--- /dev/null
+# Created by Octave 3.6.1, Wed Apr 04 09:02:21 2012 UTC <root@t61>
+# name: cache
+# type: cell
+# rows: 3
+# columns: 61
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+basisfun
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 722
+ 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.
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 40
+ 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: 745
+ 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.
+
+ 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 2 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: 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 2 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 2 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 2 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 42
+ BSPKNTINS: Insert knots into a B-Spline
+
+
+
+
+# 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 2 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 2 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 2 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 73
+ 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 2 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 2 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 2 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 2 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
+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 2 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: 974
+ 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 (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:
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 40
+ 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: 1227
+ 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 (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:
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 52
+ 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 2 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 2 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: 753
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 68
+
+ 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: 662
+ NRBCTRLPLOT: Plot a NURBS entity along with its control points.
+
+ Calling Sequence:
+
+ nrbctrlplot (nurbs)
+
+ INPUT:
+
+ nurbs: NURBS curve or surface, 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 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 2 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 2 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: 1358
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 72
+
+ 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 2 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 2 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: 1803
+
+ 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 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 2 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: 690
+
+ NRBEXPORT: export NURBS geometries to a format compatible with the one used in GeoPDEs (version 0.6).
+
+ Calling Sequence:
+
+ nrbexport (nurbs, filename);
+
+ INPUT:
+
+ nurbs : NURBS curve, surface or volume, see nrbmak.
+ filename : name of the output file.
+
+
+ Description:
+
+ The data of the nurbs structure is written in the file, in a format
+ that can be read by GeoPDEs.
+
+ 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 2 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: 1011
+
+ NRBEXTRACT: construct NURBS curves by extracting the boundaries of a NURBS surface, or NURBS surfaces by extracting the boundary of a NURBS volume.
+
+ 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 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 2 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 sur
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+nrbextrude
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1243
+
+ 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 2 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
+ constr
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+nrbkntins
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1961
+
+ 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 2 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: 582
+ 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 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 2 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 2 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: 3867
+
+ 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 2 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
+ and
+
+
+
+# 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 58
+
+ NRBNUMBASISFUN: Numbering of basis functions for NURBS
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+nrbplot
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1117
+
+ 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
+
+ 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 2 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 2 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: 618
+
+ NRBREVERSE: Reverse the evaluation direction of a NURBS curve or surface.
+
+ Calling Sequence:
+
+ rnrb = nrbreverse(nrb);
+
+ INPUT:
+
+ nrb : NURBS data structure, see nrbmak.
+
+ OUTPUT:
+
+ rnrb : Reversed NURBS.
+
+ Description:
+
+ Utility function to reverse the evaluation direction of a NURBS
+ curve or 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 75
+
+ NRBREVERSE: Reverse the evaluation direction of a NURBS curve or surface.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+nrbrevolve
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1710
+
+ 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 2 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
+ constr
+
+
+
+# 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 2 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 71
+
+ 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 2 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: 339
+ 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 2 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: 1287
+
+ 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 simple constructed by the functions
+ vecscale, vectrans, 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, 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 2 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 2 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: 11
+numbasisfun
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 626
+ 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))
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 79
+ 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
+
+ rad = deg2rad(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 2 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 2 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 2 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 2 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 2 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: 967
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 46
+
+ 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 2 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 2 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 2 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: 817
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 34
+
+ VECNORM: Normalise the vectors.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+vecrot
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 737
+
+ 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 x axis
+ by the defined 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 2 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 2 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 2 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: 1125
+
+ 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 2 of the License, or
+ (at your option) any later version.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 67
+
+ 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 2 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 2 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.
+
+
+
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff