SCIENTIA SINICA Informationis, Volume 47, Issue 4: 401-415(2017) https://doi.org/10.1360/N112016-00179

## Developable surface reconstruction from noisy data with $\boldsymbol L_{\rm 0}$-norm minimization

• AcceptedOct 24, 2016
• PublishedMar 1, 2017
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### Abstract

A novel method is proposed for developable surface reconstruction from noisy model. An optimization approach is employed to smooth normal vector field of given model via $L_0$-norm minimization. This optimization method has the capability of preserving geometric information concerning developability. Based on the optimized normal vector field, a variational shape approximation procedure is utilized to divide the target model into a sequence of planar segments. After each segment is assigned with an initial B-spline surface, a patch merging procedure is used to obtain a B-spline ruled surface which is nearly developable and covers the whole target model. Finally, a developable surface fitting process is used to improve the quality of fitting surface both in approximation error and developability. The presented method shows pleasing performance in recovering developable information in noisy model and consequently is capable of reconstructing high quality developable surfaces. Some experiments are included to demonstrate the performance of the presented method.

### Funded by

• Figure 1

(Color online) Optimization of normal vector field preserving developability. (a) Original noisy model with normal vector field; (b) neighborhood of data points; (c) optimized normal vector field; (d) original normal vectors on Gaussian sphere (up) and optimized normal vectors on Gaussian sphere (down)

• Table 1   Computation time
 Model #Vertex $d$ in Eq. (eqn:noise) Time of normal optimization (s) Time of surface fitting (s) Figure 2 820 0.08 20 7 Figure 3 2720 0.08 61 13 Figure 4 1999 0.05 42 9 Figure 5 4769 0.08 133 25 Figure 6 5297 0.1 178 31 Figure 7 992 0.08 28 11

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