Surface Modeling for 3D Shape Reconstruction from Measurement Data

Hyung Jun Park


The electronic version of his PhD dissertation is now available.
For its access, please contact him. (Email:)
Abstract

As the measurement data of physical objects can be easily obtained in large quantities and of high precision, the importance of surface reconstruction from these data is rapidly increasing in many application domains. Since the surface of interest is usually modeled as a composite surface composed of a number of surface patches, it is an important concern to ensure that the transition between adjacent patches is smooth. At least G1 continuity across patch boundaries is required in the aesthetic and functional aspects of the surface. Moreover, since measurement data usually take large storage, it is another important concern to obtain a compact representation defined by a smaller number of surface patches.

This reconstruction problem has been studied by numerous researchers. However, much efforts are still required to develop efficient methods for surface approximation to either cross sectional data or scattered data. Moreover, it is also necessary to develop an efficient multiple branching algorithm for surface reconstruction from cross sectional data.

This dissertation presents three methods for surface reconstruction from measurement data in the form of either cross sectional data or scattered data. First, a triangular surface-based method is described for surface reconstruction from a sequence of 2D cross sections. The method first generates a triangular net from the given cross sections and then constructs a triangular Bezier G1 surface on the triangular net. Since the method includes an efficient algorithm for handling multiple branching structures, it can provide good solutions for representation of topologically complex shaped objects.

Second, a hybrid surface-based method is described for surface approximation to a sequence of 2D cross sections. Since the method also includes an efficient multiple branching algorithm, it can allow for the representation of complex shaped objects. The resulting surface is a hybrid G1 surface represented by a mesh of triangular and rectangular Bezier patches defined on skinning, branching, or capping regions. Each skinning region is approximated with a B-spline surface, which is transformed into a mesh of rectangular Bezier patches. Triangular G1 surfaces are constructed over branching and capping regions such that the connections between the triangular surfaces and their neighboring (skinning or triangular) surfaces are G1 continuous. Since each skinning region is represented by an approximated rectangular C2 surface instead of an interpolated triangular G1 surface, the hybrid surface-based method can provide more smooth surfaces and realize more efficient data reduction than triangular surface-based methods.

Third, an adaptive method has been described for triangular surface approximation to scattered 3D points. The resulting surface is represented by a triangular Bezier C1 surface. The method begins with a rough approximation of the surface and progressively refines it in successive steps in the regions where the data are poorly approximated. The adaptive method is simple in concept, yet realizes efficient data reduction. Furthermore, as it refines locally the triangular surface without reconstructing the entire surface, the method is efficient in computational time.

The methods described in this dissertation have advantages in the smoothness of the surface and the compactness of the representation. All the three methods provide composite surfaces possessing at least G1 continuity across patch boundaries. The hybrid surface-based method can accomplish more efficient surface approximation than conventional triangular surface-based methods. Also, the adaptive method for surface approximation to scattered data can realize efficient data reduction.

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