- Parametric Evaluation: Splines are typically defined by parametric equations. To find the endpoint, you can evaluate the spline function at its endpoint parameter value. This value may be explicitly defined or inferred from the spline’s control points.
- Control Points: In many cases, splines are defined by control points (e.g., Bezier or B-spline control points). The endpoint can be one of these control points or derived from them.
- Length-Based: If you want to find a specific endpoint based on a certain length along the spline, you can iterate along the spline, accumulating the arc length until you reach the desired length. This can be useful for animations or simulations where you need to travel a certain distance along the spline.
- Interpolation: For splines that interpolate a set of keyframes or waypoints, the endpoint may be defined explicitly as the last keyframe or waypoint.
- Tangent or Normal Vector: Depending on your use case, you might be interested in the tangent or normal vector at the endpoint. These vectors can be calculated using differentiation techniques or geometric properties of the spline.