Uniform B - spline curve: When the spacing between Knot values is constant, the resulting curve is called a uniform B- spline. Blending function for B- spline curves are defined by cox- deboor recursion formulas: Where each blending, function is defined over d subintervals of the total range of u. the selected set of subinterval end points u_{j }is referred to as a Knot vector. B- spline curves have the following properties:
1.the polynomial curve has degree d - 1 and C^{d-2 }continuity over the range of u.
2. For n + 1 control points, the curve is described with n + 1 blending functions.
3. Each blending function B is defined over subintervals of the total range of u starting at knot value u.
4. The range of parameter u is divided into n + d subintervals by the n + d + 1 values specified in knot vector.
5. With knot values lableled as the resulting B-spline curve is defined only in the interval from knot value upto knot value.
6. Each section of the spline curve is influenced by d control points.
7. Any one central point can affect the shap of at most d curve section.
8. In addition B-spline curve lies within the convex hull of at must d + 1 control points so that B-spline are lightly bound to the positions.
9. For any values of u in the interval from knot value the sum over all basis functions is 1.