Interactive Spatial Hermite Curves and Boundary-Constrained Triangulated Surfaces in a Coordinate-Frame Editor

This paper documents an interactive geometric construction pipeline in which editable three-dimensional curves provide the boundary of a triangulated surface. A curve consists of spatial positions and tangent vectors, connected by cubic Hermite spans and edited in three orthographic views. A closed curve is sampled, projected into a locally constructed coordinate frame, triangulated as a simple polygon, refined according to spatial edge length, improved by constrained edge flips and interior relaxation, and lifted to a harmonic height field with fixed three-dimensional boundary values. We give the equations, topology and quality checks, implementation choices, and reproducible measurements for planar, concave, and nonplanar loops. The resulting surface interpolates its sampled boundary and has disk topology for accepted input; it is not an exact NURBS surface. The coordinate-frame viewpoint supplies a convenient local chart and geometric metric, while the implemented curve state remains a position–tangent Hermite representation rather than a complete rational frame-curve model.