This study presents a new method for reconstructing an adaptive underlying surface, $$\tilde{\varvec{S}}$$ S ~ , from scanned data for styling design objects. $$\tilde{\varvec{S}}$$ S ~ is usually generated by sweeping a curve that varies its shape gradually while being swept. However, when $$\tilde{\varvec{S}}$$ S ~ is reconstructed from a segmented part of the scanned data, it is generally more difficult to control the gradual variation as the ratio of the segmented part to the area of $$\tilde{\varvec{S}}$$ S ~ becomes smaller. Therefore, this study represents $$\tilde{\varvec{S}}$$ S ~ by the sum of two surfaces, $$\tilde{\varvec{S}}={\varvec{S}}^{\mathrm{U}}+{\varvec{S}}^\Delta $$ S ~ = S U + S Δ . Here, an underlying surface $${\varvec{S}}^{\mathrm{U}}$$ S U is generated by the standard sweep method and the difference surface $${\varvec{S}}^\Delta $$ S Δ not only compensates for the error between $$\tilde{\varvec{S}}$$ S ~ and the scanned data but also exhibits monotonous change in the curvatures. Consequently, the gradual change in a curve being swept is represented by $${\varvec{S}}^\Delta $$ S Δ , which does not encounter the aforementioned problem because it is intended to control the deviation from the “reference” $${\varvec{S}}^{\mathrm{U}}$$ S U under the constraint of “curvature monotonicity.” The experimental results demonstrate the validity of surface reconstruction from real-world scanned data as well as an application of the proposed method.

中文翻译：

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从扫描数据重建自适应扫描表面以进行造型设计

这项研究提出了一种新方法，用于从样式设计对象的扫描数据重建自适应底层表面 $$\tilde{\varvec{S}}$$ S ~ 。$$\tilde{\varvec{S}}$$ S ~ 通常是通过扫描一条在扫描时逐渐改变其形状的曲线生成的。然而，当 $$\tilde{\varvec{S}}$$S ~ 从扫描数据的分割部分重建时，通常更难以控制分割部分与面积的比率的渐变变化。 $$\tilde{\varvec{S}}$$ S ~ 变小。因此，本研究将 $$\tilde{\varvec{S}}$$ S ~ 表示为两个表面之和， $$\tilde{\varvec{S}}={\varvec{S}}^{\mathrm {U}}+{\varvec{S}}^\Delta $$ S ~ = SU + S Δ 。这里，下垫面 $${\varvec{S}}^{\mathrm{U}}$$ SU 由标准扫描方法生成，差异面 $${\varvec{S}}^\Delta $$ S Δ不仅补偿了 $$\tilde{\varvec{S}}$$ S ~ 和扫描数据之间的误差，而且还表现出曲率的单调变化。因此，被扫过的曲线的渐变表示为 $${\varvec{S}}^\Delta $$ S Δ ，它不会遇到上述问题，因为它旨在控制与“参考”的偏差$${\varvec{S}}^{\mathrm{U}}$$ SU 在“曲率单调性”的约束下。实验结果证明了从真实世界扫描数据进行表面重建的有效性以及所提出方法的应用。