The technique of time-of-flight scattering and recoiling spectrometry (TOF-SARS) is used for quantitative structural characterization of the reconstructed (1 x 2) missing-row Pt{110} clean surface. The results are presented as scans of scattered intensity versus incident angle at two scattering angles and are interpreted in terms of simple classical concepts (shadowing, blocking, focusing). Measured critical incident and exit angles corresponding to interatomic spacings unaffected by reconstruction are used to calibrate the screening constant of the interaction potential employed in the trajectory simulations. Analysis of the surface reconstruction is performed by combining experimental data and calibrated computations. The results indicate a contraction of the first-to-second interlayer spacing (-0.22 +/- 0.07 angstrom, i.e., -16 +/- 5%), a buckling of amplitude 0.19 +/- 0.13 angstrom in the third layer and, possibly, a row-pairing in the second layer. These observations are in agreement with LEED, MEIS, GXRD, and RHEED experiments.