B-Spline (Basis Spline) are used for curve fitting and numerical differentiation with a minimal support wrt a given degree, smoothness, and domain partition. When order changes B-spline curve behaves differently. The level of smoothness depends on number of knots selected. 

Order 1- Point

Order 2 - line

Order 3 - Cubic Spline

and so on... 

It is a method to approximate a function (or curve). So you can always use it when you need to deal with any function. For examples, we could construct a finite difference scheme with the help of B-Spline for solving PDEs; and more typically, NURBS (Non-uniform rational basis spline) has become the industry standard in computer graphics for generating and representing curves and surfaces.

I enclose for you a very useful thesis that shows the application of the different forms of interpolations on the area of digital signal processing.

good Luck.

Prof. S. EL-Rabaie

Thank you Dear Dr. El-Sayed

This thesis is very useful 

https://www.researchgate.net/publication/292323255_Spl_Exponenta

https://www.researchgate.net/publication/255821660_sptools

https://www.researchgate.net/publication/236236757_Interpolating_splines_in_digital_signal_processing?ev=prf_pub

Data Spl Exponenta

Data sptools

Article Interpolating splines in digital signal processing

Dear Shelevytsky

I am intersting the techniqe which are nice work , and thank you

Famous application in spline interpolation I need

Thanks for raising such an interesting question. Probably some people would be interested in the following special issue.

"Modern Geometric Modeling: Theory and Applications II" (IF=2.258) (Deadline: February 28, 2022)

URL: https://www.mdpi.com/journal/mathematics/special_issues/Modern_Geometric_Modeling_Theory_Applications_II

Video: https://www.youtube.com/watch?v=aomv_9-FGkU

The scope of the Special Issue includes but is not limited to original research works within the subject of geometric modeling and its applications in engineering, arts, physics, biology, medicine, computer graphics, architecture, etc., as well as theoretical mathematics and geometry which can be applied to problems of geometric modeling. For this Special Issue, we plan to accept the following types of manuscripts:

• Overviews;
• Research manuscripts;
• Short manuscripts which discuss open problems in geometric modeling.