# Curvy Surface Reconstruction

## TL;DR

This paper reviews curvy surface reconstruction, combining geometry and physical fields to better understand real-world 3D objects.

## Contribution

It introduces 'general curvy surface reconstruction' integrating both geometric and physical dimensions for the first time.

## Key findings

- Current reconstruction methods are limited to geometric shapes and lack integration of physical fields.
- Advanced measurement techniques and AI algorithms offer new opportunities for curvy surface reconstruction.
- Non-contact and contact measurement methods each have distinct advantages and limitations.

## Abstract

The physical world around us is inherently curvy, dynamic, and variable, yet modern industrial civilization is grounded in the planar, rigid paradigms of science and technology. This fundamental disconnect between two‐dimensional (2D) techniques and three‐dimensional (3D) realities significantly restricts our ability to fully perceive and to understand the complexity of real‐world objects. Over the past several decades, driven by application demands across various industries, advancements in high‐speed, high‐accuracy, and high‐resolution sensors, as well as ever‐increasing AI algorithms and computational power, curvy surface reconstruction that can reconstruct continuous, smooth geometrical and physical fields from discrete data by algorithms and mathematics have experienced tremendous developments. However, previous reviews in this field have primarily focused on geometric shapes, optical measurement techniques, or reconstruction algorithms, leaving a comprehensive overview that integrates both geometric and physical dimensions still lacking. Here, for the first time, we bridge this gap by expanding the scope from special curvy imaging to general curvy reconstruction incorporating physical fields, with a particular emphasis on measurement techniques, especially the emerging opportunities from advanced techniques. Initially, a brief overview starts with introducing the theoretical underpinnings and primary issues of curvy surface reconstruction. Next, an in‐depth discussion of the main non‐contact and contact measurement methods is presented, detailing their operational principles, progress, merits and demerits, and future efforts. Following that, several reconstruction algorithms and their applications are discussed. Finally, our insights on the ongoing challenges and opportunities in this field are summarized.

This review introduces the concept of “general curvy surface reconstruction,” which incorporates both geometric and physical dimensions, representing an upgrade over conventional geometric reconstruction that focuses solely on spatial relationships. Particular emphasis is placed on the emerging opportunities enabled by advanced measurement techniques, rapidly evolving AI algorithms, and increasing computational power.