Reconstructed Geometric Model By V-system Of Degree 2 Over Triangulated Domains

V-system is a new complete orthogonal system,which has definition on not only L2[0,1] but also triangulated domains. It can be used for signal analysis and image processing and so on, particularly, it has outstanding advantage in the representation of geometric information and the reconstruction. V-system over triangulated domains can be used to reconstruct and express continuous geometric information as well as discontinuous ones which are common in CAGD, it also can eliminate Gibbs phenomena effectively. In particularly, the important applications of the V-system over triangular domain will display its talent in the problems of frequency spectrum for 3D complex group of geometric models.The point-cloud surface data, the main carrier of digital geometry media, provides a way to represents 3D geometry shape completely or discretely. Which not only greatly alleviate dependence to model representation in model drawing and accelerate the model drawing process by remove useless connective relationships, but also open a new path for data space processing method based on fully discrete geometric model and signal processing technology in frequency domain.The central works are as follows:1.The detailed mathematic expression of orthogonal V-system of degree 2 over triangulated domains is presented. As a practical application of this new system, the orthogonal representation of surface model is discussed. A surface model, which can be represented by piecewise polynomial of degree 2 in two variables, can be precisely reconstructed with finite terms of the V-series, so orthogonal decomposition and reconstruction of a geometry object can be realized, furthermore geometry information can be transformed from the space domain into the spectral domain. It lays foundation for data compression, characteristic classification and model retrieval.2.This paper proposes a new piecewise conicoid fitting method for point-cloud data. This method realizes point-cloud data fitting by least-squares-fitting principle and choosing V-system, a complete orthogonal function system over triangulated domain, as a selected fitting function system. Its advantage is that the point-cloud data can be expressed by piecewise conicoid, and the amount of data hardly affects the fitting result. When point-cloud distribute over several segments, the global representation can be obtained without need of point-cloud segmentation previously. Its procession is convenient and concise. Moreover, it is more favorable for feature extraction using orthogonal system to represent point-cloud data.