. Thus, our proposed area function scheme promises nearly complete descriptions of articulatory configuration together with a smooth interface for sound radiation with minor modifications.