Abstract
Curvature is known as an important geometrical property for curve generation in engineering applications. For example, in designing a car body, its curvature distribution has much effect on its fairness. In a usual mathematical curve, it needs complex calculation to obtain curvature distribution. This calculation causes the difficulty of the control of curvature distribution. If we can directly specify curvature distribution, this problem can be solved. A new curve is introduced by assigning its tangent with commutative addition of transformations. This method is expected to make it possible to directly specify its curvature distribution.
