An improved and efficient method to estimate quadric parameters of imaged objects using structured light is presented. In contrast with our previous work Busboom and Schalkoff (1996) and Sorgel and Schalkoff (1997), the algorithm employs a closed-form solution and therefore iteration is unnecessary. This is possible due to the development of the line-to-curve mapping (LCM) algorithm. The algorithm relies on the fitting of a 2-D, second order curve to a passive ‘‘stripe’’ image resulting from the projection of structured light. The capabilities and shortcomings of the method are illustrated by a series of simulations and experiments. Improvements of the critical second order curve fit in the passive image are introduced and the performance of the enhanced algorithm is analyzed.