COMSOL Multiphysics™

BSplineMfd
BSplineMfd
Supported Versions 0
Subtype of
Fields
Manifold
The class is defined by the following fields
ENTITY/
OBJECT
VARIABLE
DESCRIPTION
integer
Version
integer d Space dimension
Transform
Transformation class
integer
Dimension (1 if curve, 2 if surface)
integer p, q Degree in each dimension (1 or 2 integers)
boolean
If rational equal to1
integer
Number of knot vectors (1 for curves, 2 for
surfaces)
integer m1 Length of first knot vector
double[m1] U First knot vector
integer m2 Length of second knot vector (not for curves)
double[m2] V Second knot vector (not for curves)
integer n1 Number of control points in first parameter
direction
integer n2 Number of control points in second parameter
dimension
integer n3 Number of coordinates per control point
double
[n1][n2][n3]
P
Matrix of coordinates where the last dimension is
increased by 1 to store the weights if the manifold
is rational
Description
The BSplineMfd type is the abstract base type for BSplineCurve and
BSplineSurf, that represents general spline curves and surfaces respectively.
They are represented using B-spline basis functions. Let U = { u 0
,…,
u m
} be a
non decreasing sequence of real numbers. U is called the knot vector and the
elements u i of U are called knots. The ith B-spline basis function of p-degree,
p
N i ( u),
is defined as
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