/usr/share/octave/packages/nurbs-1.3.10/doc-cache is in octave-nurbs 1.3.10-1.
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# name: cache
# type: cell
# rows: 3
# columns: 68
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
basisfun
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 775
BASISFUN: Basis function for B-Spline
Calling Sequence:
N = basisfun(iv,uv,p,U)
INPUT:
iv - knot span ( from FindSpan() )
uv - parametric points
p - spline degree
U - knot sequence
OUTPUT:
N - Basis functions vector(numel(uv)*(p+1))
Adapted from Algorithm A2.2 from 'The NURBS BOOK' pg70.
See also:
numbasisfun, basisfunder, findspan
Copyright (C) 2000 Mark Spink
Copyright (C) 2007 Daniel Claxton
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
BASISFUN: Basis function for B-Spline
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
basisfunder
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 795
BASISFUNDER: B-Spline Basis function derivatives.
Calling Sequence:
ders = basisfunder (ii, pl, uu, k, nd)
INPUT:
ii - knot span index (see findspan)
pl - degree of curve
uu - parametric points
k - knot vector
nd - number of derivatives to compute
OUTPUT:
ders - ders(n, i, :) (i-1)-th derivative at n-th point
Adapted from Algorithm A2.3 from 'The NURBS BOOK' pg72.
See also:
numbasisfun, basisfun, findspan
Copyright (C) 2009,2011 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
BASISFUNDER: B-Spline Basis function derivatives.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
basiskntins
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1197
Compute the coefficient matrix for non-uniform B-splines subdivision.
This represents the B-spline basis given by a coarse knot vector
in terms of the B-spline basis of a finer knot vector.
The function is implemented for the univariate case. It is based on
the paper:
G. Casciola, L. Romani, A general matrix representation for non-uniform
B-spline subdivision with boundary control, ALMA-DL, University of Bologna (2007)
Calling Sequence:
S = basiskntins (deg, t, u);
INPUT:
deg - degree of the first knot vector
t - coarse knot vector
u - fine knot vector
OUTPUT:
B - Value of the basis functions at the points
size(B)=[numel(u),(p+1)] for curves
or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
N - Indices of the basis functions that are nonvanishing at each
point. size(N) == size(B)
Copyright (C) 2015 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 70
Compute the coefficient matrix for non-uniform B-splines subdivision.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
bspdegelev
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 703
BSPDEGELEV: Degree elevate a univariate B-Spline.
Calling Sequence:
[ic,ik] = bspdegelev(d,c,k,t)
INPUT:
d - Degree of the B-Spline.
c - Control points, matrix of size (dim,nc).
k - Knot sequence, row vector of size nk.
t - Raise the B-Spline degree t times.
OUTPUT:
ic - Control points of the new B-Spline.
ik - Knot vector of the new B-Spline.
Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
BSPDEGELEV: Degree elevate a univariate B-Spline.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
bspderiv
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 766
BSPDERIV: B-Spline derivative.
MATLAB SYNTAX:
[dc,dk] = bspderiv(d,c,k)
INPUT:
d - degree of the B-Spline
c - control points double matrix(mc,nc)
k - knot sequence double vector(nk)
OUTPUT:
dc - control points of the derivative double matrix(mc,nc)
dk - knot sequence of the derivative double vector(nk)
Modified version of Algorithm A3.3 from 'The NURBS BOOK' pg98.
Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
BSPDERIV: B-Spline derivative.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
bspeval
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 713
BSPEVAL: Evaluate B-Spline at parametric points.
Calling Sequence:
p = bspeval(d,c,k,u)
INPUT:
d - Degree of the B-Spline.
c - Control Points, matrix of size (dim,nc).
k - Knot sequence, row vector of size nk.
u - Parametric evaluation points, row vector of size nu.
OUTPUT:
p - Evaluated points, matrix of size (dim,nu)
Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton, 2010 C. de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
BSPEVAL: Evaluate B-Spline at parametric points.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
bspkntins
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 855
BSPKNTINS: Insert knots into a B-Spline
Calling Sequence:
[ic,ik] = bspkntins(d,c,k,u)
INPUT:
d - spline degree integer
c - control points double matrix(mc,nc)
k - knot sequence double vector(nk)
u - new knots double vector(nu)
OUTPUT:
ic - new control points double matrix(mc,nc+nu)
ik - new knot sequence double vector(nk+nu)
Modified version of Algorithm A5.4 from 'The NURBS BOOK' pg164.
Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton, 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
BSPKNTINS: Insert knots into a B-Spline
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
crvkntremove
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1150
CRVKNTREMOVE: Remove one knot from the knot-vector of a NURBS curve.
Calling Sequence:
[rcrv, remflag] = crvkntremove (crv, u, r, s, num, d);
INPUT:
crv : NURBS curve, see nrbmak.
u : knot to be removed.
r : index of the knot to be removed.
s : multiplicity of the knot to be removed.
num : number of knot removals requested.
d : curve deviation tolerance.
OUTPUT:
rcrv : new NURBS structure for the curve with knot u remuved.
t : actual number of knot removals performed.
DESCRIPTION:
Remove knot u from the NURBS curve crv at most num times.
Check that the maximum deviation of the curve be less than d.
Based on algorithm A5.8 NURBS Book (pag183)
SEE ALSO:
nrbkntins
Copyright (C) 2013 Jacopo Corno
Copyright (C) 2013 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 71
CRVKNTREMOVE: Remove one knot from the knot-vector of a NURBS curve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
curvederivcpts
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 970
Compute control points of n-th derivatives of a B-spline curve.
usage: pk = curvederivcpts (n, p, U, P, d)
pk = curvederivcpts (n, p, U, P, d, r1, r2)
If r1, r2 are not given, all the control points are computed.
INPUT:
n+1 = number of control points
p = degree of the spline
d = maximum derivative order (d<=p)
U = knots
P = control points
r1 = first control point to compute
r2 = auxiliary index for the last control point to compute
OUTPUT:
pk(k,i) = i-th control point of (k-1)-th derivative, r1 <= i <= r2-k
Adaptation of algorithm A3.3 from the NURBS book, pg98.
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Compute control points of n-th derivatives of a B-spline curve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
curvederiveval
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 754
CURVEDERIVEVAL: Compute the derivatives of a B-spline curve.
usage: ck = curvederiveval (n, p, U, P, u, d)
INPUT:
n+1 = number of control points
p = spline order
U = knots
P = control points
u = evaluation point
d = derivative order
OUTPUT:
ck (k+1) = curve differentiated k times
Adaptation of algorithm A3.4 from the NURBS book, pg99
Copyright (C) 2009 Carlo de Falco
Copyright (C) 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
CURVEDERIVEVAL: Compute the derivatives of a B-spline curve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
deg2rad
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 696
DEG2RAD: Convert degrees to radians.
Calling Sequence:
rad = deg2rad(deg);
INPUT:
deg : Angle in degrees.
OUTPUT:
rad : Angle in radians.
Description:
Convenient utility function for converting degrees to radians, which are
often the required angular units for functions in the NURBS toolbox.
Examples:
// Convert 35 degrees to radians
rad = deg2rad(35);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
DEG2RAD: Convert degrees to radians.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
findspan
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 634
FINDSPAN Find the span of a B-Spline knot vector at a parametric point
Calling Sequence:
s = findspan(n,p,u,U)
INPUT:
n - number of control points - 1
p - spline degree
u - parametric point
U - knot sequence
OUTPUT:
s - knot span index
Modification of Algorithm A2.1 from 'The NURBS BOOK' pg68
Copyright (C) 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
FINDSPAN Find the span of a B-Spline knot vector at a parametric point
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
kntbrkdegmult
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 917
KNTBRKDEGMULT: Construct an open knot vector by giving the sequence of
knots, the degree and the multiplicity.
knots = kntbrkdegreg (breaks, degree)
knots = kntbrkdegreg (breaks, degree, mult)
INPUT:
breaks: sequence of knots.
degree: polynomial degree of the splines associated to the knot vector.
mult: multiplicity of the knots.
OUTPUT:
knots: knot vector.
If MULT has as many entries as BREAKS, or as the number of interior
knots, a different multiplicity will be assigned to each knot. If
MULT is not present, it will be taken equal to 1.
Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
KNTBRKDEGMULT: Construct an open knot vector by giving the sequence of
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
kntbrkdegreg
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 939
KNTBRKDEGREG: Construct an open knot vector by giving the sequence of
knots, the degree and the regularity.
knots = kntbrkdegreg (breaks, degree)
knots = kntbrkdegreg (breaks, degree, regularity)
INPUT:
breaks: sequence of knots.
degree: polynomial degree of the splines associated to the knot vector.
regularity: splines regularity.
OUTPUT:
knots: knot vector.
If REGULARITY has as many entries as BREAKS, or as the number of interior
knots, a different regularity will be assigned to each knot. If
REGULARITY is not present, it will be taken equal to DEGREE-1.
Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
KNTBRKDEGREG: Construct an open knot vector by giving the sequence of
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
kntrefine
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1327
KNTREFINE: Refine a given knot vector by dividing each interval uniformly,
maintaining the continuity in previously existing knots.
[rknots] = kntrefine (knots, n_sub, degree, regularity)
[rknots, zeta] = kntrefine (knots, n_sub, degree, regularity)
[rknots, zeta, new_knots] = kntrefine (knots, n_sub, degree, regularity)
INPUT:
knots: initial knot vector.
n_sub: number of new knots to be added in each interval.
degree: polynomial degree of the refined knot vector
regularity: maximum global regularity
OUTPUT:
rknots: refined knot vector
zeta: refined knot vector without repetitions
new_knots: new knots, to apply the knot insertion
The regularity at the new inserted knots is the one given by the user.
At previously existing knots, the regularity is the minimum
between the previous regularity, and the one given by the user.
This ensures optimal convergence rates in the context of IGA.
Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
KNTREFINE: Refine a given knot vector by dividing each interval uniformly,
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
kntuniform
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 716
KNTUNIFORM: generate uniform open knot vectors in the reference domain.
[csi, zeta] = kntuniform (num, degree, regularity)
INPUT:
num: number of breaks (in each direction)
degree: polynomial degree (in each direction)
regularity: global regularity (in each direction)
OUTPUT:
csi: knots
zeta: breaks = knots without repetitions
Copyright (C) 2009, 2010 Carlo de Falco
Copyright (C) 2011 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
KNTUNIFORM: generate uniform open knot vectors in the reference domain.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nrb2iges
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 736
NRB2IGES : Write a NURBS curve or surface to an IGES file.
Calling Sequence:
nrb2iges (nurbs, filename);
INPUT:
nurbs : NURBS curve or surface, see nrbmak.
filename : name of the output file.
Description:
The data of the nurbs structure is written in a file following the IGES
format. For a more in-depth explanation see, for example:
<http://engineeronadisk.com/V2/notes_design/engineeronadisk-76.html>.
Copyright (C) 2014 Jacopo Corno
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
NRB2IGES : Write a NURBS curve or surface to an IGES file.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nrb4surf
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1088
NRB4SURF: Constructs a NURBS bilinear surface.
Calling Sequence:
srf = nrb4surf(p11,p12,p21,p22)
INPUT:
p11 : Cartesian coordinate of the lhs bottom corner point.
p12 : Cartesian coordinate of the rhs bottom corner point.
p21 : Cartesian coordinate of the lhs top corner point.
p22 : Cartesian coordinate of the rhs top corner point.
OUTPUT:
srf : NURBS bilinear surface, see nrbmak.
Description:
Constructs a bilinear surface defined by four coordinates.
The position of the corner points
^ V direction
|
----------------
|p21 p22|
| |
| SRF |
| |
|p11 p12|
-------------------> U direction
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
NRB4SURF: Constructs a NURBS bilinear surface.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
nrbbasisfun
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1176
NRBBASISFUN: Basis functions for NURBS
Calling Sequence:
B = nrbbasisfun (u, crv)
B = nrbbasisfun ({u, v}, srf)
[B, N] = nrbbasisfun ({u, v}, srf)
[B, N] = nrbbasisfun (pts, srf)
INPUT:
u - parametric coordinates along u direction
v - parametric coordinates along v direction
pts - array of scattered points in parametric domain, array size: (2,num_points)
crv - NURBS curve
srf - NURBS surface
If the parametric coordinates are given in a cell-array, the values
are computed in a tensor product set of points
OUTPUT:
B - Value of the basis functions at the points
size(B)=[numel(u),(p+1)] for curves
or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
N - Indices of the basis functions that are nonvanishing at each
point. size(N) == size(B)
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
NRBBASISFUN: Basis functions for NURBS
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
nrbbasisfunder
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1429
NRBBASISFUNDER: NURBS basis functions derivatives
Calling Sequence:
Bu = nrbbasisfunder (u, crv)
[Bu, N] = nrbbasisfunder (u, crv)
[Bu, Bv] = nrbbasisfunder ({u, v}, srf)
[Bu, Bv, N] = nrbbasisfunder ({u, v}, srf)
[Bu, Bv, N] = nrbbasisfunder (pts, srf)
INPUT:
u - parametric coordinates along u direction
v - parametric coordinates along v direction
pts - array of scattered points in parametric domain, array size: (2,num_points)
crv - NURBS curve
srf - NURBS surface
If the parametric coordinates are given in a cell-array, the values
are computed in a tensor product set of points
OUTPUT:
Bu - Basis functions derivatives WRT direction u
size(Bu)=[numel(u),(p+1)] for curves
or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
Bv - Basis functions derivatives WRT direction v
size(Bv)=[numel(v),(p+1)] for curves
or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
N - Indices of the basis functions that are nonvanishing at each
point. size(N) == size(B)
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
NRBBASISFUNDER: NURBS basis functions derivatives
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
nrbcirc
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 999
NRBCIRC: Construct a circular arc.
Calling Sequence:
crv = nrbcirc()
crv = nrbcirc(radius)
crv = nrbcirc(radius,center)
crv = nrbcirc(radius,center,sang,eang)
INPUT:
radius : Radius of the circle, default 1.0
center : Center of the circle, default (0,0,0)
sang : Start angle, default 0 radians (0 degrees)
eang : End angle, default 2*pi radians (360 degrees)
OUTPUT:
crv : NURBS curve for a circular arc.
Description:
Constructs NURBS data structure for a circular arc in the x-y plane. If
no rhs arguments are supplied a unit circle with center (0.0,0.0) is
constructed.
Angles are defined as positive in the anti-clockwise direction.
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
NRBCIRC: Construct a circular arc.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nrbcoons
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2143
NRBCOONS: Construction of a Coons patch.
Calling Sequence:
srf = nrbcoons(ucrv1, ucrv2, vcrv1, vcrv2)
INPUT:
ucrv1 : NURBS curve defining the bottom U direction boundary of
the constructed NURBS surface.
ucrv2 : NURBS curve defining the top U direction boundary of
the constructed NURBS surface.
vcrv1 : NURBS curve defining the bottom V direction boundary of
the constructed NURBS surface.
vcrv2 : NURBS curve defining the top V direction boundary of
the constructed NURBS surface.
OUTPUT:
srf : Coons NURBS surface patch.
Description:
Construction of a bilinearly blended Coons surface patch from four NURBS
curves that define the boundary.
The orientation of the four NURBS boundary curves.
^ V direction
|
| ucrv2
------->--------
| |
| |
vcrv1 ^ Surface ^ vcrv2
| |
| |
------->-----------> U direction
ucrv1
Examples:
// Define four NURBS curves and construct a Coons surface patch.
pnts = [ 0.0 3.0 4.5 6.5 8.0 10.0;
0.0 0.0 0.0 0.0 0.0 0.0;
2.0 2.0 7.0 4.0 7.0 9.0];
crv1 = nrbmak(pnts, [0 0 0 1/3 0.5 2/3 1 1 1]);
pnts= [ 0.0 3.0 5.0 8.0 10.0;
10.0 10.0 10.0 10.0 10.0;
3.0 5.0 8.0 6.0 10.0];
crv2 = nrbmak(pnts, [0 0 0 1/3 2/3 1 1 1]);
pnts= [ 0.0 0.0 0.0 0.0;
0.0 3.0 8.0 10.0;
2.0 0.0 5.0 3.0];
crv3 = nrbmak(pnts, [0 0 0 0.5 1 1 1]);
pnts= [ 10.0 10.0 10.0 10.0 10.0;
0.0 3.0 5.0 8.0 10.0;
9.0 7.0 7.0 10.0 10.0];
crv4 = nrbmak(pnts, [0 0 0 0.25 0.75 1 1 1]);
srf = nrbcoons(crv1, crv2, crv3, crv4);
nrbplot(srf,[20 20],220,45);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
NRBCOONS: Construction of a Coons patch.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
nrbcrvderiveval
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 752
NRBCRVDERIVEVAL: Evaluate n-th order derivatives of a NURBS curve.
usage: skl = nrbcrvderiveval (crv, u, d)
INPUT:
crv : NURBS curve structure, see nrbmak
u : parametric coordinate of the points where we compute the derivatives
d : number of partial derivatives to compute
OUTPUT:
ck (i, j, l) = i-th component derived j-1 times at the l-th point.
Adaptation of algorithm A4.2 from the NURBS book, pg127
Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
NRBCRVDERIVEVAL: Evaluate n-th order derivatives of a NURBS curve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
nrbctrlplot
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 676
NRBCTRLPLOT: Plot a NURBS entity along with its control points.
Calling Sequence:
nrbctrlplot (nurbs)
INPUT:
nurbs: NURBS curve, surface or volume, see nrbmak.
Example:
Plot the test curve and test surface with their control polygon and
control net, respectively
nrbctrlplot(nrbtestcrv)
nrbctrlplot(nrbtestsrf)
See also:
nrbkntplot
Copyright (C) 2011, 2012 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
NRBCTRLPLOT: Plot a NURBS entity along with its control points.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
nrbcylind
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 988
NRBCYLIND: Construct a cylinder or cylindrical patch.
Calling Sequence:
srf = nrbcylind()
srf = nrbcylind(height)
srf = nrbcylind(height,radius)
srf = nrbcylind(height,radius,center)
srf = nrbcylind(height,radius,center,sang,eang)
INPUT:
height : Height of the cylinder along the axis, default 1.0
radius : Radius of the cylinder, default 1.0
center : Center of the cylinder, default (0,0,0)
sang : Start angle relative to the origin, default 0.
eang : End angle relative to the origin, default 2*pi.
OUTPUT:
srf : cylindrical surface patch
Description:
Construct a cylinder or cylindrical patch by extruding a circular arc.
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
NRBCYLIND: Construct a cylinder or cylindrical patch.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbdegelev
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1411
NRBDEGELEV: Elevate the degree of the NURBS curve, surface or volume.
Calling Sequence:
ecrv = nrbdegelev(crv,utimes);
esrf = nrbdegelev(srf,[utimes,vtimes]);
evol = nrbdegelev(vol,[utimes,vtimes,wtimes]);
INPUT:
crv : NURBS curve, see nrbmak.
srf : NURBS surface, see nrbmak.
vol : NURBS volume, see nrbmak.
utimes : Increase the degree along U direction utimes.
vtimes : Increase the degree along V direction vtimes.
wtimes : Increase the degree along W direction vtimes.
OUTPUT:
ecrv : new NURBS structure for a curve with degree elevated.
esrf : new NURBS structure for a surface with degree elevated.
evol : new NURBS structure for a volume with degree elevated.
Description:
Degree elevates the NURBS curve or surface. This function uses the
B-Spline function bspdegelev, which interface to an internal 'C'
routine.
Examples:
Increase the NURBS surface twice along the V direction.
esrf = nrbdegelev(srf, [0, 2]);
See also:
bspdegelev
Copyright (C) 2000 Mark Spink, 2010 Rafel Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
NRBDEGELEV: Elevate the degree of the NURBS curve, surface or volume.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nrbderiv
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1370
NRBDERIV: Construct the first and second derivative representation of a
NURBS curve, surface or volume.
Calling Sequence:
ders = nrbderiv (nrb);
[ders, ders2] = nrbderiv (nrb);
INPUT:
nrb : NURBS data structure, see nrbmak.
OUTPUT:
ders: A data structure that represents the first
derivatives of a NURBS curve, surface or volume.
ders2: A data structure that represents the second
derivatives of a NURBS curve, surface or volume.
Description:
The derivatives of a B-Spline are themselves a B-Spline of lower degree,
giving an efficient means of evaluating multiple derivatives. However,
although the same approach can be applied to NURBS, the situation for
NURBS is more complex. We have followed in this function the same idea
that was already used for the first derivative in the function nrbderiv.
The second derivative data structure can be evaluated later with the
function nrbdeval.
See also:
nrbdeval
Copyright (C) 2000 Mark Spink
Copyright (C) 2010 Carlo de Falco
Copyright (C) 2010, 2011 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBDERIV: Construct the first and second derivative representation of a
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nrbdeval
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1418
NRBDEVAL: Evaluation of the derivative and second derivatives of NURBS curve, surface or volume.
[pnt, jac] = nrbdeval (crv, dcrv, tt)
[pnt, jac] = nrbdeval (srf, dsrf, {tu tv})
[pnt, jac] = nrbdeval (vol, dvol, {tu tv tw})
[pnt, jac, hess] = nrbdeval (crv, dcrv, dcrv2, tt)
[pnt, jac, hess] = nrbdeval (srf, dsrf, dsrf2, {tu tv})
[pnt, jac, hess] = nrbdeval (vol, dvol, {tu tv tw})
INPUTS:
crv, srf, vol - original NURBS curve, surface or volume.
dcrv, dsrf, dvol - NURBS derivative representation of crv, srf
or vol (see nrbderiv2)
dcrv2, dsrf2, dvol2 - NURBS second derivative representation of crv,
srf or vol (see nrbderiv2)
tt - parametric evaluation points
If the nurbs is a surface or a volume then tt is a cell
{tu, tv} or {tu, tv, tw} are the parametric coordinates
OUTPUT:
pnt - evaluated points.
jac - evaluated first derivatives (Jacobian).
hess - evaluated second derivatives (Hessian).
Copyright (C) 2000 Mark Spink
Copyright (C) 2010 Carlo de Falco
Copyright (C) 2010, 2011 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBDEVAL: Evaluation of the derivative and second derivatives of NURBS curve, s
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
nrbeval
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1809
NRBEVAL: Evaluate a NURBS at parametric points.
Calling Sequences:
[p,w] = nrbeval(crv,ut)
[p,w] = nrbeval(srf,{ut,vt})
[p,w] = nrbeval(vol,{ut,vt,wt})
[p,w] = nrbeval(srf,pts)
INPUT:
crv : NURBS curve, see nrbmak.
srf : NURBS surface, see nrbmak.
vol : NURBS volume, see nrbmak.
ut : Parametric evaluation points along U direction.
vt : Parametric evaluation points along V direction.
wt : Parametric evaluation points along W direction.
pts : Array of scattered points in parametric domain
OUTPUT:
p : Evaluated points on the NURBS curve, surface or volume as
Cartesian coordinates (x,y,z). If w is included on the lhs argument
list the points are returned as homogeneous coordinates (wx,wy,wz).
w : Weights of the homogeneous coordinates of the evaluated
points. Note inclusion of this argument changes the type
of coordinates returned in p (see above).
Description:
Evaluation of NURBS curves, surfaces or volume at parametric points along
the U, V and W directions. Either homogeneous coordinates are returned
if the weights are requested in the lhs arguments, or as Cartesian coordinates.
This function utilises the 'C' interface bspeval.
Examples:
Evaluate the NURBS circle at twenty points from 0.0 to 1.0
nrb = nrbcirc;
ut = linspace(0.0,1.0,20);
p = nrbeval(nrb,ut);
See also:
bspeval
Copyright (C) 2000 Mark Spink
Copyright (C) 2010 Carlo de Falco
Copyright (C) 2010, 2011, 2015 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
NRBEVAL: Evaluate a NURBS at parametric points.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
nrbexport
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1378
NRBEXPORT: export NURBS geometries to a format compatible with the one used in GeoPDEs.
Calling Sequence:
nrbexport (nurbs, filename);
nrbexport (nurbs, interfaces, boundaries, filename);
nrbexport (nurbs, interfaces, boundaries, subdomains, filename);
nrbexport (nurbs, filename, version);
nrbexport (nurbs, interfaces, boundaries, filename, version);
nrbexport (nurbs, interfaces, boundaries, subdomains, filename, version);
INPUT:
nurbs : NURBS curve, surface or volume, see nrbmak.
interfaces: interface information for GeoPDEs (see nrbmultipatch)
boundaries: boundary information for GeoPDEs (see nrbmultipatch)
filename : name of the output file.
version : either '-V0.7' or '-V2.1', to select the file format
Description:
The data of the nurbs structure is written in the file, in a format
that can be read by GeoPDEs. By default, the file is saved in the
format used by GeoPDEs 2.1. For the format of GeoPDEs 2.0 use the
option '-v0.7'. Earlier versions of GeoPDEs are not supported.
Copyright (C) 2011, 2014, 2015 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBEXPORT: export NURBS geometries to a format compatible with the one used in
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbextract
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1117
NRBEXTRACT: construct NURBS curves by extracting the boundaries of a NURBS surface, or NURBS surfaces by extracting the boundary of a NURBS volume.
It only works for geometries constructed with open knot vectors.
Calling Sequence:
crvs = nrbextract(surf);
INPUT:
surf : NURBS surface or volume, see nrbmak.
OUTPUT:
crvs : array of NURBS curves or NURBS surfaces extracted.
Description:
Constructs either an array of four NURBS curves, by extracting the boundaries
of a NURBS surface, or an array of six surfaces, by extracting the boundaries
of a NURBS volume. The new entities are ordered in the following way
1: U = 0
2: U = 1
3: V = 0
4: V = 1
5: W = 0 (only for volumes)
6: W = 1 (only for volumes)
Copyright (C) 2010,2014 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBEXTRACT: construct NURBS curves by extracting the boundaries of a NURBS su
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbextrude
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1283
NRBEXTRUDE: Construct a NURBS surface by extruding a NURBS curve, or
construct a NURBS volume by extruding a NURBS surface.
Calling Sequence:
srf = nrbextrude(crv,vec);
INPUT:
crv : NURBS curve or surface to extrude, see nrbmak.
vec : Vector along which the entity is extruded.
OUTPUT:
srf : NURBS surface or volume constructed.
Description:
Constructs either a NURBS surface by extruding a NURBS curve along a
defined vector, or a NURBS volume by extruding a NURBS surface. In the
first case, the NURBS curve forms the U direction of the surface edge, and
is extruded along the vector in the V direction. In the second case, the
original surface forms the U and V direction of the volume, and is extruded
along the W direction.
Examples:
Form a hollow cylinder by extruding a circle along the z-axis.
srf = nrbextrude(nrbcirc, [0,0,1]);
Copyright (C) 2000 Mark Spink
Copyright (C) 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBEXTRUDE: Construct a NURBS surface by extruding a NURBS curve, or
cons
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
nrbkntins
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2029
NRBKNTINS: Insert a single or multiple knots into a NURBS curve,
surface or volume.
Calling Sequence:
icrv = nrbkntins(crv,iuknots);
isrf = nrbkntins(srf,{iuknots ivknots});
ivol = nrbkntins(vol,{iuknots ivknots iwknots});
INPUT:
crv : NURBS curve, see nrbmak.
srf : NURBS surface, see nrbmak.
srf : NURBS volume, see nrbmak.
iuknots : Knots to be inserted along U direction.
ivknots : Knots to be inserted along V direction.
iwknots : Knots to be inserted along W direction.
OUTPUT:
icrv : new NURBS structure for a curve with knots inserted.
isrf : new NURBS structure for a surface with knots inserted.
ivol : new NURBS structure for a volume with knots inserted.
Description:
Inserts knots into the NURBS data structure, these can be knots at
new positions or at the location of existing knots to increase the
multiplicity. Note that the knot multiplicity cannot be increased
beyond the order of the spline. Knots along the V direction can only
inserted into NURBS surfaces, not curve that are always defined along
the U direction. This function use the B-Spline function bspkntins,
which interfaces to an internal 'C' routine.
Examples:
Insert two knots into a curve, one at 0.3 and another
twice at 0.4
icrv = nrbkntins(crv, [0.3 0.4 0.4])
Insert into a surface two knots as (1) into the U knot
sequence and one knot into the V knot sequence at 0.5.
isrf = nrbkntins(srf, {[0.3 0.4 0.4] [0.5]})
See also:
bspkntins
Note:
No knot multiplicity will be increased beyond the order of the spline.
Copyright (C) 2000 Mark Spink, 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBKNTINS: Insert a single or multiple knots into a NURBS curve,
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbkntplot
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 588
NRBKNTPLOT: Plot a NURBS entity with the knots subdivision.
Calling Sequence:
nrbkntplot(nurbs)
INPUT:
nurbs: NURBS curve, surface or volume, see nrbmak.
Example:
Plot the test surface with its knot vector
nrbkntplot(nrbtestsrf)
See also:
nrbctrlplot
Copyright (C) 2011, 2012 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
NRBKNTPLOT: Plot a NURBS entity with the knots subdivision.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
nrbline
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 762
NRBLINE: Construct a straight line.
Calling Sequence:
crv = nrbline()
crv = nrbline(p1,p2)
INPUT:
p1 : 2D or 3D cartesian coordinate of the start point.
p2 : 2D or 3D cartesian coordinate of the end point.
OUTPUT:
crv : NURBS curve for a straight line.
Description:
Constructs NURBS data structure for a straight line. If no rhs
coordinates are included the function returns a unit straight
line along the x-axis.
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
NRBLINE: Construct a straight line.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
nrbmak
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3966
NRBMAK: Construct the NURBS structure given the control points
and the knots.
Calling Sequence:
nurbs = nrbmak(cntrl,knots);
INPUT:
cntrl : Control points, these can be either Cartesian or
homogeneous coordinates.
For a curve the control points are represented by a
matrix of size (dim,nu), for a surface a multidimensional
array of size (dim,nu,nv), for a volume a multidimensional array
of size (dim,nu,nv,nw). Where nu is number of points along
the parametric U direction, nv the number of points along
the V direction and nw the number of points along the W direction.
dim is the dimension. Valid options
are
2 .... (x,y) 2D Cartesian coordinates
3 .... (x,y,z) 3D Cartesian coordinates
4 .... (wx,wy,wz,w) 4D homogeneous coordinates
knots : Non-decreasing knot sequence spanning the interval
[0.0,1.0]. It's assumed that the geometric entities
are clamped to the start and end control points by knot
multiplicities equal to the spline order (open knot vector).
For curve knots form a vector and for surfaces (volumes)
the knots are stored by two (three) vectors for U and V (and W)
in a cell structure {uknots vknots} ({uknots vknots wknots}).
OUTPUT:
nurbs : Data structure for representing a NURBS entity
NURBS Structure:
Both curves and surfaces are represented by a structure that is
compatible with the Spline Toolbox from Mathworks
nurbs.form .... Type name 'B-NURBS'
nurbs.dim .... Dimension of the control points
nurbs.number .... Number of Control points
nurbs.coefs .... Control Points
nurbs.order .... Order of the spline
nurbs.knots .... Knot sequence
Note: the control points are always converted and stored within the
NURBS structure as 4D homogeneous coordinates. A curve is always stored
along the U direction, and the vknots element is an empty matrix. For
a surface the spline order is a vector [du,dv] containing the order
along the U and V directions respectively. For a volume the order is
a vector [du dv dw]. Recall that order = degree + 1.
Description:
This function is used as a convenient means of constructing the NURBS
data structure. Many of the other functions in the toolbox rely on the
NURBS structure been correctly defined as shown above. The nrbmak not
only constructs the proper structure, but also checks for consistency.
The user is still free to build his own structure, in fact a few
functions in the toolbox do this for convenience.
Examples:
Construct a 2D line from (0.0,0.0) to (1.5,3.0).
For a straight line a spline of order 2 is required.
Note that the knot sequence has a multiplicity of 2 at the
start (0.0,0.0) and end (1.0 1.0) in order to clamp the ends.
line = nrbmak([0.0 1.5; 0.0 3.0],[0.0 0.0 1.0 1.0]);
nrbplot(line, 2);
Construct a surface in the x-y plane i.e
^ (0.0,1.0) ------------ (1.0,1.0)
| | |
| V | |
| | Surface |
| | |
| | |
| (0.0,0.0) ------------ (1.0,0.0)
|
|------------------------------------>
U
coefs = cat(3,[0 0; 0 1],[1 1; 0 1]);
knots = {[0 0 1 1] [0 0 1 1]}
plane = nrbmak(coefs,knots);
nrbplot(plane, [2 2]);
Copyright (C) 2000 Mark Spink, 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBMAK: Construct the NURBS structure given the control points
a
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbmeasure
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1359
NRBMEASURE: Compute the distance between two given points along a NURBS curve.
Calling Sequence:
[dist, ddistds, ddistde] = nrbmeasure (nrb)
[dist, ddistds, ddistde] = nrbmeasure (nrb, s, e)
[dist, ddistds, ddistde] = nrbmeasure (nrb, s, e, tol)
INPUT:
nrb : a NURBS curve, see nrbmak.
s : starting point in the parametric domain.
e : ending point in the parametric domain.
tol : tolerance for numerical quadrature, to be used in quad.
OUTPUT:
dist : distance between the two points along the NURBS curve.
ddistds: derivative of the distance function with respect to the point s.
ddistde: derivative of the distance function with respect to the point e.
Description:
Compute the distance between two given points along a NURBS curve, using
quad for numerical integration. The points are given by their coordinates
in the parametric domain.
Examples:
Compute the length of a circular arc constructed as a NURBS.
c = nrbcirc (1, [0 0], 0, pi/2);
s = 0; e = 1;
l = nrbmeasure (c, s, e, 1e-7);
Copyright (C) 2013 Carlo de Falco
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 79
NRBMEASURE: Compute the distance between two given points along a NURBS curve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
nrbmultipatch
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1226
NRBMULTIPATCH: construct the information for gluing conforming NURBS patches, using the same format as in GeoPDEs.
Calling Sequence:
[interfaces, boundary] = nrbmultipatch (nurbs);
INPUT:
nurbs : an array of NURBS surfaces or volumes (not both), see nrbmak.
OUTPUT:
interfaces: array with the information for each interface, that is:
- number of the first patch (patch1), and the local side number (side1)
- number of the second patch (patch2), and the local side number (side2)
- flag (faces and volumes), ornt1, ornt2 (only volumes): information
on how the two patches match, see below.
boundary: array with the boundary faces that do not belong to any interface
- nsides: total number of sides on the boundary array (numel(boundary))
- patches: number of the patch to which the boundary belongs to
- sides: number of the local side on the patch
Copyright (C) 2014 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBMULTIPATCH: construct the information for gluing conforming NURBS patches,
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
nrbnumbasisfun
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 797
NRBNUMBASISFUN: Numbering of basis functions for NURBS
Calling Sequence:
N = nrbnumbasisfun (u, crv)
N = nrbnumbasisfun ({u, v}, srf)
N = nrbnumbasisfun (p, srf)
INPUT:
u or p(1,:,:) - parametric points along u direction
v or p(2,:,:) - parametric points along v direction
crv - NURBS curve
srf - NURBS surface
OUTPUT:
N - Indices of the basis functions that are nonvanishing at each
point. size(N) == size(B)
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
NRBNUMBASISFUN: Numbering of basis functions for NURBS
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbpermute
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 874
NRBPERMUTE: Rearrange the directions of a NURBS volume or surface.
Calling Sequence:
tvol = nrbpermute(vol,order)
INPUT:
vol : NURBS volume or surface, see nrbmak.
order : the order to rearrange the directions of the NURBS entity.
OUTPUT:
tvol : NURBS volume or surface with rearranged directions.
Description:
Utility function that rearranges the directions of a NURBS volume or
surface. For surfaces, nrbpermute(srf,[1 2]) is the same as
nrbtransp(srf). NURBS curves cannot be rearranged.
Example:
nrbpermute (vol, [1 3 2])
Copyright (C) 2013 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 69
NRBPERMUTE: Rearrange the directions of a NURBS volume or surface.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
nrbplot
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1155
NRBPLOT: Plot a NURBS curve or surface, or the boundary of a NURBS volume.
Calling Sequence:
nrbplot (nrb, subd)
nrbplot (nrb, subd, p, v)
INPUT:
nrb : NURBS curve, surface or volume, see nrbmak.
npnts : Number of evaluation points, for a surface or volume, a row
vector with the number of points along each direction.
[p,v] : property/value options
Valid property/value pairs include:
Property Value/{Default}
-----------------------------------
light {off} | on
colormap {'copper'}
Example:
Plot the test surface with 20 points along the U direction
and 30 along the V direction
nrbplot(nrbtestsrf, [20 30])
Copyright (C) 2000 Mark Spink
Copyright (C) 2010 Carlo de Falco, Rafael Vazquez
Copyright (C) 2012 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 77
NRBPLOT: Plot a NURBS curve or surface, or the boundary of a NURBS volume.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
nrbrect
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 854
NRBRECT: Construct NURBS representation of a rectangular curve.
Calling Sequence:
crv = nrbrect()
crv = nrbrect(size)
crv = nrbrect(width, height)
INPUT:
size : Size of the square (width = height).
width : Width of the rectangle (along x-axis).
height : Height of the rectangle (along y-axis).
OUTPUT:
crv : NURBS curve, see nrbmak.
Description:
Construct a rectangle or square in the x-y plane with the bottom
lhs corner at (0,0,0). If no rhs arguments provided the function
constructs a unit square.
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
NRBRECT: Construct NURBS representation of a rectangular curve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbreverse
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 732
NRBREVERSE: Reverse the evaluation directions of a NURBS geometry.
Calling Sequence:
rnrb = nrbreverse(nrb);
rnrb = nrbreverse(nrb, idir);
INPUT:
nrb : NURBS data structure, see nrbmak.
idir : vector of directions to reverse.
OUTPUT:
rnrb : Reversed NURBS.
Description:
Utility function to reverse the evaluation direction of a NURBS
curve or surface.
Copyright (C) 2000 Mark Spink
Copyright (C) 2013 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 68
NRBREVERSE: Reverse the evaluation directions of a NURBS geometry.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbrevolve
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1774
NRBREVOLVE: Construct a NURBS surface by revolving a NURBS curve, or
construct a NURBS volume by revolving a NURBS surface.
Calling Sequence:
srf = nrbrevolve(crv,pnt,vec[,ang])
INPUT:
crv : NURBS curve or surface to revolve, see nrbmak.
pnt : Coordinates of the point used to define the axis
of rotation.
vec : Vector defining the direction of the rotation axis.
ang : Angle to revolve the curve, default 2*pi
OUTPUT:
srf : constructed surface or volume
Description:
Construct a NURBS surface by revolving the profile NURBS curve around
an axis defined by a point and vector.
Examples:
Construct a sphere by rotating a semicircle around a x-axis.
crv = nrbcirc(1.0,[0 0 0],0,pi);
srf = nrbrevolve(crv,[0 0 0],[1 0 0]);
nrbplot(srf,[20 20]);
NOTE:
The algorithm:
1) vectrans the point to the origin (0,0,0)
2) rotate the vector into alignment with the z-axis
for each control point along the curve
3) determine the radius and angle of control
point to the z-axis
4) construct a circular arc in the x-y plane with
this radius and start angle and sweep angle theta
5) combine the arc and profile, coefs and weights.
next control point
6) rotate and vectrans the surface back into position
by reversing 1 and 2.
Copyright (C) 2000 Mark Spink
Copyright (C) 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
NRBREVOLVE: Construct a NURBS surface by revolving a NURBS curve, or
cons
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nrbruled
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 892
NRBRULED: Construct a ruled surface between two NURBS curves.
Calling Sequence:
srf = nrbruled(crv1, crv2)
INPUT:
crv1 : First NURBS curve, see nrbmak.
crv2 : Second NURBS curve, see nrbmak.
OUTPUT:
srf : Ruled NURBS surface.
Description:
Constructs a ruled surface between two NURBS curves. The ruled surface is
ruled along the V direction.
Examples:
Construct a ruled surface between a semicircle and a straight line.
cir = nrbcirc(1,[0 0 0],0,pi);
line = nrbline([-1 0.5 1],[1 0.5 1]);
srf = nrbruled(cir,line);
nrbplot(srf,[20 20]);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
NRBRULED: Construct a ruled surface between two NURBS curves.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
nrbsurfderiveval
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 772
NRBSURFDERIVEVAL: Evaluate n-th order derivatives of a NURBS surface
usage: skl = nrbsurfderiveval (srf, [u; v], d)
INPUT:
srf : NURBS surface structure, see nrbmak
u, v : parametric coordinates of the point where we compute the
derivatives
d : number of partial derivatives to compute
OUTPUT:
skl (i, j, k, l) = i-th component derived j-1,k-1 times at the
l-th point.
Adaptation of algorithm A4.4 from the NURBS book, pg137
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 70
NRBSURFDERIVEVAL: Evaluate n-th order derivatives of a NURBS surface
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbtestcrv
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 338
NRBTESTCRV: Constructs a simple test curve.
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
NRBTESTCRV: Constructs a simple test curve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbtestsrf
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 347
NRBTESTSRF: Constructs a simple test surface.
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
NRBTESTSRF: Constructs a simple test surface.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nrbtform
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1315
NRBTFORM: Apply transformation matrix to the NURBS.
Calling Sequence:
tnurbs = nrbtform(nurbs,tmatrix);
INPUT:
nurbs : NURBS data structure (see nrbmak for details).
tmatrix : Transformation matrix, a matrix of size (4,4) defining
a single or multiple transformations.
OUTPUT:
tnurbs : The return transformed NURBS data structure.
Description:
The NURBS is transform as defined a transformation matrix of size (4,4),
such as a rotation, translation or change in scale. The transformation
matrix can define a single transformation or multiple series of
transformations. The matrix can be simply constructed by the functions
vecscale, vectrans and vecrot, and also vecrotx, vecroty, and vecrotz.
Examples:
Rotate a square by 45 degrees about the z axis.
rsqr = nrbtform(nrbrect(), vecrotz(deg2rad(45)));
nrbplot(rsqr, 1000);
See also:
vecscale, vectrans, vecrot, vecrotx, vecroty, vecrotz
Copyright (C) 2000 Mark Spink
Copyright (C) 2010 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
NRBTFORM: Apply transformation matrix to the NURBS.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
nrbtransp
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 673
NRBTRANSP: Transpose a NURBS surface, by swapping U and V directions.
Calling Sequence:
tsrf = nrbtransp(srf)
INPUT:
srf : NURBS surface, see nrbmak.
OUTPUT:
tsrf : NURBS surface with U and V diretions transposed.
Description:
Utility function that transposes a NURBS surface, by swapping U and
V directions. NURBS curves cannot be transposed.
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
NRBTRANSP: Transpose a NURBS surface, by swapping U and V directions.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
nrbunclamp
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 914
NRBUNCLAMP: Compute the knot vector and control points of the unclamped curve
Calling Sequence:
ucrv = nrbrunclamp (crv, k)
ucrv = nrbrunclamp (crv, k, dim)
INPUT:
crv : NURBS curve, see nrbmak.
k : continuity for the unclamping (from 0 up to p-1)
dim : dimension in which to unclamp (all by default).
OUTPUT:
ucrv: NURBS curve with unclamped knot vector, see nrbmak
Description:
Unclamps a curve, removing the open knot vector. Computes the new
knot vector and control points of the unclamped curve.
Adapted from Algorithm A12.1 from 'The NURBS BOOK' pg577.
Copyright (C) 2013, 2014 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 78
NRBUNCLAMP: Compute the knot vector and control points of the unclamped curve
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
numbasisfun
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 666
NUMBASISFUN: List non-zero Basis functions for B-Spline in a given knot-span
Calling Sequence:
N = numbasisfun(i,u,p,U)
INPUT:
i - knot span ( from FindSpan() )
u - parametric point
p - spline degree
U - knot sequence
OUTPUT:
N - Basis functions (numel(u)x(p+1))
See also:
basisfun, basisfunder
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 78
NUMBASISFUN: List non-zero Basis functions for B-Spline in a given knot-span
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
rad2deg
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 697
RAD2DEG: Convert radians to degrees.
Calling Sequence:
rad = rad2deg(deg);
INPUT:
rad : Angle in radians.
OUTPUT:
deg : Angle in degrees.
Description:
Convenient utility function for converting radians to degrees, which are
often the required angular units for functions in the NURBS toolbox.
Examples:
Convert 0.3 radians to degrees
deg = rad2deg(0.3);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
RAD2DEG: Convert radians to degrees.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
surfderivcpts
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 933
SURFDERIVCPTS: Compute control points of n-th derivatives of a NURBS surface.
usage: pkl = surfderivcpts (n, p, U, m, q, V, P, d)
INPUT:
n+1, m+1 = number of control points
p, q = spline order
U, V = knots
P = control points
d = derivative order
OUTPUT:
pkl (k+1, l+1, i+1, j+1) = i,jth control point
of the surface differentiated k
times in the u direction and l
times in the v direction
Adaptation of algorithm A3.7 from the NURBS book, pg114
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 79
SURFDERIVCPTS: Compute control points of n-th derivatives of a NURBS surface.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
surfderiveval
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 870
SURFDERIVEVAL: Compute the derivatives of a B-spline surface
usage: skl = surfderiveval (n, p, U, m, q, V, P, u, v, d)
INPUT:
n+1, m+1 = number of control points
p, q = spline order
U, V = knots
P = control points
u,v = evaluation points
d = derivative order
OUTPUT:
skl (k+1, l+1) = surface differentiated k
times in the u direction and l
times in the v direction
Adaptation of algorithm A3.8 from the NURBS book, pg115
Copyright (C) 2009 Carlo de Falco
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
SURFDERIVEVAL: Compute the derivatives of a B-spline surface
usage: skl = s
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
tbasisfun
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 925
TBASISFUN: Compute a B- or T-Spline basis function, and its derivatives, from its local knot vector.
usage:
[N, Nder] = tbasisfun (u, p, U)
[N, Nder] = tbasisfun ([u; v], [p q], {U, V})
[N, Nder] = tbasisfun ([u; v; w], [p q r], {U, V, W})
INPUT:
u or [u; v] : points in parameter space where the basis function is to be
evaluated
U or {U, V} : local knot vector
p or [p q] : polynomial order of the basis function
OUTPUT:
N : basis function evaluated at the given parametric points
Nder : basis function gradient evaluated at the given parametric points
Copyright (C) 2009 Carlo de Falco
Copyright (C) 2012 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
TBASISFUN: Compute a B- or T-Spline basis function, and its derivatives, from
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
vecangle
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 920
VECANGLE: An alternative to atan, returning an arctangent in the
range 0 to 2*pi.
Calling Sequence:
ang = vecmag2(num,dum)
INPUT:
num : Numerator, vector of size (1,nv).
dem : Denominator, vector of size (1,nv).
OUTPUT:
ang : Arctangents, row vector of angles.
Description:
The components of the vector ang are the arctangent of the corresponding
enties of num./dem. This function is an alternative for
atan, returning an angle in the range 0 to 2*pi.
Examples:
Find the atan(1.2,2.0) and atan(1.5,3.4) using vecangle
ang = vecangle([1.2 1.5], [2.0 3.4]);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
VECANGLE: An alternative to atan, returning an arctangent in the
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
veccross
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1004
VECCROSS: The cross product of two vectors.
Calling Sequence:
cross = veccross(vec1,vec2);
INPUT:
vec1 : An array of column vectors represented by a matrix of
vec2 size (dim,nv), where is the dimension of the vector and
nv the number of vectors.
OUTPUT:
cross : Array of column vectors, each element is corresponding
to the cross product of the respective components in vec1
and vec2.
Description:
Cross product of two vectors.
Examples:
Determine the cross products of:
(2.3,3.4,5.6) and (1.2,4.5,1.2)
(5.1,0.0,2.3) and (2.5,3.2,4.0)
cross = veccross([2.3 5.1; 3.4 0.0; 5.6 2.3],[1.2 2.5; 4.5 3.2; 1.2 4.0]);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
VECCROSS: The cross product of two vectors.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
vecdot
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 946
VECDOT: The dot product of two vectors.
Calling Sequence:
dot = vecdot(vec1,vec2);
INPUT:
vec1 : An array of column vectors represented by a matrix of
vec2 size (dim,nv), where is the dimension of the vector and
nv the number of vectors.
OUTPUT:
dot : Row vector of scalars, each element corresponding to
the dot product of the respective components in vec1 and
vec2.
Description:
Scalar dot product of two vectors.
Examples:
Determine the dot product of
(2.3,3.4,5.6) and (1.2,4.5,1.2)
(5.1,0.0,2.3) and (2.5,3.2,4.0)
dot = vecdot([2.3 5.1; 3.4 0.0; 5.6 2.3],[1.2 2.5; 4.5 3.2; 1.2 4.0]);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
VECDOT: The dot product of two vectors.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
vecmag
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 807
VECMAG: Magnitude of the vectors.
Calling Sequence:
mvec = vecmag(vec)
INPUT:
vec : An array of column vectors represented by a matrix of
size (dim,nv), where is the dimension of the vector and
nv the number of vectors.
OUTPUT:
mvec : Magnitude of the vectors, vector of size (1,nv).
Description:
Determines the magnitude of the vectors.
Examples:
Find the magnitude of the two vectors (0.0,2.0,1.3) and (1.5,3.4,2.3)
mvec = vecmag([0.0 1.5; 2.0 3.4; 1.3 2.3]);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
VECMAG: Magnitude of the vectors.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
vecmag2
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 855
VECMAG2: Squared magnitude of a set of vectors.
Calling Sequence:
mvec = vecmag2(vec)
INPUT:
vec : An array of column vectors represented by a matrix of
size (dim,nv), where dim is the dimension of the vector and
nv the number of vectors.
OUTPUT:
mvec : Squared magnitude of the vectors, vector of size (1,nv).
Description:
Determines the squared magnitude of the vectors.
Examples:
Find the squared magnitude of the two vectors (0.0,2.0,1.3)
and (1.5,3.4,2.3)
mvec = vecmag2([0.0 1.5; 2.0 3.4; 1.3 2.3]);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
VECMAG2: Squared magnitude of a set of vectors.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
vecnorm
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 850
VECNORM: Normalise the vectors.
Calling Sequence:
nvec = vecnorn(vec);
INPUT:
vec : An array of column vectors represented by a matrix of
size (dim,nv), where is the dimension of the vector and
nv the number of vectors.
OUTPUT:
nvec : Normalised vectors, matrix the smae size as vec.
Description:
Normalises the array of vectors, returning the unit vectors.
Examples:
Normalise the two vectors (0.0,2.0,1.3) and (1.5,3.4,2.3)
nvec = vecnorm([0.0 1.5; 2.0 3.4; 1.3 2.3]);
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
VECNORM: Normalise the vectors.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
vecrot
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 751
VECROT: Transformation matrix for a rotation around the axis given by a vector.
Calling Sequence:
rx = vecrot (angle, vector);
INPUT:
angle : rotation angle defined in radians
vector: vector defining the rotation axis
OUTPUT:
rx: (4x4) Transformation matrix.
Description:
Return the (4x4) Transformation matrix for a rotation about the axis
defined by vector, and by the given angle.
See also:
nrbtform
Copyright (C) 2011 Rafael Vazquez
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
VECROT: Transformation matrix for a rotation around the axis given by a vecto
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
vecrotx
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1098
VECROTX: Transformation matrix for a rotation around the x axis.
Calling Sequence:
rx = vecrotx(angle);
INPUT:
angle : rotation angle defined in radians
OUTPUT:
rx : (4x4) Transformation matrix.
Description:
Return the (4x4) Transformation matrix for a rotation about the x axis
by the defined angle.
The matrix is:
[ 1 0 0 0]
[ 0 cos(angle) -sin(angle) 0]
[ 0 sin(angle) cos(angle) 0]
[ 0 0 0 1]
Examples:
Rotate the NURBS line (0.0 0.0 0.0) - (3.0 3.0 3.0) by 45 degrees
around the x-axis
line = nrbline([0.0 0.0 0.0],[3.0 3.0 3.0]);
trans = vecrotx(%pi/4);
rline = nrbtform(line, trans);
See also:
nrbtform
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
VECROTX: Transformation matrix for a rotation around the x axis.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
vecroty
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1138
VECROTY: Transformation matrix for a rotation around the y axis.
Calling Sequence:
ry = vecroty(angle);
INPUT:
angle : rotation angle defined in radians
OUTPUT:
ry : (4x4) Transformation matrix.
Description:
Return the (4x4) Transformation matrix for a rotation about the y axis
by the defined angle.
The matrix is:
[ cos(angle) 0 sin(angle) 0]
[ 0 1 0 0]
[ -sin(angle) 0 cos(angle) 0]
[ 0 0 0 1]
Examples:
Rotate the NURBS line (0.0 0.0 0.0) - (3.0 3.0 3.0) by 45 degrees
around the y-axis
line = nrbline([0.0 0.0 0.0],[3.0 3.0 3.0]);
trans = vecroty(%pi/4);
rline = nrbtform(line, trans);
See also:
nrbtform
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
VECROTY: Transformation matrix for a rotation around the y axis.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
vecrotz
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1172
VECROTZ: Transformation matrix for a rotation around the z axis.
Calling Sequence:
rz = vecrotz(angle);
INPUT:
angle : rotation angle defined in radians
OUTPUT:
rz : (4x4) Transformation matrix.
Description:
Return the (4x4) Transformation matrix for a rotation about the z axis
by the defined angle.
The matrix is:
[ cos(angle) -sin(angle) 0 0]
[ -sin(angle) cos(angle) 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
Examples:
Rotate the NURBS line (0.0 0.0 0.0) - (3.0 3.0 3.0) by 45 degrees
around the z-axis
line = nrbline([0.0 0.0 0.0],[3.0 3.0 3.0]);
trans = vecrotz(%pi/4);
rline = nrbtform(line, trans);
See also:
nrbtform
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 68
VECROTZ: Transformation matrix for a rotation around the z axis.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
vecscale
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1061
VECSCALE: Transformation matrix for a scaling.
Calling Sequence:
ss = vecscale(svec)
INPUT:
svec : A vectors defining the scaling along the x,y and z axes.
i.e. [sx, sy, sy]
OUTPUT:
ss : Scaling Transformation Matrix
Description:
Returns a (4x4) Transformation matrix for scaling.
The matrix is:
[ sx 0 0 0]
[ 0 sy 0 0]
[ 0 0 sz 0]
[ 0 0 0 1]
Example:
Scale up the NURBS line (0.0,0.0,0.0) - (1.0,1.0,1.0) by 3 along
the x-axis, 2 along the y-axis and 4 along the z-axis.
line = nrbline([0.0 0.0 0.0],[1.0 1.0 1.0]);
trans = vecscale([3.0 2.0 4.0]);
sline = nrbtform(line, trans);
See also:
nrbtform
Copyright (C) 2000 Mark Spink, 2007 Daniel Claxton
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
VECSCALE: Transformation matrix for a scaling.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
vectrans
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1066
VECTRANS: Transformation matrix for a translation.
Calling Sequence:
st = vectrans(tvec)
INPUT:
tvec : A vectors defining the translation along the x,y and
z axes. i.e. [tx, ty, ty]
OUTPUT:
st : Translation Transformation Matrix
Description:
Returns a (4x4) Transformation matrix for translation.
The matrix is:
[ 1 0 0 tx ]
[ 0 1 0 ty ]
[ 0 0 1 tz ]
[ 0 0 0 1 ]
Examples:
Translate the NURBS line (0.0,0.0,0.0) - (1.0,1.0,1.0) by 3 along
the x-axis, 2 along the y-axis and 4 along the z-axis.
line = nrbline([0.0 0.0 0.0],[1.0 1.0 1.0]);
trans = vectrans([3.0 2.0 4.0]);
tline = nrbtform(line, trans);
See also:
nrbtform
Copyright (C) 2000 Mark Spink
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
VECTRANS: Transformation matrix for a translation.
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