Ramified objects, one kind of ubiquitous objects, compose a great challenge in computer graphics due to their complex topological and geometric structures. Traditional methods for modeling and visualizing ramified objects can mainly be divided into two kinds. One is based on the parametric surface, which focuses on the fast global modeling and visualization while doesn’t care too much on local details in ramification. The other is based on the implicit surface, which shows unmatched advantages in generating smooth blending surface while have difficulty in real-time rendering. Through general research for modeling and visualizing ramified objects, both considering the local details in ramification and the fast global rendering, we adopt an implicitly modeling method and propose a point sampling algorithm. The main works and contributions of this thesis are listed as following: 1. Due to ramified objects having complex structures and self-similarity in certain degree, we propose a substructure-based point sampling method. By recursively dividing the full system into a set of substructures with certain orders and finally into the linear combination of basic branches, the structure complexity has been reduced. Meanwhile, we build up a sampling point library for basic branches in the low level, and get the sampling points for the full system by copying, transforming operations in the high level. Since this method shrinks and simplifies the sampling target in low level, it speeds up the sampling process and solves the problem of choosing parameters when we directly sample the full system. Additionally, the application of substructures helps to avoid the repetitious works for modeling and sampling the same or similar substructures, so it further improves the efficiency of sampling algorithm. 2. Utilizing the blending property of implicit surface, we propose to apply a merging operation to those particles that come from different substructures and locate in ramifications. We respectively implement the elliptic-merging, skeleton-reduction and super-elliptic merging operations and do a deep analysis and comparison. Finally, we suggest a modified super-elliptic merging operation, which separate the different regions that the two connected branches caused and applied different merging operations to the particles locating in different regions. After merging operation, all these particles have moved to the smooth blending surface and no unexpected bulge will exist. 3. We develop the software for our substructure-based point sampling method. According to different branching structure inputs, we can acquire all the sampling points for the merged surface fast and efficiently.
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