Differences Between Bezier And B-spline Curves-converted 5w5m6m

Computer Graphics (CS502)

Q. List out the differences between Bezier curves and B-spline curves.

Bezier Curves

B-spline Curves

It is defined by Approximating tangents on the It is defined as a linear combination of control curve by using control points points and a B-spline basis function, the basis function specifies the span/influence of each control point. The Bezier approximation provides the global control of curve shape. If a single control point is changed, the shape of curve is disturbed.

The B-spline approximation provides the local control of curve shape. If a single control point is changed, only parts of the curve lying under the influence of that control point are disturbed.

It is a special case of a B-spline curve, where It is a generalized version of a Bezier curve the basis function defines the span/influence that consists of Bezier curves as segments. of each point on the entire curve. The degree of the polynomial defining the The degree of the polynomial defining the curve segment is one less than the number of curve segment is independent of the number defining polygon/control points. of defining polygon/control points. It is invariant under an affine transformation (scaling/translation/ rotation).

By applying an affine transformation to the vertices of the defining polygon, the curve shape is affected.

It always es through the first and last control points.

It may or may not through the first and last control points.

It has limited control and flexibility on the curve.

It offers more control and flexibility on the curve.

These are found in painting and drawing packages as well as in CAD applications

These are used to construct blending curves.

It can represent any polynomial curve.

It cannot represent some polynomial curves, like simple circles and ellipses.