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Advanced Building Skins
Ellipsoid of Revolution (Spheroid)
An ellipsoid of revolution is a comparatively constant geometry. It needs a comparatively low amount
of component sections, because it is both in horizontal and vertical direction axially symmetric (figure
10). As the name suggests, the ellipsoid of revolution can be produced due to the revolution of the
longitudinal curve in the x-axis. All components contained in the z- and y-axis are identical because of
the rotation. Furthermore, all of these components are mirrored in the x-axes.
Figure 10: Ellipsoid of revolution Figure 11: Triaxial Ellipsoid
Triaxial Ellipsoid
The triaxial ellipsoid can be produced only with a large number of individual parts, because there are
different curvatures in all three axes (figure 11). Nevertheless, the triaxial ellipsoid is both in the y-
and z-axis symmetrical. In addition, just like the ellipsoid of revolution, through the axial symmetry in
the x-axis, all components in the y- and z-axis are mirrored.
3.3 Double-Curved Anticlastic Geometries
A double-curved anticlastic geometry can be identified for example in the geometry of a hyperbolic
paraboloid (figure 12).
Figure 12: Double in the opposite direction curved Geometry
This can be manufactured either with only one component or it is composed of several components.
The geometry is axial symmetric to the center point. Thus, the geometry can produce two identical
components or modular systems (depending on meshing) with the second part being a mirror of the
first part (figure 12). However, this principle can only be applied if the geometry is curved constantly
in both axes.
3.4 Conclusion of the Modularization of rule Geometries
It is not possible to define a modular component system and to create different freeform geometries
out of this. If a freeform geometry with the correct degree of curvature is to be split in a component
system, it needs to be divided into its own modular set of components. It is also assumed that no
component is similar to a segment of a different geometry. If freeform geometries are modularized in
modular component systems, other computer-based tools will have to be used.
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