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In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
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Curvy Surface Reconstruction.

Chen Shang1,2,3, Haoyu Qi2,3, Zhigang Wang4

  • 1College of Mechanical and Electrical Engineering, Shaanxi University of Science and Technology, Xi'an, China.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|January 4, 2026
PubMed
Summary
This summary is machine-generated.

Modern industry relies on 2D methods, but the real world is 3D and curvy. This review integrates geometric and physical dimensions for advanced curvy surface reconstruction, addressing limitations in prior research.

Keywords:
AI reconstruction algorithmsadvanced measurement methodsconformal design and fabricationcurvy surface reconstruction

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Area of Science:

  • Computer Vision
  • Geometric Modeling
  • Metrology

Background:

  • The physical world is inherently curvy, contrasting with the planar paradigms of current industrial technology.
  • Existing two-dimensional (2D) techniques limit the perception and understanding of complex three-dimensional (3D) realities.
  • Advancements in sensors, AI, and computation have driven progress in curvy surface reconstruction.

Purpose of the Study:

  • To provide a comprehensive overview of curvy surface reconstruction, integrating both geometric and physical dimensions.
  • To bridge the gap left by previous reviews focusing narrowly on geometry, optics, or algorithms.
  • To highlight emerging opportunities in advanced measurement techniques for general curvy reconstruction.

Main Methods:

  • Discussion of theoretical underpinnings and challenges in curvy surface reconstruction.
  • In-depth analysis of non-contact and contact measurement methods, including principles, progress, and limitations.
  • Review of various reconstruction algorithms and their practical applications.

Main Results:

  • A holistic framework for understanding curvy surface reconstruction beyond geometric shapes.
  • Detailed comparison of diverse measurement techniques for capturing complex 3D surfaces.
  • Exploration of algorithms enabling the reconstruction of continuous, smooth fields from discrete data.

Conclusions:

  • Curvy surface reconstruction is crucial for bridging the gap between 3D reality and 2D industrial paradigms.
  • Advanced measurement techniques and integrated geometric-physical approaches offer significant opportunities.
  • Further research is needed to address ongoing challenges and fully exploit the potential of this field.