Conical Mesh of Revolution and its Application in Glass Structures and Steel Structures

Conical mesh is a novel class of planar quad mesh with nice offset property,and is well suited for glass/steel structure design.Surfaces of revolution often appear in architecture design.By introducing the definition of conical mesh,conical mesh of revolution is proposed and a simple method for the construction of conical mesh of revolution is also presented in this paper.We proved that for a surface of revolution r(u,v)=(f(u)cos v,f(u)sin v,g(u)),if the division in v direction is uniform,then the resulting quad mesh with arbitrary division in u direction from r(u,v) is a conical mesh.We also investigate the special construction method in the cases of cones and cylinders.Some modeling examples of glass/steel structure based on conical mesh of revolution are presented.The methods are simple and easy to implement,and are valuable for modeling of glass/steel structure in computer aided architecture design.