Which statement best defines a spline?

Which statement best defines a spline?

• A. A type of curve interpolated between two endpoints and two or more tangent vectors.
• B. A sequence of vertices connected by straight lines.
• C. The portion of a NURBS curve between two control points.
• D. A method to render textures on a patch.

Answer: (A)

Splines are smooth curves defined so that the curve passes through specific endpoints while the tangent directions at those points control how the curve leaves and approaches each end. This combination—endpoints with associated tangents—lets the curve interpolate smoothly between points and shape the bending between them, which is exactly what a spline does in modeling tools. The other descriptions don’t capture this behavior: a sequence of straight-line segments describes a polyline, not a smooth curve; a portion of a NURBS curve between control points is a specific segment of a broader NURBS surface/curve and isn’t defined simply by two endpoints with tangents; and rendering textures on a patch is unrelated to how a curve is constructed.

Splines are smooth curves defined so that the curve passes through specific endpoints while the tangent directions at those points control how the curve leaves and approaches each end. This combination—endpoints with associated tangents—lets the curve interpolate smoothly between points and shape the bending between them, which is exactly what a spline does in modeling tools.

The other descriptions don’t capture this behavior: a sequence of straight-line segments describes a polyline, not a smooth curve; a portion of a NURBS curve between control points is a specific segment of a broader NURBS surface/curve and isn’t defined simply by two endpoints with tangents; and rendering textures on a patch is unrelated to how a curve is constructed.