Splineille

Splineille is a term used in computer-aided geometric design to describe a compact, locally defined spline fragment. The name combines 'spline' with the French diminutive '-ille', signaling its role as a small, controllable piece within a larger spline network. In practice, a splineille denotes a cubic polynomial piece that is active only on a limited parameter interval and is connected to neighboring pieces through a chosen knot vector and basis functions. Each splineille is defined by a small set of control points and associated weights, and it yields a smooth curve segment when blended with adjacent segments. The construction typically ensures continuity of position and tangent direction across internal junctions, and often also curvature continuity up to the second derivative within its support.

Splineilles are used to provide fine-grained local control in digital modeling and animation. They allow designers to push or pull localized shape features without affecting distant parts of the model, reducing the need for full-rebuild refinements of global spline structures. They can be integrated into existing B-spline or NURBS frameworks by decomposing a global curve into a sequence of splineilles, each responsible for a short interval.

Advantages include efficient local edits, predictable modification behavior, and compatibility with standard basis functions. Limitations can include handling of boundary conditions, texture mapping along the curve, and ensuring seamless transitions in complex networks.

Related topics: splines, Bezier curves, B-splines, NURBS.