Smooth conjugation of two intersecting planes arbitrarily oriented in space

The method of smooth conjugation of two intersecting planes arbitrarily oriented in space is considered on the example of horizontal and sloping planes. The testing was performed in the MathCad 14 symbolic mathematics package. The smooth conjugation is carried out by the vector polynomial of the fifth power under boundary conditions. The coefficients are found when six vector boundary conditions are fulfilled. An example is given of a smooth conjunction of a horizontal and a sloping plane, which form a riding slide. The proposed technical requirement is a smooth transmission from the inclined plane of the slide into the horizontal surface of the proposed playground. The tangents to the trajectory of the motion must be the same in the transmission points. The curvature at these points is zero. When these requirements are fulfilled, a continuous change of the overload of g-force is achieved. A smooth conjunction surface can be defined as a polynomial of the fifth power. The direction vector is a unit vector of the intersection line for the two surfaces. The proposed method is invariant for the system it's applied to.