Bsplinekäyristä

Bsplinekäyristä (B-spline curves) are a type of piecewise polynomial curve used in computer graphics, geometric modeling, and data interpolation. They offer a flexible and efficient way to represent smooth curves and surfaces. Unlike Bézier curves, B-splines provide local control, meaning that moving a single control point only affects a localized portion of the curve. This makes them easier to manipulate and edit.

The shape of a B-spline curve is determined by a set of control points and a knot vector. The control points define the overall shape, while the knot vector dictates how the polynomial pieces are joined together. The degree of the polynomial segments determines the smoothness of the curve. Higher degrees result in smoother curves but require more computation.

B-splines are defined recursively using the Cox-de Boor formula. This formula allows for the calculation of points on the curve based on the control points and knot vector. A key advantage of B-splines is their ability to represent a wide range of shapes, from simple straight lines to complex, freeform curves. They also possess desirable properties such as affine invariance and convex hull property. Their versatility and control make them a fundamental tool in computer-aided design and manufacturing.