A butterfly subdivision scheme for surface interpolation with tension control

1990 ◽  
Vol 9 (2) ◽  
pp. 160-169 ◽  
Author(s):  
Nira Dyn ◽  
David Levine ◽  
John A. Gregory
Keyword(s):  
Tension Control ◽  
Subdivision Scheme ◽  
Surface Interpolation

Cable Tension Control of Cable-Stayed Bridge Using Fuzzy Satisfaction Method and Genetic Algorithm

2001 ◽  
Vol 84 (3) ◽  
pp. 39-46
Author(s):  
Hitoshi Furuta ◽  
Masakatsu Kaneyoshi ◽  
Hiroshi Tanaka ◽  
Eiichi Watanabe
Keyword(s):  
Genetic Algorithm ◽  
Tension Control ◽  
Cable Tension ◽  
Cable Stayed Bridge

scholarly journals Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Computer Graphics ◽  
Geometric Modeling ◽  
Tension Control ◽  
Free Form ◽  
Subdivision Surfaces ◽  
Smooth Curves ◽  
Practical Applications ◽  
Tension Parameter ◽  
Exact Reproduction ◽  
Free Form Surfaces

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

scholarly journals An Adaptive Surface Interpolation Filter Using Cloth Simulation and Relief Amplitude for Airborne Laser Scanning Data

2021 ◽  
Vol 13 (15) ◽  
pp. 2938
Author(s):  
Feng Li ◽  
Haihong Zhu ◽  
Zhenwei Luo ◽  
Hang Shen ◽  
Lin Li
Keyword(s):  
Laser Scanning ◽  
Point Clouds ◽  
Airborne Laser Scanning ◽  
Superior Performance ◽  
Cloth Simulation ◽  
Cloud Data ◽  
Interpolation Filter ◽  
Landscape Characteristics ◽  
Surface Interpolation ◽  
Airborne Laser

Separating point clouds into ground and nonground points is an essential step in the processing of airborne laser scanning (ALS) data for various applications. Interpolation-based filtering algorithms have been commonly used for filtering ALS point cloud data. However, most conventional interpolation-based algorithms have exhibited a drawback in terms of retaining abrupt terrain characteristics, resulting in poor algorithmic precision in these regions. To overcome this drawback, this paper proposes an improved adaptive surface interpolation filter with a multilevel hierarchy by using a cloth simulation and relief amplitude. This method uses three hierarchy levels of provisional digital elevation model (DEM) raster surfaces with thin plate spline (TPS) interpolation to separate ground points from unclassified points based on adaptive residual thresholds. A cloth simulation algorithm is adopted to generate sufficient effective initial ground seeds for constructing topographic surfaces with high quality. Residual thresholds are adaptively constructed by the relief amplitude of the examined area to capture complex landscape characteristics during the classification process. Fifteen samples from the International Society for Photogrammetry and Remote Sensing (ISPRS) commission are used to assess the performance of the proposed algorithm. The experimental results indicate that the proposed method can produce satisfying results in both flat areas and steep areas. In a comparison with other approaches, this method demonstrates its superior performance in terms of filtering results with the lowest omission error rate; in particular, the proposed approach retains discontinuous terrain features with steep slopes and terraces.

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