Model reconstruction from points scanned on existing physical objects is much important in a variety of situations such as reverse engineering for mechanical products, computer vision and recovery of biological shapes from two dimensional contours. With the development of measuring equipment, cloud points that contain more details of the object can be obtained conveniently. On the other hand, large quantity of sampled points brings difficulties to model reconstruction method. This paper first presents an algorithm to automatically reduce the number of cloud points under given tolerance. Triangle mesh surface from the simplified data set is reconstructed by the marching cubes algorithm. For various reasons, reconstructed mesh usually contains unwanted holes. An approach to create new triangles is proposed with optimized shape for covering the unexpected holes in triangle meshes. After hole filling, watertight triangle mesh can be directly output in STL format, which is widely used in rapid prototype manufacturing. Practical examples are included to demonstrate the method.
A new algorithm called the weighted least square discrete parameterization (WLSDP) is presented for the parameterization of triangular meshes over a convex planar region. This algorithm is the linear combination of the discrete Conformal mapping(DCM) and the discrete Authalic mapping(DAM). It provides the good properties of both DCM and DAM, such as robustness and low distortion. By adjusting the scaling factor q embedded in the WLSDP, satisfactory parameterizations in different special applications can be achieved.
