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A method for constructing a cam profile for high performance engines was developed by breaking the cam profile into ten separate polynomial events, defined by boundary conditions at both ends of each event. The separate events allowed the cam profile to meet several kinematic constraints and gave the profile fifteen degrees of freedom for optimization. The degree position of the camshaft was ‘locally nondimensionalized’ with respect to each event in order to simplify the solution of polynomial coefficients. In addition, the cam profile was made ‘mathematically symmetric,’ applying the coefficient solutions from the opening side to the closing side.