Architectural Geometry Generated Through Curve Functions

Klein Surface is investigated in terms of architectural geometry which represents a usable volume. It is a non-orientable closed surface which is homeomorphic to a connected sum of a number of copies of the real projective plane. 

//Parameters : range values (β, μ); re-built curve values

//Definitions of curve functions

Function X = (1 + cos(β /2)*sin(μ) – sin(β /2)*sin(2* μ))*cos(β)

Function Y = (1 +cos(β /2)*sin(μ) – sin(β /2)*sin(2* μ))*sin(β)

Function Z = sin(β /2)*sin(μ) + cos(β /2)*sin(2* μ)

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