1. A system of identifying a position and a shape of a portion of an object in a three-dimensional (3D) space, the system comprising: one or more processors coupled to a memory, the memory loaded with computer instructions that, when executed on the one or more processors, implement a method including: capturing, with a single camera having a particular vantage point, two or more images generated by casting an output from at least one source onto the portion of the object; analyzing the two or more images captured by the camera from the particular vantage point to computationally represent the portion of the object, as captured, as one or more mathematically represented 3D surfaces, each 3D surface corresponding to a cross-section of the portion of the object, based at least in part on a plurality of edge points of the portion of the object in the image, tangent lines extending from the camera to at least two edge points of the plurality of edge points and a centerline corresponding to the tangent lines; and reconstructing the position of and the shape fitting at least the portion of the object in the 3D space based at least in part on the plurality of edge points and the centerline.