# line_ncc_rule

line_ncc_rule, a C code which computes a Newton Cotes Closed (NCC) quadrature rule, using equally spaced points over the interior of a line segment in 1D.

### Languages:

line_ncc_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

ccn_rule, a C code which defines one of a set of nested Clenshaw Curtis quadrature rules of

CLENSHAW_CURTIS_RULE, a C code which defines a Clenshaw Curtis quadrature rule.

LEGENDRE_RULE, a C code which computes a 1D Gauss-Legendre quadrature rule.

LINE_FEKETE_RULE, a C code which approximates the location of Fekete points in an interval [A,B]. A family of sets of Fekete points, indexed by size N, represents an excellent choice for defining a polynomial interpolant.

LINE_FELIPPA_RULE, a C code which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

LINE_GRID, a C code which computes a grid of points over the interior of a line segment in 1D.

LINE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

LINE_MONTE_CARLO, a C code which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

LINE_NCO_RULE, a C code which defines a Newton Cotes Open (NCO) rule using equally spaced points over the interior of a line segment in 1D.

TRIANGLE_FEKETE_RULE, a C code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a C code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

WEDGE_FELIPPA_RULE, a C code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

### Reference:

1. Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.

### Source Code:

Last revised on 12 July 2019.