Do Complex Objects Have Equations?

[question99]

For example, if someone with an architectural modeling software designed a beautiful mansion or other type of intricate and ornate structure, is there some equation in the computer or some type of mathematical structure to what was designed? Are there potential mathematical blueprints for all possible objects?

Clearly some type of geometry is involved.

 

[Borek]

In general - no. But there are definitely architectural objects deliberately built around curves (or shapes) described by some interesting functions.

 

[Blackberg]

Certainly not a sinlgle one, but you could come up with very many. Such as y = 8 ft for a celing. That's a horizontal plane. And y = (8 + x) ft for half of a 45 deg inclined roof. Is that what you mean? You can also calculate how heavy a roof a given frame can support. There are equations for that.

 

[russ_watters]

Anything drawn on a computer using CAD software has a "mathematical structure" to it. For the most part, each element of the design is represented by its own equation. For example, line segments and arcs.

Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygons—all of which are based on mathematical expressions—to represent images in computer graphics.

http://en.wikipedia.org/wiki/Vector_graphics

 

[wabbit]

I understand that this used to be the case (and may still be mostly) for architecture software, allowing only for surfaces defined by an equation. I remember reading that when he wanted to escape such constraints, Frank Gehry used CAD software built for aviation to get the flexibility he wanted in his designs. He uses numerisation of physical models built from cardboard etc. to input complex shapes into the computer.

(Removed link because it might not be appropriate here. Google "Gehry CATIA")