The three-dimensional (3D) dental arch curve, representing the spatial trajectory of dentition in either the maxilla or mandible, exhibits systematic alignment of tightly and orderly arranged teeth along its path. This structural configuration underscores its critical role as comprehensive anatomical guidance in digital dentistry, enabling high-precision tooth segmentation. In this study, we present a novel method for 3D dental arch curve detection from the volumetric cone beam computed tomography (CBCT) image, which, to our knowledge, represents the first successful implementation of 3D dental arch curve detection from the volumetric data. Specifically, we: (1) formulates and validates a dental arch curve fitting function, (2) identifies 3D uniformly distributed feature points proximal to the true dental arch curve through a feature point network framework, and (3) optimizes model parameters of the fitting function through a modified Expectation-Maximization (EM) algorithm with gradient descent. The proposed detection is then used to guide tooth segmentation through the curvilinear volume parameterization that unwind the vicinity of the dental arch curve. Experimental results demonstrate the accuracy for 3D dental arch curve detection and performance enhancements in the downstream task of tooth segmentation, improving segmentation precision compared to conventional approaches.