in Autodesk Maya when an user creates an animation of two keyframes the program displays the animation curve like in the pictures below. There's a curve with a start and an end point, spline interpolated, the user can edit the angle on both ends to edit it like this.
In math, I've found how to interpolate via several methods between two points, but I haven't found how to get the shape of a curve like in the second picture, and with an angle on both points as a parameter to edit.
I might be some kind of cubic parametric curve.
Curve might be represented as Hermite spline or in Bezier form - the most widely used form in computer graphics.
Bezier curve description requires end points and control points that define direction (angle) and magnitude of derivatives at the ends.
