We have obtained velocity-resolved spectra of the H2 1-0 S(1) ( lambda = 2.1218 micron ) emission line at 2'' angular resolution (or 0.08 pc spatial resolution) in four regions within the central 10 pc of the Galaxy where the supernova-like remnant Sgr A East is colliding with molecular clouds. To investigate the kinematic, physical, and positional relationships between the important gaseous components in the center, we compared the H2 data cube with previously published NH3 data. The projected interaction-boundary of Sgr A East is determined to be an ellipse with its center offset 1.5 pc from Sgr A* and dimensions of 10.8 pc * 7.6 pc. This H2 boundary is larger than the synchrotron emission shell but consistent with the dust ring which is believed to trace the shock front of Sgr A East. Since Sgr A East is driving shocks into its nearby molecular clouds, we can determine their positional relationships using the shock directions as indicators. As a result, we suggest a revised model for the three-dimensional structure of the central 10 pc. The actual contact between Sgr A East and all of the surrounding molecular material, including the circum-nuclear disk and the southern streamer, makes the hypothesis of infall into the nucleus and feeding of Sgr A* very likely.