Multi-level Differential Surface Representation

Based on Local Transformations

Dong Xu, Wei Chen, Hongxin Zhang, Hujun Bao

State Key Lab. of CAD&CG, Zhejiang University

Abstract

One crucial issue of multi-resolution surface representations is how to effectively record and reconstruct geometric details among surface levels. Standard multi-resolution techniques encode details directly as local displacements in the vertices, and may produce unplausible results when the base level endures large deformations. In this paper we propose an alternative detail representation and reconstruction scheme, based on local transformations on a per-triangle basis. While more storages are required, recording details as local transformations favors global coupling of geometric details and allows for large-scale surface manipulations. By modeling the scale components of the surface modifications as a set of deforming factors, detail-preserving reconstruction results are achieved naturally under very large deformations. Comprehensive experimental results verify the efficiency and robustness of our approach.

Keywords: Multi-level Editing, Detail Representation, Surface Reconstruction, Large Deformation, Local Transformations

Video

Surface Decomposition of the Dragon Model
Currently, our major tool for surface decomposition is by means of constrained fairing. That is, the user need to select the region of interest and set the smoothing parameters (such as the size of feature) and our system generate the smooth result. To effectively remove large amount of details (such as the claw of the Dragon model), we perform the constrained fairing by minimizing discrete energies (such as the membrane energy used in this demo).

We present an interactive surface decomposition demo by decomposing the Dragon model into seven levels step by step. The first detail level contains the squama on the body [avi, 0.8M]. The second detail level contains the squama on the back [avi, 1M]. The third detail level represents the wave pattern, major on the front body [avi, 0.8M]. The fourth detail level groups the four claws. See [avi, 1.4M] for details on how to smooth one claw and [avi, 0.6M] for the model with four claws smoothed. The fifth detail level corresponds to high-frequency details on the head and the tail [avi, 0.5M] while the sixth detail level corresponds to middle-frequency details on the same region [avi, 0.5M].

The final decomposition of seven levels (one base level and six detail levels) is presented in [avi, 0.3M].

Multi-level Editing of the Dragon Model
We deform the base level by our Poisson-based deformation tool. First, we select the handle curve around the neck of the Dragon model. Then, we select the constrained region. After pre-computation, we interactively deform the base level by moving the handle curve. Finally, we reconstruct the detail level with respect to the deformed base level. [avi, 2M].

Multi-level Filtering of the Dragon Model
With the pre-decomposed seven levels of the Dragon model, we can filter certain detail levels and generate interesting result. First, we reconstruct result with all detail levels. Then, we hide the sixth detail level and reconstruct again and get the result like band-stop filtering. Next, we select the first detail level, and set the influence weights to 0, and obtain the result without details corresponding to this detail level. Next, we reset the influence weights to 3, and obtain the result with enhanced details. Finally, we modify the influence weight of the second detail level to -1 and obtain the result with inverted details. Note that in the whole sequence, pre-made modifications are integrated into the final results. [avi, 5M].

The Effect of the Deforming Factors
Finally, we demonstrate the effect of the deforming factors by comparing the different results reconstructed from a deformed base level with and without incorporating the deforming factors. Generally speaking, the deforming factors resize the normal component of geometric details properly. Therefore, reconstruction results with them keep the geometric details as similar as possible to the original ones.

First, we shrink the head of the Dragon model significantly and reconstruct the result without the deforming factors. From the zoom-in view, we can find self-intersections appear. Second, we reconstruct the result with the deforming factors. It is clear that the result with the deforming factors avoid self-intersections and is more visual pleasing [avi, 2M]. Another comparison is shown in [avi, 2M].

Publications

Dong Xu, Wei Chen, Hongxin Zhang, Hujun Bao. Multi-level Differential Surface Representation Based on Local Transformations. The Visual Computer (Priprint), accepted.

Acknowledgements

We wish to thank the anonymous reviewers for their valuable comments and Dr. Hongwei Lin for helpful discussions. Models are courtesy of Cyberware and Stanford University. This work is supported in part by The National Basic Research Program of China (973 Program) under Grant No.2002CB312102, Natural Science Foundation of China under Grant No.60021201, and The Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China under Grant No.705027.

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