Structured light is a perception method that allows us to obtain 3D information from images of the scene by projecting synthetic features with a light emitter. Traditionally, this method considers a rigid configuration, where the position and orientation of the light emitter with respect to the camera are known and calibrated beforehand. In this paper we propose a new omnidirectional structured light system in flexible configuration, which overcomes the rigidness of the traditional structured light systems. We propose the use of an omnidirectional camera combined with a conic pattern light emitter. Since the light emitter is visible in the omnidirectional image, the computation of its location is possible. With this information and the projected conic in the omnidirectional image, we are able to compute the conic reconstruction, i.e., the 3D information of the conic in the space. This reconstruction considers the recovery of the depth and orientation of the scene surface where the conic pattern is projected. One application of our proposed structured light system in flexible configuration consists of a wearable omnicamera with a low-cost laser in hand for visual impaired personal assistance.