3D object construction by reverse engineering falls into two categories: surface reconstruction and solid model reconstruction. The 3D surface reconstruction techniques are intended to extract only the geometric information from the measured point cloud and are commonly used in computer graphics and computer vision, whereas the 3D solid model reconstruction techniques are expected to extract the geometric as well as the topological information from the measured point cloud and has application in the field of CAD/CAM. This paper presents a novel framework for 3D solid model reconstruction, which will enable reconstruction of a B-rep model of a physical object based on the 3D point cloud data captured from the surface of the object. In this framework, we use a magnetic position sensor for measuring the data from the surface of the object. This has numerous advantages over conventional methods of data acquisition that use laser scanner or coordinate measuring machine. For segmenting the measured point cloud data into sub-regions, a non-iterative region growing algorithm is developed and implemented. Our surface detection scheme is based on a Modified Gaussian image (MGI) of the sub-region and least-square techniques are used for fitting a surface to the points in a sub-region. The reconstructed B-Rep model is stored in an ISO 10303 (STEP) file format so that it can be imported in to standard CAD/CAM systems for future modifications or analysis.