Author Archives: Matthew Whitcomb


Curve/ Spline/ Knot Vector

Knots or knot vector

Each NURBS curve has a list of numbers associated with it that is called a knot vector.  Knots are a little harder to understand and set, but luckily there are SDK functions that do the job for you.

Knot multiplicity

Number of times a knot value is duplicated is called the knot’s multiplicity. Any knot value can not be duplicated more than the curve degree. Here are few things that would be good to know about knots.

Full multiplicity knot

Clamped curves have knots with full multiplicity at the two ends of the curve and this is why end control points coincide with curve end points. If there were full multiplicity knot in the middle of the knot vector, then the curve will go through the control point and there would be a kink.

Simple knot: is a knot with value appearing only once.

Uniform knot vector satisfies 2 conditions:

1. Number of knots = number of control points + degree – 1.

2. Knots start with a full multiplicity knot, is followed by simple knots, terminates with a full multiplicity knot, and the values are increasing and equally spaced.

P1_Matthew Whitcomb_01

This was a competition entry for “The Room in London” competition.  The structure uses a computational geometric algorithm leading to a balanced subdivision of the outer shell oh the rooms and also matching coherent organization of the space inside.  Program implies itself on the interior as well as logic of structure and detailing processes.  The result is an assembly of modules that fit perfectly into one another.

The Theory behind the structure is through the basis of the Dirichlet Tessellation.  This is a decomposition of a metric space determined by distances to a specific set of objects in space.  This sequence was used to determine the subdivision of space and distance between points in space in a 2-D and 3-D.   The process of the division of space facilitates also in the handlings, assembly, and reuse of the structure.  The manufacturing process benefits from the accuracy of the 3-D model using fast prototyping abilities.  Planning furniture design form the beginning assures the best possible fit and maximum production efficiency.

The structure is made from an aluminum space frames offering numerous designs reacting to environmental concerns through geometric perfection.  Space frame structures are used in the design allowing credibility for green qualifications since structures are lightweight, made of high content recycled material, use less energy to produce, cost less to deliver and install, come with a low maintenance/low environmental impact finish and are flexible in design to the point that they can be easily de-commissioned and moved, stored or installed in another location.