The 9 + 2 axoneme is a microtubule-based machine that powers the oscillatory beating of cilia and flagella. Its highly regulated movement is essential for the normal function of many organs; ciliopathies cause congenital defects, chronic respiratory tract infections and infertility. We present an efficient method to obtain a quantitative description of flagellar motion, with high spatial and temporal resolution, from high speed video recording of bright field images. This highly automated technique provides the shape, shear angle, curvature, and bend propagation speeds along the length of the flagellum, with approximately 200 temporal samples per beat. We compared the waveforms of uniflagellated wild-type and ida3 mutant cells, which lack the I1 inner dynein complex. Video images were captured at 350 fps. Rigid-body motion was eliminated by fast Fourier transform (FFT)-based registration, and the Cartesian (x-y) coordinates of points on the flagellum were identified. These x-y "point clouds" were embedded in two data dimensions using Isomap, a nonlinear dimension reduction method, and sorted by phase in the flagellar cycle. A smooth surface was fitted to the sorted point clouds, which provides high-resolution estimates of shear angle and curvature. Wild-type and ida3 cells exhibit large differences in shear amplitude, but similar maximum and minimum curvature values. In ida3 cells, the reverse bend begins earlier and travels more slowly relative to the principal bend, than in wild-type cells. The regulation of flagellar movement must involve I1 dynein in a manner consistent with these results.