Search results
Results from the WOW.Com Content Network
A NURBS curve is defined by its order, a set of weighted control points, and a knot vector. [6] NURBS curves and surfaces are generalizations of both B-splines and Bézier curves and surfaces, the primary difference being the weighting of the control points, which makes NURBS curves rational.
Order, an academic journal on order theory; Dense order, a total order wherein between any unequal pair of elements there is always an intervening element in the order; Glossary of order theory; Lexicographical order, an ordering method on sequences analogous to alphabetical order on words; List of order topics, list of order theory topics
The development of non-uniform rational B-spline (NURBS) originated with seminal work at Boeing and Structural Dynamics Research Corporation in the 1980s and 1990s, a company that led in mechanical computer-aided engineering (CAE) in those years. [1] Boeing's involvement in NURBS dates back to 1979, when they began developing their own ...
This means that if a knot t i appears more than n + 1 times in an extended knot vector, all instances of it in excess of the (n + 1) th can be removed without changing the character of the spline, since all multiplicities n + 1, n + 2, n + 3, etc. have the same meaning. It is commonly assumed that any knot vector defining any type of spline has ...
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
Every well-ordered set is order-equivalent to exactly one ordinal number, by definition. The ordinal numbers are taken to be the canonical representatives of their classes, and so the order type of a well-ordered set is usually identified with the corresponding ordinal. Order types thus often take the form of arithmetic expressions of ordinals.
[1] When is not a commutative ring, the idea of order is still important, but the phenomena are different. For example, the Hurwitz quaternions form a maximal order in the quaternions with rational co-ordinates; they are not the quaternions with integer coordinates in the most obvious sense. Maximal orders exist in general, but need not be ...
Trapezoidal rule — second-order method, based on (piecewise) linear approximation; Simpson's rule — fourth-order method, based on (piecewise) quadratic approximation Adaptive Simpson's method; Boole's rule — sixth-order method, based on the values at five equidistant points; Newton–Cotes formulas — generalizes the above methods