Nosecurves

Nosecurves is a term used in digital geometry to describe a class of parametric curves that model the profile of a human nose. It covers smooth, continuous curves that capture the dorsum, bridge, and nasal tip, with emphasis on curvature control and positional continuity along the nasal axis. In 2D representations, a nosecurve may be described as a function y = f(x) with constraints that maintain monotonic progression from the bridge to the tip; in 3D, a nosecurve is typically expressed as a parametric curve P(t) = (x(t), y(t), z(t)) for t in [0,1], often built from Bezier, B-spline, or NURBS bases.

Construction and fitting: Nosecurves are commonly derived from 3D nasal scans, CT/MRI data, or anthropometric measurements. Fitting methods include least-squares spline fitting, constrained optimization to preserve smoothness, and regularization to avoid excessive bending. The resulting curves are evaluated by curvature continuity, length, and alignment with anatomical landmarks.

Applications: They are used in surgical planning for rhinoplasty, prosthetic nose design, and computer graphics and animation for character faces. They enable consistent interpolation between reference profiles and support digital manipulation while preserving plausible anatomy.

Limitations: Nosecurves depend on data quality and chosen representation; overfitting or underfitting can produce anatomically implausible results. Ongoing work aims to integrate tissue mechanics, asymmetry handling, and population-based averaging.