The overarching theme of this research project is to build a machine-accessible and mathematically precise abstraction of human body movement through experiments in programming an articulated puppet that imitates the human body structure and mobility within a "Real-Time Interactive Computer Animation" (RTICA). Human movement has been the subject of research in science, art, and engineering, to design mental models, practices, and technology for observing, exercising, performing, and interpreting movements. With the advent of motion capture technology, it is possible to design software and hardware interfaces for human-machine interaction through movement, such as games and virtual environments for rehabilitation, education, and entertainment. A problem in designing "application programs" for the human body is the lack of a machine-accessible movement "notation system" for transcribing human movement and its properties, such as the expressed intention and mood. Such a notation system serves as an interface that encodes the shape and dynamics of a performer's movement into sequences of parameters that can be interpreted and reconstructed by a computer program, while the parametrization remains invariant to the geometric structure, position, and orientation of the performer's body, as observed in the space of the motion capture camera. Through experiments in programming a real-time interactive computer animation, we explore the instances of a training-learning paradigm in which a "teacher" demonstrates a movement to a "student" who tries to learn the performance by imitating the teacher. The teacher and the student RTICAs are two instances of an articulated puppet that mimics the "mechanical linkage" of the human body by a hierarchy of "Euclidean transformations" that control the oscillation of each puppet limb in the coordinate system of the limb's preceding joint. The teacher RTICA represents a "clockwork automaton" that can be programmed to move using an "animation program," which specifies the puppet's "keypose" at certain intervals of the movement. We extend the design of the teacher RTICA with an abstraction of the brain's "mirror system," to construct the student RTICA, which represents an "interactive automaton" that can imitate the "motion data" of a human movement to parametrize the performance into an animation program. The student RTICA serves as an "Application Programming Interface" (API) for human body movement, which permits the interaction between a performer and the controller system of an application program for the human body. The API encodes the motion data of a performer's movement by the sequences of keypose data that parametrize the oscillation of the individual limbs, which are then interpolated and superimposed over the graph structure of the puppet's mechanical linkage to reconstruct the movement. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]