| Summary: | 碩士 === 國立成功大學 === 資訊工程學系碩博士班 === 92 === This paper present an efficient and systematic algorithm, which can transform a point-based geometry model to a simplified cluster model and each cluster of this simplified model has a base plane, an origin , a coordinate system and a MLS polynomial to represent the surface of the cluster. Using this kind of representation the original points data don’t need to be recorded, which helps us to save a lot of data space. With the continuity of MLS surface, we can arbitrarily project any point anywhere inside the cluster to the MLS surface and dynamically adjust the number of point in the cluster.
In our method, we consider every MLS polynomial of the cluster as a continuous displacement. After using FFD to deform a point-based geometry model we only compute the positions of each cluster and its one-ring neighbor clusters before and after deformations to find the corresponding relation between the original coordinate system of the cluster and the deformed coordinate system of the cluster. This corresponding relation is used to find the corresponding displacement on the original MLS surface of the new point we want to project after deformations. The normal vector of the new point is calculated from the cluster point and its one-ring neighbors with a similar algorithm.
We present a fast and creative algorithm to achieve free-form deformation of point-based geometry; the basic concept is constructed on the characteristics of polynomial and the Linear Algebra transformation matrix. Our algorithm has better performance than the traditional point-based geometry deformation has in both saving data space and computation time. We believe that in the near future, real-time point-based geometry deformation can be achieved.
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