What is the name of the curve that is interpolated between two endpoints using tangents?

What is the name of the curve that is interpolated between two endpoints using tangents?

• A. Bezier Curve
• B. Spline
• C. NURBS Curve
• D. Line

Answer: (B)

A spline is designed for smooth interpolation between points, using tangent directions at the endpoints to shape the curve as it passes from one end to the other. This setup—specifying tangents to control how the curve enters and exits the endpoints—produces a smooth, continuous path, which is exactly what “interpolated between two endpoints using tangents” describes. Bezier curves do achieve smoothness with control handles (tangents) but are defined by those handles in addition to the endpoints, making them a more specific construction within the broader idea of spline interpolation. NURBS are a more general framework that can represent many shapes, not necessarily characterized by a simple two-endpoint tangent interpolation. A line, of course, has no curvature at all. So the best fit for the description is a spline.

A spline is designed for smooth interpolation between points, using tangent directions at the endpoints to shape the curve as it passes from one end to the other. This setup—specifying tangents to control how the curve enters and exits the endpoints—produces a smooth, continuous path, which is exactly what “interpolated between two endpoints using tangents” describes. Bezier curves do achieve smoothness with control handles (tangents) but are defined by those handles in addition to the endpoints, making them a more specific construction within the broader idea of spline interpolation. NURBS are a more general framework that can represent many shapes, not necessarily characterized by a simple two-endpoint tangent interpolation. A line, of course, has no curvature at all. So the best fit for the description is a spline.