A constant slope surface and its application

Abstract

A kind of constant slope surface whose tangent planes have a fixed inclination angle with xy-plane is commonly applied in civil engineering. With the idea of any horizantal curve on the surface being the envelope of family of circles, the equations of the surface are built. Also, it is proved that the normal vector of the surface is always enclosed to the z-axis. Finally, with the help the Maple, the parameterized 3D surface model is implemented. By two examples and an engineering examples of multi-level dam modelling, the equations proposed are verified and its results are accurate.