NURBS stands for Non-Uniform Rational B-Splines.

NURBS stands for Non-Uniform Rational B-Splines.

• A. Non-Uniform Rational B-Splines
• B. Non-Uniform Rational Basis Splines
• C. Uniform Rational B-Splines
• D. Non-Uniform Real Basis Splines

Answer: (A)

NURBS are built from B-Splines with weights, and the way they’re named reflects that combination. The correct form uses Non-Uniform for the knot vector, Rational to show the inclusion of weights, and B-Splines as the basis functions. The B-Splines part is the mathematical family that defines how control points influence the curve. The Rational bit means each basis function is weighted, which is what lets NURBS represent conic sections exactly and gives precise control over shaping. The Non-Uniform part refers to the knot vector having non-equal spacing, which provides greater flexibility in parameterization and local control of the curve. The other options drift in wording or meaning: using “Basis Splines” instead of the standard “B-Splines” is a common but less precise variant; calling the knot spacing “Uniform” would reduce flexibility; and “Real” instead of “Rational” changes the fundamental concept from weighted (rational) to unweighted (polynomial) splines.

NURBS are built from B-Splines with weights, and the way they’re named reflects that combination. The correct form uses Non-Uniform for the knot vector, Rational to show the inclusion of weights, and B-Splines as the basis functions. The B-Splines part is the mathematical family that defines how control points influence the curve. The Rational bit means each basis function is weighted, which is what lets NURBS represent conic sections exactly and gives precise control over shaping. The Non-Uniform part refers to the knot vector having non-equal spacing, which provides greater flexibility in parameterization and local control of the curve.

The other options drift in wording or meaning: using “Basis Splines” instead of the standard “B-Splines” is a common but less precise variant; calling the knot spacing “Uniform” would reduce flexibility; and “Real” instead of “Rational” changes the fundamental concept from weighted (rational) to unweighted (polynomial) splines.