Monotone and convex Hermite interpolants generated by an adaptive subdivision scheme

2001 ◽  
Vol 333 (5) ◽  
pp. 493-497 ◽  
Author(s):  
Jean-Louis Merrien ◽  
Paul Sablonnière
Keyword(s):  
Subdivision Scheme ◽  
Adaptive Subdivision

An Adjustable Adaptive Subdivision Surface Modeling Based on Triangle Meshes

2010 ◽  
Vol 26-28 ◽  
pp. 702-705
Author(s):  
Fu Qing Zhao ◽  
Xin Ai
Keyword(s):  
Standard Technique ◽  
Adjustable Parameter ◽  
Shape Modeling ◽  
Subdivision Surfaces ◽  
Subdivision Scheme ◽  
Subdivision Surface ◽  
Triangle Meshes ◽  
Good Surface ◽  
Adaptive Subdivision ◽  
Loop Scheme

Subdivision surfaces have become a standard technique for free shape modeling. But tradition subdivision scheme does not adjust the shape of subdivision results. In this paper, We introd uce adjustable adaptive subdivision as a new adaptive subdivision method for triangle meshes. This method applied to the method of adaptive subdivision constructs a new subdivision rule by introducing adjustable parameter to the traditional Loop scheme. The experiment shows that this method not only use fewer meshes to obtain the performance good surface but also can adjust the hape of subdivision surface to satisfy the actual need.

scholarly journals A note on magnitude bounds for the mask coefficients of the interpolatory Dubuc–Deslauriers subdivision scheme

2014 ◽  
Vol 17 (1) ◽  
pp. 226-232
Author(s):  
H. E. Bez ◽  
N. Bez
Keyword(s):  
Recent Result ◽  
Operator Norm ◽  
Subdivision Scheme ◽  
Sharp Bounds

AbstractWe analyse the mask associated with the $2n$-point interpolatory Dubuc–Deslauriers subdivision scheme $S_{a^{[n]}}$. Sharp bounds are presented for the magnitude of the coefficients $a^{[n]}_{2i-1}$ of the mask. For scales $i \in [1,\sqrt{n}]$ it is shown that $|a^{[n]}_{2i-1}|$ is comparable to $i^{-1}$, and for larger power scales, exponentially decaying bounds are obtained. Using our bounds, we may precisely analyse the summability of the mask as a function of $n$ by identifying which coefficients of the mask contribute to the essential behaviour in $n$, recovering and refining the recent result of Deng–Hormann–Zhang that the operator norm of $S_{a^{[n]}}$ on $\ell ^\infty $ grows logarithmically in $n$.

scholarly journals Convexity preservation of the four-point interpolatory subdivision scheme

1999 ◽  
Vol 16 (8) ◽  
pp. 789-792 ◽  
Author(s):  
Nira Dyn ◽  
Frans Kuijt ◽  
David Levin ◽  
Ruud van Damme
Keyword(s):  
Subdivision Scheme ◽  
Interpolatory Subdivision

scholarly journals A Distortion-Free Data Hiding Scheme for Triangular Meshes Based on Recursive Subdivision

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Yuan-Yu Tsai
Keyword(s):  
Principal Component Analysis ◽  
Data Hiding ◽  
Similarity Transformation ◽  
Principal Component ◽  
Secret Message ◽  
Subdivision Scheme ◽  
Data Embedding ◽  
Embedding Capacity ◽  
Free Data ◽  
Reversible Data Embedding

This study adopts a triangle subdivision scheme to achieve reversible data embedding. The secret message is embedded into the newly added vertices. The topology of added vertex is constructed by connecting it with the vertices of located triangle. For further raising the total embedding capacity, a recursive subdivision mechanism, terminated by a given criterion, is employed. Finally, a principal component analysis can make the stego model against similarity transformation and vertex/triangle reordering attacks. Our proposed algorithm can provide a high and adjustable embedding capacity with reversibility. The experimental results demonstrate the feasibility of our proposed algorithm.

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