tiegeometria

Tiegeometria is a multidisciplinary field that studies the geometry of ties and tie knots, addressing mathematical properties of knot forms, fabric drape, and visual balance. It draws on geometry, topology, computational design, and textile science to model how neckwear occupies space on the body and interacts with fabric behavior.

The term is informal and not widely recognized as a standalone academic discipline; it appears mainly in design discourse and fashion-technology discussions to describe approaches that formalize the shapes and folds of neckwear.

Core concepts include knot geometry (types of knots, angular constraints, symmetry), drape geometry (curvature along the length, gravity effects), pose and alignment (knot height and tilt), fabric properties (thickness, stiffness, elasticity), and pattern geometry (tessellations and motif placement around the knot).

Methods involve parametric modeling, 3D scanning, finite element simulations of fabric, and visualization tools, often combining CAD with mathematical analysis to explore how changes in length, width, or fabric stiffness alter the overall silhouette.

Applications span fashion design and customization, education and outreach in geometry, digital fabrication and patterning, and research on handling flexible objects in robotics.

See also: knot theory, geometric modeling, textile engineering, fashion mathematics. Further reading includes general resources on knot theory and textile geometry; there are no fixed standards for terminology or measurement in tie geometry.