What is a Piecewise (Cubic) Hermite Curve?
A piecewise cubic hermite curve is a curve that is represented with four degrees of freedom. Two degrees of freedom are defined as the positions of the two end points of the curve. The other two degrees of freedom are defined as the tangents to the endpoints of the curve. Pictorially this is displayed on the “Curve Editor:” canvas with the beginning control point of the hermite curve displayed in red, and the end control point displayed in green. The tangent of the beginning point is in blue, and the tangent of the end point is in pink. The point in time of this parametric curve is displayed by a black dot on the “Curve Editor” canvas and by a black vertical line on the hermite basis functions canvas. This point in time is determined by adding the red basis function’s value times the red control point, plus the green basis function’s value times the green control point, plus the blue basis function’s value times the blue tangent, pluse the pink basis function’s valuet imes the pink tan
