What is B-spline curve in computer graphics?

B-spline allows the local control over the curve surface because each vertex affects the shape of a curve only over a range of parameter values where its associated basis function is nonzero. The curve exhibits the variation diminishing property. The curve generally follows the shape of defining polygon.

What are spline curves and B-spline curve?

A spline curve is a mathematical representation for which it is easy to build an interface that will allow a user to design and control the shape of complex curves and surfaces. 2. B-Spline : B-Spline is a basis function that contains a set of control points.

What are the characteristics of B-spline curves?

Properties of B-spline Curve :

• Each basis function has 0 or +ve value for all parameters.
• Each basis function has one maximum value except for k=1.
• The degree of B-spline curve polynomial does not depend on the number of control points which makes it more reliable to use than Bezier curve.

What is B-spline surface and explain it?

4 B-spline surface. The surface analogue of the B-spline curve is the B-spline surface (patch). This is a tensor product surface defined by a topologically rectangular set of control points , , and two knot vectors and associated with each parameter , .

What are the advantages of B-spline curve?

Explanation: B-splines produce the nicest and cleanest curves among many of the encoding options available, without any overshooting. A Bezier spline has the benefit that you might have complete control over most of the form of that same motion, at the cost of having further adjustments to produce a smooth slope.

How do splines work?

The spline bends a sheet of rubber that passes through the input points while minimizing the total curvature of the surface. It fits a mathematical function to a specified number of nearest input points while passing through the sample points.

Why are the B-splines a basis?

B-splines play the role of basis functions for the spline function space, hence the name. This property follows from the fact that all pieces have the same continuity properties, within their individual range of support, at the knots.

What is B-spline basis functions?

A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions enable the creation and management of complex shapes and surfaces using a number of points.

What are the advantages of B-spline curve over Bezier curve?

Why is B-spline curve better than Bezier curve?

Firstly, a B-Spline curve can be a Bezier curve whenever the programmer so desires. Further B-Spline curve offers more control and flexibility than Bezier curve. It is possible to use lower degree curves and still maintain a large number of control points.

What are the two advantages of B-splines over Bezier curve?

B-splines produce the nicest and cleanest curves among many of the encoding options available, without any overshooting. A Bezier spline has the benefit that you might have complete control over most of the form of that same motion, at the cost of having further adjustments to produce a smooth slope.

What is the advantages of B-spline over Bezier curve?

What is a B-spline curve?

Concept of B-spline curve came to resolve the disadvantages having by Bezier curve, as we all know that both curves are parametric in nature. In Bezier curve we face a problem, when we change any of the control point respective location the whole curve shape gets change.

What are the total knots vectors of a B-spline curve?

Total no. of seg = n – k + 2 = 7 – 4 + 2 = 5. The point between two segments of a curve that joins each other such points are known as knots in B-spline curve. In the case of the cubic polynomial degree curve, the knots are “n+4”. But in other common cases, we have “n+k+1” knots. So, for the above curve, the total knots vectors will be –

How do you subdivide a B spline surface?

3. 3 B-spline surface Subdivision • A B-spline surface is subdivided by separately subdividing polygon grid lines in one or both parametric direction • The flexibility of B-spline curves and surfaces is increased by raising the order of the basis function and hence the defining polygon/grid segments.

What are B-splines and how are they formed?

As we see above that the B-splines curves are independent of the number of control points and made up of joining the several segments smoothly, where each segment shape is decided by some specific control points that come in that region of segment. Consider a curve given below – We have “n+1” control points in the above, so, n+1=8, so n=7.