Daily Archives: 09/16/2011

Planarity Analysis

There are various ways to subdivide complex surfaces and build curvilinear forms. Planar quadrilateral panels obtain a number of important advantages over triangular panels, considering discrete surface solutions; since they have smaller number of edges, resulting in smaller number of supporting beams following the edges. Planarity Analysis by Evolute plug-in for the software Rhinoceros 4 has been undertaken to map problem areas.

Two types of solution is considered as feasible. The panels are generated via the points located on the U & V curves of the surface.

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Variations for Panelization of the Architectural Geometry

To realize complex freeform surfaces, one has to segment the shape into simpler parts, so-called panels ( Schiftner, N. Baldassini, P. Bo, H. Pottmann, 2008). Various methods to subdivide the geometry have been investigated including quadrilateral, triangular, diamond shaped panels.

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)