GEOMETRY

Geometry lies at the core of the architectural design process. It is omnipresent, from initial form-finding stages to actual construction. It also underlies the main communication medium; namely, graphical representations obtained by precise geometric rules. Whereas the variety of shapes that could be treated by traditional geometric methods has been rather limited, modern computing technologies have led to real geometry revolution.

Cardboard "Sliceforms"

These model below were made by John Sharp in 1998 using similar techniques to those used by Alexander Brill over 120 years earlier.

1. Cone

2. Two Cassinian ovals

3. Tetrahedron

4. Conoid

5. Monkey saddle

6. Parabola of revolution

Inventory: 1999-42,44,45,46,48,49 and 50 Source: John Sharp

Boolean operations

Boolean operations are named after the English mathematician George Boole (1815-1864).

From the mathematical point of view, Boolean union and intersection are commutative operations. This means that the order in which the objects are fed into the operation does not matter. Nevertheless, in CAD the sequence of selecting the involved objects influences the attributes of the emerging objects. The newly created object inherits the attributes of the first selected object. Sometimes CAD software seems to fail mysteriously in completing Boolean operations. Why does this matter, and how can we avoid such problems? To understand why Boolean operations do not succeed, one has to consider that these operations are multistep processes. They basically combine the following.

1. Computing the intersection curves

2. Splitting all involved objects along these curves

3. Deleting those parts not contained in the solution

4. Joining all remaining parts

Boolean operations typically fail because the calculation of the intersection curves creates curves with gaps due to badly modeled objects or inaccuracy of computations. To support your CAD software in performing Boolean operations you should observe the following.

" Try to extend your trimming objects beyond the faces of the modified object.

" Avoid combining objects with co-planar faces.

" Avoid nearly tangent surfaces.