Four new closed-form methods are present to find rotation points of a skeleton from motion capture data. A generic skeleton can be directly extracted from noisy data with no previous knowledge of skeleton measurements. The new methods are ten times faster than the next fastest and a hundred times faster than the most widely accepted method. Two phases are used to produce an accurate skeleton of the captured data. The first phase, fitting the skeleton, is robust even with noisy motion capture data. The formulae use an asymptotically unbiased version of the Generalized Delogne-Kasa (GDKE) Hyperspherical Estimation (first estimator: UGDK). The second estimator takes advantage of multiple markers located at different distances from the rotation point (MGDK) thereby increasing accuracy. The third estimator removes singularities to allow for cylindrical joint motion (SGDK). The fourth estimator incrementally improves an answer and has advantages of constant memory requirements suitable for firmware applications (IGDK). The UGDK produces the answer faster than any previous algorithm and with the same efficiency with respect to the Cramér-Rao Lower Bound for fitting spheres and circles. The UGDK method significantly reduces the amount of work needed for calculating rotation points by only requiring 26N flops for each joint. The next fastest method, Linear Least-Squares requires 236N flops. In-depth statistical analysis shows the UGDK method converges to the actual rotation point with an error of O(σ/√N) improving on the GDKE's biased answer of O(σ). The second phase is a real-time algorithm to draw the skeleton at each time frame with as little as one point on a segment. Flexibility of motion is displayed in detail as the figure follows the captured motion more closely. The main contributions in this dissertation are the new unbiased center formulae; the full statistical analysis of this new formula; and the analysis of when the best measurement conditions are to initiate the formula. The dissertation further establishes the application of these new formulae to motion capture to produce a real-time method of drawing skeletons of arbitrary articulated figures.