A recent rib structure study developed in GC.

The depth of the ribs is controlled by a variable which is calculated in relation Dot.Product function. Dot Product: In mathematics, the dot product, also known as the scalar product, is an operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity. It is the standard inner product of the Euclidean space.In Euclidean geometry, the dot product, length, and angle are related: For a vector a, a•a is the square of its length, and, more generally, if b is another vector, a * b = |a| *|b| *cos(?) where|a| and |b| denote the length (magnitude) of a and b , and ? is the angle between them. Since |a|cos(?) is the scalar projection of a onto b, the dot product can be understood geometrically as the product of the length of this projection and the length of b.

(http://en.wikipedia.org/wiki/Dot_product )

The variable created in this example takes the Arccosine of the Dot Product for 2 vectors, which are the Z direction of the base coordinate system and the Z direction of the coordinate system created on the surface. Since the result will be an angle between 0 and 180, the Arccosine of the Dot Product is divided to 180, thus producing a variable between 0 and 1.

Posted: March 15th, 2008 under Parametric Design.
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