Interval Extension Of The C-curve And Statistical Non-linear Relationship

OBezier curves and C-B-spline curves (NUAT B-spline curves) are defined over Γ_n-span{1,t ,..., t^n-2,sint ,cost}, so they can deal with free form curves, conic sections and transcendental curves in uniformness.In this paper, we first analyse the high order derivatives of OBezier basis and OB-spline basis, then the positivity of OBezier basis and uniform OB-spline basis are also studied. Based on these terms, we extend α from [0, π ] to [0, 2 π] in OBezier curves, and show a can be larger while elevating the order of uniform OB-spline curves. As a result , we derive the representation of arc with OBezier curves.On the other hand, the nonlinear relations among statistical indicators have been hot topics and difficulties in recent years. As members of Statistical Bureau of Zhejiang province, we solve the matter by using other subject concerned nonlinear relations, such as polynomial-spline function and artifical neural network. In order to apply these methods suitably, we present the principle, algorithm and effect.