Abstract: This paper introduces the three-layer data structure and correlative algorithms of the open source kernel T-SPLINE,so as to facilitate the application for global users.Firstly,the fundamentals of T-SPLINE open source kernel and its three-layer data structure are introduced,which brings significant efficiency in computing and storing.Secondly,a set of efficient algorithms are designed according to the three-layer data structure,such as the face-oriented knots initialization,the extraction of critical parameters,efficient basis functions,the management of multiple knots,etc.Finally,some examples are tested to analyze and verify the space and time complexities.Experimental results show that the efficiency of the T-SPLINE kernel has obvious advantages in space and time complexities.