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here is the log from the commit of package octave-forge-nurbs for
openSUSE:Factory checked in at 2025-08-27 21:35:07
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Comparing /work/SRC/openSUSE:Factory/octave-forge-nurbs (Old)
and /work/SRC/openSUSE:Factory/.octave-forge-nurbs.new.30751 (New)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Package is "octave-forge-nurbs"
Wed Aug 27 21:35:07 2025 rev:6 rq:1301568 version:1.4.4
Changes:
--------
--- /work/SRC/openSUSE:Factory/octave-forge-nurbs/octave-forge-nurbs.changes
2024-02-26 19:48:05.527768009 +0100
+++
/work/SRC/openSUSE:Factory/.octave-forge-nurbs.new.30751/octave-forge-nurbs.changes
2025-08-27 21:36:09.746397790 +0200
@@ -1,0 +2,6 @@
+Tue Aug 26 18:11:15 UTC 2025 - Stefan Brüns <stefan.bru...@rwth-aachen.de>
+
+- Update to version 1.4.4:
+ * Update to work with upcoming Octave 10 release
+
+-------------------------------------------------------------------
Old:
----
nurbs-1.4.3.tar.gz
New:
----
nurbs-1.4.4.tar.gz
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Other differences:
------------------
++++++ octave-forge-nurbs.spec ++++++
--- /var/tmp/diff_new_pack.H9wBZF/_old 2025-08-27 21:36:10.414425679 +0200
+++ /var/tmp/diff_new_pack.H9wBZF/_new 2025-08-27 21:36:10.418425847 +0200
@@ -1,7 +1,7 @@
#
# spec file for package octave-forge-nurbs
#
-# Copyright (c) 2022 SUSE LLC
+# Copyright (c) 2025 SUSE LLC and contributors
#
# All modifications and additions to the file contributed by third parties
# remain the property of their copyright owners, unless otherwise agreed
@@ -18,12 +18,12 @@
%define octpkg nurbs
Name: octave-forge-%{octpkg}
-Version: 1.4.3
+Version: 1.4.4
Release: 0
Summary: Routines for Non-Uniform Rational B-Splines for Octave
License: GPL-3.0-or-later
Group: Productivity/Scientific/Math
-URL: https://octave.sourceforge.io/%{octpkg}/
+URL: https://gnu-octave.github.io/packages/nurbs/
Source0:
https://downloads.sourceforge.net/octave/%{octpkg}-%{version}.tar.gz
# PATCH-FIX-UPSTREAM nurbs-openmp.patch -- Fix build with openmp
Patch1: nurbs-openmp.patch
++++++ nurbs-1.4.3.tar.gz -> nurbs-1.4.4.tar.gz ++++++
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/DESCRIPTION new/nurbs-1.4.4/DESCRIPTION
--- old/nurbs-1.4.3/DESCRIPTION 2021-03-29 12:11:45.775919014 +0200
+++ new/nurbs-1.4.4/DESCRIPTION 2025-02-10 14:35:08.000000000 +0100
@@ -1,6 +1,6 @@
Name: nurbs
-Version: 1.4.3
-Date: 2021-03-29
+Version: 1.4.4
+Date: 2025-02-10
Author: Mark Spink, Daniel Claxton, Carlo de Falco, Rafael Vazquez
Maintainer: Carlo de Falco and Rafael Vazquez
Title: Nurbs.
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/NEWS new/nurbs-1.4.4/NEWS
--- old/nurbs-1.4.3/NEWS 2021-03-29 12:11:45.779919075 +0200
+++ new/nurbs-1.4.4/NEWS 2025-02-10 14:35:08.000000000 +0100
@@ -1,3 +1,10 @@
+Summary of important user-visible changes for next release of nurbs:
+-------------------------------------------------------------------
+
+Summary of important user-visible changes for nurbs 1.4.4:
+-------------------------------------------------------------------
+Update to work with upcoming Octave 10 release
+
Summary of important user-visible changes for nurbs 1.4.3:
-------------------------------------------------------------------
* inst/nrbctrlplot: allow the number of points for the plot as input
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/inst/basisfun.m
new/nurbs-1.4.4/inst/basisfun.m
--- old/nurbs-1.4.3/inst/basisfun.m 2021-03-29 12:11:45.779919075 +0200
+++ new/nurbs-1.4.4/inst/basisfun.m 2025-02-10 14:35:08.000000000 +0100
@@ -1,91 +1,81 @@
-function B = basisfun (iv, uv, p, U)
-
-% 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.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see <http://www.gnu.org/licenses/>.
-
-B = zeros(numel(uv), p+1);
-
-for jj = 1:numel(uv)
-
- i = iv(jj) + 1; %% findspan uses 0-based numbering
- u = uv(jj);
-
- left = zeros(p+1,1);
- right = zeros(p+1,1);
-
- N(1) = 1;
- for j=1:p
- left(j+1) = u - U(i+1-j);
- right(j+1) = U(i+j) - u;
- saved = 0;
-
- for r=0:j-1
- temp = N(r+1)/(right(r+2) + left(j-r+1));
- N(r+1) = saved + right(r+2)*temp;
- saved = left(j-r+1)*temp;
- end
-
- N(j+1) = saved;
- end
-
- B (jj, :) = N;
-
-end
-
-end
-
-%!test
-%! n = 3;
-%! U = [0 0 0 1/2 1 1 1];
-%! p = 2;
-%! u = linspace (0, 1, 10);
-%! s = findspan (n, p, u, U);
-%! Bref = [1.00000 0.00000 0.00000
-%! 0.60494 0.37037 0.02469
-%! 0.30864 0.59259 0.09877
-%! 0.11111 0.66667 0.22222
-%! 0.01235 0.59259 0.39506
-%! 0.39506 0.59259 0.01235
-%! 0.22222 0.66667 0.11111
-%! 0.09877 0.59259 0.30864
-%! 0.02469 0.37037 0.60494
-%! 0.00000 0.00000 1.00000];
-%! B = basisfun (s, u, p, U);
-%! assert (B, Bref, 1e-5);
+function B = basisfun (mu, x, p, knots)
+
+% BASISFUN: Basis function for B-Spline
+%
+% Calling Sequence:
+%
+% N = basisfun(mu,x,p,knots)
+%
+% INPUT:
+%
+% mu - knot span ( from FindSpan() )
+% x - parametric points
+% p - spline degree
+% knots - 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
+% Copyright (C) 2022 Yannis Voet
+%
+% 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.
+
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+mu = mu + 1;
+% Making sure x and mu are both column vectors
+x = x(:);
+mu = mu(:);
+
+Np = length(x);
+B = ones(Np,1);
+
+for k = 1:p
+ i1 = mu + ((1-k):0);
+ i2 = mu + (1:k);
+ t1 = reshape(knots(i1(:)), Np, k);
+ t2 = reshape(knots(i2(:)), Np, k);
+ omega = (x-t1)./(t2-t1);
+ omega(t2-t1<1e-15) = 0; % "Anything divided by zero is zero" convention
+ B = [(1-omega).*B zeros(Np,1)] + [zeros(Np,1) omega.*B];
+end
+
+end
+
+%!test
+%! n = 3;
+%! U = [0 0 0 1/2 1 1 1];
+%! p = 2;
+%! u = linspace (0, 1, 10);
+%! s = findspan (n, p, u, U);
+%! Bref = [1.00000 0.00000 0.00000
+%! 0.60494 0.37037 0.02469
+%! 0.30864 0.59259 0.09877
+%! 0.11111 0.66667 0.22222
+%! 0.01235 0.59259 0.39506
+%! 0.39506 0.59259 0.01235
+%! 0.22222 0.66667 0.11111
+%! 0.09877 0.59259 0.30864
+%! 0.02469 0.37037 0.60494
+%! 0.00000 0.00000 1.00000];
+%! B = basisfun (s, u, p, U);
+%! assert (B, Bref, 1e-5);
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/inst/basisfunder.m
new/nurbs-1.4.4/inst/basisfunder.m
--- old/nurbs-1.4.3/inst/basisfunder.m 2021-03-29 12:11:45.779919075 +0200
+++ new/nurbs-1.4.4/inst/basisfunder.m 2025-02-10 14:35:08.000000000 +0100
@@ -1,155 +1,119 @@
-function dersv = basisfunder (ii, pl, uu, u_knotl, nders)
-
-% 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.
-
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see <http://www.gnu.org/licenses/>.
-
- dersv = zeros(numel(uu), nders+1, pl+1);
-
- for jj = 1:numel(uu)
-
- i = ii(jj)+1; %% convert to base-1 numbering of knot spans
- u = uu(jj);
-
- ders = zeros(nders+1,pl+1);
- ndu = zeros(pl+1,pl+1);
- left = zeros(pl+1);
- right = zeros(pl+1);
- a = zeros(2,pl+1);
- ndu(1,1) = 1;
- for j = 1:pl
- left(j+1) = u - u_knotl(i+1-j);
- right(j+1) = u_knotl(i+j) - u;
- saved = 0;
- for r = 0:j-1
- ndu(j+1,r+1) = right(r+2) + left(j-r+1);
- temp = ndu(r+1,j)/ndu(j+1,r+1);
- ndu(r+1,j+1) = saved + right(r+2)*temp;
- saved = left(j-r+1)*temp;
- end
- ndu(j+1,j+1) = saved;
- end
- for j = 0:pl
- ders(1,j+1) = ndu(j+1,pl+1);
- end
- for r = 0:pl
- s1 = 0;
- s2 = 1;
- a(1,1) = 1;
- for k = 1:nders %compute kth derivative
- d = 0;
- rk = r-k;
- pk = pl-k;
- if (r >= k)
- a(s2+1,1) = a(s1+1,1)/ndu(pk+2,rk+1);
- d = a(s2+1,1)*ndu(rk+1,pk+1);
- end
- if (rk >= -1)
- j1 = 1;
- else
- j1 = -rk;
- end
- if ((r-1) <= pk)
- j2 = k-1;
- else
- j2 = pl-r;
- end
- for j = j1:j2
- a(s2+1,j+1) = (a(s1+1,j+1) - a(s1+1,j))/ndu(pk+2,rk+j+1);
- d = d + a(s2+1,j+1)*ndu(rk+j+1,pk+1);
- end
- if (r <= pk)
- a(s2+1,k+1) = -a(s1+1,k)/ndu(pk+2,r+1);
- d = d + a(s2+1,k+1)*ndu(r+1,pk+1);
- end
- ders(k+1,r+1) = d;
- j = s1;
- s1 = s2;
- s2 = j;
- end
- end
- r = pl;
- for k = 1:nders
- for j = 0:pl
- ders(k+1,j+1) = ders(k+1,j+1)*r;
- end
- r = r*(pl-k);
- end
-
- dersv(jj, :, :) = ders;
-
- end
-
-end
-
-%!test
-%! k = [0 0 0 0 1 1 1 1];
-%! p = 3;
-%! u = rand (1);
-%! i = findspan (numel(k)-p-2, p, u, k);
-%! ders = basisfunder (i, p, u, k, 1);
-%! sumders = sum (squeeze(ders), 2);
-%! assert (sumders(1), 1, 1e-15);
-%! assert (sumders(2:end), 0, 1e-15);
-
-%!test
-%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
-%! p = 3;
-%! u = rand (1);
-%! i = findspan (numel(k)-p-2, p, u, k);
-%! ders = basisfunder (i, p, u, k, 7);
-%! sumders = sum (squeeze(ders), 2);
-%! assert (sumders(1), 1, 1e-15);
-%! assert (sumders(2:end), zeros(rows(squeeze(ders))-1, 1), 1e-13);
-
-%!test
-%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
-%! p = 3;
-%! u = rand (100, 1);
-%! i = findspan (numel(k)-p-2, p, u, k);
-%! ders = basisfunder (i, p, u, k, 7);
-%! for ii=1:10
-%! sumders = sum (squeeze(ders(ii,:,:)), 2);
-%! assert (sumders(1), 1, 1e-15);
-%! assert (sumders(2:end), zeros(rows(squeeze(ders(ii,:,:)))-1, 1), 1e-13);
-%! end
-%! assert (ders(:, (p+2):end, :), zeros(numel(u), 8-p-1, p+1), 1e-13)
-%! assert (all(all(ders(:, 1, :) <= 1)), true)
-
-
-
+function dersv = basisfunder (mu, p, x, knots, nders)
+
+% BASISFUNDER: B-Spline Basis function derivatives.
+%
+% Calling Sequence:
+%
+% ders = basisfunder (mu, p, x, knots, nders)
+%
+% INPUT:
+%
+% mu - knot span index (see findspan)
+% p - degree of curve
+% x - parametric points
+% knots - knot vector
+% nders - 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
+% Copyright (C) 2022 Yannis Voet, 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.
+
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+x = x(:);
+mu = mu(:);
+
+r = min([nders p]);
+mu = mu+1;
+N = length(x);
+D = cell(1, r+1);
+B = basisfun(mu-1, x, p-r, knots);
+D{r+1} = B;
+
+for k = p-r+1:p
+
+ i1 = mu + ((1-k):0);
+ i2 = mu + (1:k);
+ t1 = reshape(knots(i1(:)), N, k);
+ t2 = reshape(knots(i2(:)), N, k);
+
+ omega = (x-t1)./(t2-t1);
+ omega(t2-t1<1e-15) = 0; % "Anything divided by zero is zero" convention
+ B = [(1-omega).*B zeros(N,1)]+[zeros(N,1) omega.*B];
+
+ % Save for the next iteration
+ D{p-k+1} = B;
+
+ % Compute the derivative
+ omega = 1./(t2-t1);
+ omega(t2-t1<1e-15) = 0; % "Anything divided by zero is zero" convention
+ for j = 1:k-p+r
+ D{end-j+1} = [-omega.*D{end-j+1} zeros(N,1)]+[zeros(N,1)
omega.*D{end-j+1}];
+ end
+end
+
+for k = 1:nders-p
+ D{r+1+k} = zeros(N, p+1);
+end
+
+D = reshape(cell2mat(D), N, p+1, nders+1);
+v = 0:nders;
+v(v>r) = r;
+f = reshape(factorial(p)./factorial(p-v), 1, 1, nders+1);
+dersv = f.*D;
+dersv = permute(dersv, [1 3 2]);
+
+
+%!test
+%! k = [0 0 0 0 1 1 1 1];
+%! p = 3;
+%! u = rand (1);
+%! i = findspan (numel(k)-p-2, p, u, k);
+%! ders = basisfunder (i, p, u, k, 1);
+%! sumders = sum (squeeze(ders), 2);
+%! assert (sumders(1), 1, 1e-15);
+%! assert (sumders(2:end), 0, 1e-15);
+
+%!test
+%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
+%! p = 3;
+%! u = rand (1);
+%! i = findspan (numel(k)-p-2, p, u, k);
+%! ders = basisfunder (i, p, u, k, 7);
+%! sumders = sum (squeeze(ders), 2);
+%! assert (sumders(1), 1, 1e-15);
+%! assert (sumders(2:end), zeros(rows(squeeze(ders))-1, 1), 1e-13);
+
+%!test
+%! k = [0 0 0 0 1/3 2/3 1 1 1 1];
+%! p = 3;
+%! u = rand (100, 1);
+%! i = findspan (numel(k)-p-2, p, u, k);
+%! ders = basisfunder (i, p, u, k, 7);
+%! for ii=1:10
+%! sumders = sum (squeeze(ders(ii,:,:)), 2);
+%! assert (sumders(1), 1, 1e-15);
+%! assert (sumders(2:end), zeros(rows(squeeze(ders(ii,:,:)))-1, 1), 1e-13);
+%! end
+%! assert (ders(:, (p+2):end, :), zeros(numel(u), 8-p-1, p+1), 1e-13)
+%! assert (all(all(ders(:, 1, :) <= 1)), true)
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/inst/findspan.m
new/nurbs-1.4.4/inst/findspan.m
--- old/nurbs-1.4.3/inst/findspan.m 2021-03-29 12:11:45.783919136 +0200
+++ new/nurbs-1.4.4/inst/findspan.m 2025-02-10 14:35:08.000000000 +0100
@@ -18,7 +18,7 @@
%
% Modification of Algorithm A2.1 from 'The NURBS BOOK' pg68
%
-% Copyright (C) 2010 Rafael Vazquez
+% Copyright (C) 2010, 2021 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
@@ -33,6 +33,11 @@
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
+if (isempty (u))
+ s = zeros (size(u));
+ return
+end
+
if (max(u(:))>U(end) || min(u(:))<U(1))
error('Some value is outside the knot span')
end
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/inst/nrbderiv.m
new/nurbs-1.4.4/inst/nrbderiv.m
--- old/nurbs-1.4.3/inst/nrbderiv.m 2021-03-29 12:11:45.791919259 +0200
+++ new/nurbs-1.4.4/inst/nrbderiv.m 2025-02-10 14:35:08.000000000 +0100
@@ -429,8 +429,8 @@
%! D2F(2,:) = -16*(12*x.^2-12*x+5)./w.^3;
%! D2F(3,:) = -8*(16*x.^3+60*x.^2-48*x+21)./w.^3 .* (x<0.5)
-8*(16*x.^3-36*x.^2+48*x-19)./w.^3 .* (x>0.5);
%! assert (F, pnt, 1e3*eps)
-%! assert (DF, jac, 1e3*eps)
-%! assert (D2F, hess, 1e3*eps)
+%! assert (DF, jac{1}, 1e3*eps)
+%! assert (D2F, hess{1}, 1e3*eps)
%!test
%! knots = {[0 0 0 1 1 1], [0 0 0 0.5 1 1 1]};
@@ -668,8 +668,8 @@
%! D2F(2,:) = -16*(12*x.^2-12*x+5)./w.^3;
%! D2F(3,:) = -8*(16*x.^3+60*x.^2-48*x+21)./w.^3 .* (x<0.5)
-8*(16*x.^3-36*x.^2+48*x-19)./w.^3 .* (x>0.5);
%! assert (F, pnt, 1e3*eps)
-%! assert (DF, jac, 1e3*eps)
-%! assert (D2F, hess, 1e3*eps)
+%! assert (DF, jac{1}, 1e3*eps)
+%! assert (D2F, hess{1}, 1e3*eps)
%!test
%! knots = {[0 0 0 1 1 1], [0 0 0 0.5 1 1 1]};
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/inst/nrbdeval.m
new/nurbs-1.4.4/inst/nrbdeval.m
--- old/nurbs-1.4.3/inst/nrbdeval.m 2021-03-29 12:11:45.791919259 +0200
+++ new/nurbs-1.4.4/inst/nrbdeval.m 2025-02-10 14:35:08.000000000 +0100
@@ -41,6 +41,7 @@
% Copyright (C) 2010 Carlo de Falco
% Copyright (C) 2010, 2011 Rafael Vazquez
% Copyright (C) 2018 Luca Coradello
+% Copyright (C) 2023 Pablo Antolin
%
% 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
@@ -57,12 +58,18 @@
if (nargin == 3)
tt = varargin{1};
+ dnurbs2 = [];
+ dnurbs3 = [];
+ dnurbs4 = [];
elseif (nargin == 4)
dnurbs2 = varargin{1};
+ dnurbs3 = [];
+ dnurbs4 = [];
tt = varargin{2};
elseif (nargin == 5)
dnurbs2 = varargin{1};
dnurbs3 = varargin{2};
+ dnurbs4 = [];
tt = varargin{3};
elseif (nargin == 6)
dnurbs2 = varargin{1};
@@ -81,244 +88,564 @@
error('Not a recognised NURBS representation');
end
-[cp,cw] = nrbeval(nurbs, tt);
+max_der = 1;
-if (iscell(nurbs.knots))
- if (size(nurbs.knots,2) == 3)
- % NURBS structure represents a volume
- temp = cw(ones(3,1),:,:,:);
- pnt = cp./temp;
-
- [cup,cuw] = nrbeval (dnurbs{1}, tt);
- tempu = cuw(ones(3,1),:,:,:);
- jac{1} = (cup-tempu.*pnt)./temp;
-
- [cvp,cvw] = nrbeval (dnurbs{2}, tt);
- tempv = cvw(ones(3,1),:,:,:);
- jac{2} = (cvp-tempv.*pnt)./temp;
-
- [cwp,cww] = nrbeval (dnurbs{3}, tt);
- tempw = cww(ones(3,1),:,:,:);
- jac{3} = (cwp-tempw.*pnt)./temp;
-
-% second derivatives
- if (nargout >= 3)
- if (exist ('dnurbs2'))
- [cuup, cuuw] = nrbeval (dnurbs2{1,1}, tt);
- tempuu = cuuw(ones(3,1),:,:,:);
- hess{1,1} = (cuup - (2*cup.*tempu + cp.*tempuu)./temp +
2*cp.*tempu.^2./temp.^2)./temp;
- clear cuup cuuw tempuu
-
- [cvvp, cvvw] = nrbeval (dnurbs2{2,2}, tt);
- tempvv = cvvw(ones(3,1),:,:,:);
- hess{2,2} = (cvvp - (2*cvp.*tempv + cp.*tempvv)./temp +
2*cp.*tempv.^2./temp.^2)./temp;
- clear cvvp cvvw tempvv
-
- [cwwp, cwww] = nrbeval (dnurbs2{3,3}, tt);
- tempww = cwww(ones(3,1),:,:,:);
- hess{3,3} = (cwwp - (2*cwp.*tempw + cp.*tempww)./temp +
2*cp.*tempw.^2./temp.^2)./temp;
- clear cwwp cwww tempww
-
- [cuvp, cuvw] = nrbeval (dnurbs2{1,2}, tt);
- tempuv = cuvw(ones(3,1),:,:,:);
- hess{1,2} = (cuvp - (cup.*tempv + cvp.*tempu + cp.*tempuv)./temp +
2*cp.*tempu.*tempv./temp.^2)./temp;
- hess{2,1} = hess{1,2};
- clear cuvp cuvw tempuv
-
- [cuwp, cuww] = nrbeval (dnurbs2{1,3}, tt);
- tempuw = cuww(ones(3,1),:,:,:);
- hess{1,3} = (cuwp - (cup.*tempw + cwp.*tempu + cp.*tempuw)./temp +
2*cp.*tempu.*tempw./temp.^2)./temp;
- hess{3,1} = hess{1,3};
- clear cuwp cuww tempuw
-
- [cvwp, cvww] = nrbeval (dnurbs2{2,3}, tt);
- tempvw = cvww(ones(3,1),:,:,:);
- hess{2,3} = (cvwp - (cvp.*tempw + cwp.*tempv + cp.*tempvw)./temp +
2*cp.*tempv.*tempw./temp.^2)./temp;
- hess{3,2} = hess{2,3};
- clear cvwp cvww tempvw
- else
- warning ('nrbdeval: dnurbs2 missing. The second derivative is not
computed');
- hess = [];
- end
- if (nargout > 3)
- warning ('nrbdeval: 3rd and 4th order derivatives not implemented for
volumes');
- third_der = [];
- fourth_der = [];
- end
- end
+if (nargout >= 3)
+ if (isempty (dnurbs2))
+ warning ('nrbdeval: dnurbs4 missing. The second derivative is not
computed');
+ else
+ max_der = 2;
+ end
+end
+
+if (nargout >= 4)
+ if (isempty (dnurbs3))
+ warning ('nrbdeval: dnurbs4 missing. The third derivative is not
computed');
+ else
+ max_der = 3;
+ end
+end
+
+if (nargout >= 5)
+ if (isempty (dnurbs4))
+ warning ('nrbdeval: dnurbs4 missing. The fourth derivative is not
computed');
+ else
+ max_der = 4;
+ end
+end
+
+
+% The evaluation of the NURBS can be computed as
+% X = P / W, where P and W are the cp and cw just above, respectively.
+% Thus, its four first derivatives are computed as:
+%
+% Xi = (Pi - X * Wi) / W
+%
+% Xij = (Pij - Xi * Wj - Xj * Wi - X * Wij) / W
+%
+% Xijk = (Pijk - Xij * Wk - Xik * Wj - Xjk * Wi
+% - Xi * Wjk - Xj * Wik - Xk * Wij
+% - X * Wijk) / W
+%
+% Xijkl = (Pijkl - Xijk * Wl - Xijl * Wk - Xikl * Wj - Xjkl * Wi
+% - Xij * Wkl - Xik * Wjl - Xil * Wjk - Xjk * Wil - Xjl
* Wik - Xkl * Wij
+% - Xi * Wjkl - Xj * Wikl - Xk * Wijl - Xl * Wijk
+% - X * Wijkl) / W
+%
+% where the subindices i,j,k,l mean partial derivatives respect to the i
(j,k,l) coordinates, respectively.
+
+if (is_rational(nurbs))
+
+ if (iscell(nurbs.knots))
+ ndim = size(nurbs.knots,2);
+ else
+ ndim = 1;
+ end
+
+ if (ndim == 1)
+ [X, dX, d2X, d3X, d4X] = nrbdeval_crv_rational (nurbs, dnurbs, dnurbs2,
dnurbs3, dnurbs4, tt, max_der);
+ elseif (ndim == 2)
+ [X, dX, d2X, d3X, d4X] = nrbdeval_srf_rational (nurbs, dnurbs, dnurbs2,
dnurbs3, dnurbs4, tt, max_der);
+ else % if (ndim == 3)
+ [X, dX, d2X, d3X, d4X] = nrbdeval_vol_rational (nurbs, dnurbs, dnurbs2,
dnurbs3, dnurbs4, tt, max_der);
+ end
+else
+ [X, dX, d2X, d3X, d4X] = nrbdeval_non_rational (nurbs, dnurbs, dnurbs2,
dnurbs3, dnurbs4, tt, max_der);
+end
+
+varargout{1} = X;
+varargout{2} = dX;
+if (max_der >= 2)
+ varargout{3} = d2X;
+end
+if (max_der >= 3)
+ varargout{4} = d3X;
+end
+if (max_der == 4)
+ varargout{5} = d4X;
+end
- elseif (size(nurbs.knots,2) == 2)
- % NURBS structure represents a surface
- temp = cw(ones(3,1),:,:);
- pnt = cp./temp;
-
- [cup,cuw] = nrbeval (dnurbs{1}, tt);
- tempu = cuw(ones(3,1),:,:);
- jac{1} = (cup-tempu.*pnt)./temp;
-
- [cvp,cvw] = nrbeval (dnurbs{2}, tt);
- tempv = cvw(ones(3,1),:,:);
- jac{2} = (cvp-tempv.*pnt)./temp;
-
-% second derivatives
- if (nargout >= 3)
- if (exist ('dnurbs2'))
- [cuup, cuuw] = nrbeval (dnurbs2{1,1}, tt);
- tempuu = cuuw(ones(3,1),:,:);
- hess{1,1} = (cuup - (2*cup.*tempu + cp.*tempuu)./temp +
2*cp.*tempu.^2./temp.^2)./temp;
-
- [cvvp, cvvw] = nrbeval (dnurbs2{2,2}, tt);
- tempvv = cvvw(ones(3,1),:,:);
- hess{2,2} = (cvvp - (2*cvp.*tempv + cp.*tempvv)./temp +
2*cp.*tempv.^2./temp.^2)./temp;
-
- [cuvp, cuvw] = nrbeval (dnurbs2{1,2}, tt);
- tempuv = cuvw(ones(3,1),:,:);
- hess{1,2} = (cuvp - (cup.*tempv + cvp.*tempu + cp.*tempuv)./temp +
2*cp.*tempu.*tempv./temp.^2)./temp;
- hess{2,1} = hess{1,2};
- else
- warning ('nrbdeval: dnurbs2 missing. The second derivative is not
computed');
- hess = [];
- end
- end
- if (nargout >= 4)
- if (exist ('dnurbs3'))
- [cuuup, cuuuw] = nrbeval (dnurbs3{1,1,1}, tt);
- tempuuu = cuuuw(ones(3,1),:,:);
- third_der{1,1,1} = (cuuup - 3*jac{1}.*tempuu - cp.*tempuuu -
3*hess{1,1}.*tempu)./temp;
-
- [cvvvp, cvvvw] = nrbeval (dnurbs3{2,2,2}, tt);
- tempvvv = cvvvw(ones(3,1),:,:);
- third_der{2,2,2} = (cvvvp - 3*jac{2}.*tempvv - cp.*tempvvv -
3*hess{2,2}.*tempv)./temp;
-
- [cuuvp, cuuvw] = nrbeval (dnurbs3{1,1,2}, tt);
- tempuuv = cuuvw(ones(3,1),:,:);
- third_der{1,1,2} = (cuuvp - 2*jac{1}.*tempuv - jac{2}.*tempuu -
cp.*tempuuv - 2*hess{1,2}.*tempu - hess{1,1}.*tempv)./temp;
- third_der{1,2,1} = third_der{1,1,2};
- third_der{2,1,1} = third_der{1,1,2};
-
- [cuvvp, cuvvw] = nrbeval (dnurbs3{1,2,2}, tt);
- tempuvv = cuvvw(ones(3,1),:,:);
- third_der{1,2,2} = (cuvvp - 2*jac{2}.*tempuv - jac{1}.*tempvv -
cp.*tempuvv - 2*hess{1,2}.*tempv - hess{2,2}.*tempu)./temp;
- third_der{2,2,1} = third_der{1,2,2};
- third_der{2,1,2} = third_der{1,2,2};
-
- else
- warning ('nrbdeval: dnurbs3 missing. The third derivative is not
computed');
- third_der = [];
- end
- end
- if (nargout == 5)
- if (exist ('dnurbs4'))
- [cuuuup, cuuuuw] = nrbeval (dnurbs4{1,1,1,1}, tt);
- tempuuuu = cuuuuw(ones(3,1),:,:);
- fourth_der{1,1,1,1} = (cuuuup - cp.*tempuuuu - 4*jac{1}.*tempuuu
-6*hess{1,1}.*tempuu - 4*third_der{1,1,1}.*tempu)./temp;
-
- [cvvvvp, cvvvvw] = nrbeval (dnurbs4{2,2,2,2}, tt);
- tempvvvv = cvvvvw(ones(3,1),:,:);
- fourth_der{2,2,2,2} = (cvvvvp - cp.*tempvvvv - 4*jac{2}.*tempvvv
-6*hess{2,2}.*tempvv - 4*third_der{2,2,2}.*tempv)./temp;
-
- [cuuuvp, cuuuvw] = nrbeval (dnurbs4{1,1,1,2}, tt);
- tempuuuv = cuuuvw(ones(3,1),:,:);
- fourth_der{1,1,1,2} = (cuuuvp - cp.*tempuuuv - 3*jac{1}.*tempuuv -
jac{2}.*tempuuu -3*hess{1,2}.*tempuu -3*hess{1,1}.*tempuv ...
- - third_der{1,1,1}.*tempv -
3*third_der{1,1,2}.*tempu)./temp;
-
- fourth_der{1,1,2,1} = fourth_der{1,1,1,2};
- fourth_der{1,2,1,1} = fourth_der{1,1,1,2};
- fourth_der{2,1,1,1} = fourth_der{1,1,1,2};
-
- [cuvvvp, cuvvvw] = nrbeval (dnurbs4{1,2,2,2}, tt);
- tempuvvv = cuvvvw(ones(3,1),:,:);
- fourth_der{1,2,2,2} = (cuvvvp - cp.*tempuvvv - 3*jac{2}.*tempuvv -
jac{1}.*tempvvv -3*hess{1,2}.*tempvv -3*hess{2,2}.*tempuv ...
- - third_der{2,2,2}.*tempu -
3*third_der{1,2,2}.*tempv)./temp;
-
- fourth_der{2,2,1,2} = fourth_der{1,2,2,2};
- fourth_der{2,1,2,2} = fourth_der{1,2,2,2};
- fourth_der{2,2,2,1} = fourth_der{1,2,2,2};
-
- [cuuvvp, cuuvvw] = nrbeval (dnurbs4{1,1,2,2}, tt);
- tempuuvv = cuuvvw(ones(3,1),:,:);
- fourth_der{1,1,2,2} = (cuuvvp - cp.*tempuuvv - 2*jac{1}.*tempuvv -
2*jac{2}.*tempuuv -hess{1,1}.*tempvv -hess{2,2}.*tempuu ...
- -4*hess{1,2}.*tempuv -
2*third_der{1,1,2}.*tempv - 2*third_der{1,2,2}.*tempu)./temp;
-
- fourth_der{1,2,2,1} = fourth_der{1,1,2,2};
- fourth_der{2,2,1,1} = fourth_der{1,1,2,2};
- fourth_der{1,2,1,2} = fourth_der{1,1,2,2};
- fourth_der{2,1,2,1} = fourth_der{1,1,2,2};
- fourth_der{2,1,1,2} = fourth_der{1,1,2,2};
-
- clear cuup cuuw tempuu cvvp cvvw tempvv cuvp cuvw tempuv
- clear cuuup cuuuw tempuuu cvvvp cvvvw tempvvv cuuvp cuuvw tempuuv
cuvvp cuvvw tempuvv
- clear cuuuup cuuuuw tempuuuu cvvvvp cvvvvw tempvvvv cuuuvp cuuuvw
tempuuuv cuuvvp cuuvvw tempuuvv cvvvup cvvvuw tempvvvu
-
- else
- warning ('nrbdeval: dnurbs4 missing. The fourth derivative is not
computed');
- fourth_der = [];
+end
+
+function [X, dX, d2X, d3X, d4X] = nrbdeval_non_rational (nurbs, dnurbs,
dnurbs2, dnurbs3, dnurbs4, tt, max_der)
+
+ if (iscell(nurbs.knots))
+ ndim = size(nurbs.knots,2);
+ else
+ ndim = 1;
+ end
+
+ [X, ~] = nrbeval(nurbs, tt);
+
+ if (~iscell(dnurbs))
+ dnurbs = {dnurbs};
+ end
+
+ for i = 1 : ndim
+ [dX{i}, ~] = nrbeval(dnurbs{i}, tt);
+ end
+
+ d2X = []; d3X = []; d4X = [];
+
+ if (max_der < 2)
+ return;
+ end
+
+ if (~iscell(dnurbs2))
+ dnurbs2 = {dnurbs2};
+ end
+
+ for i = 1 : ndim
+ for j = 1 : ndim
+ [d2X{i,j}, ~] = nrbeval(dnurbs2{i,j}, tt);
+ end
+ end
+
+ if (max_der < 3)
+ return;
+ end
+
+ if (~iscell(dnurbs3))
+ dnurbs3 = {dnurbs3};
+ end
+
+ for i = 1 : ndim
+ for j = 1 : ndim
+ for k = 1 : ndim
+ [d3X{i,j,k}, ~] = nrbeval(dnurbs3{i,j,k}, tt);
end
end
+ end
-
+ if (max_der < 4)
+ return;
end
-else
- % NURBS is a curve
- temp = cw(ones(3,1),:);
- pnt = cp./temp;
-
- % first derivative
- [cup,cuw] = nrbeval (dnurbs,tt);
- temp1 = cuw(ones(3,1),:);
- jac = (cup-temp1.*pnt)./temp;
-
- % second derivative
- if (nargout >= 3 && exist ('dnurbs2'))
- [cuup,cuuw] = nrbeval (dnurbs2, tt);
- temp2 = cuuw(ones(3,1),:);
- hess = (cuup - (2*cup.*temp1 + cp.*temp2)./temp +
2*cp.*temp1.^2./temp.^2)./temp;
- if (nargout >= 4 && exist ('dnurbs3'))
-
- [cuuup, cuuuw] = nrbeval (dnurbs3, tt);
- temp3 = cuuuw(ones(3,1),:);
- third_der = (cuuup - 3*jac.*temp2 - cp.*temp3 - 3*hess.*temp1)./temp;
- if (nargout >= 5 && exist ('dnurbs4'))
-
- [cuuuup, cuuuuw] = nrbeval (dnurbs4, tt);
- temp4 = cuuuuw(ones(3,1),:);
- fourth_der = (cuuuup - cp.*temp4 - 4*jac.*temp3 -6*hess.*temp2 -
4*third_der.*temp1)./temp;
- if (iscell (tt))
- fourth_der = {fourth_der};
- end
+ if (~iscell(dnurbs4))
+ dnurbs4 = {dnurbs4};
+ end
+ for i = 1 : ndim
+ for j = 1 : ndim
+ for k = 1 : ndim
+ for l = 1 : ndim
+ [d4X{i,j,k,l}, ~] = nrbeval(dnurbs4{i,j,k,l}, tt);
+ end
end
-
- if (iscell (tt))
- third_der = {third_der};
- end
end
-
- if (iscell (tt))
- hess = {hess};
- end
- end
-
- if (iscell (tt))
- jac = {jac};
end
-
end
-varargout{1} = pnt;
-varargout{2} = jac;
-if (nargout >= 3)
- varargout{3} = hess;
+
+
+function [X, dX, d2X, d3X, d4X] = nrbdeval_crv_rational (nurbs, dnurbs,
dnurbs2, dnurbs3, dnurbs4, tt, max_der)
+
+[P, W] = nrbeval(nurbs, tt);
+W = W(ones(3,1), :, :, :);
+one_div_W = 1.0 ./ W;
+
+X = one_div_W .* P;
+
+clear P;
+
+
+[dP, dW] = nrbeval(dnurbs, tt);
+dW = dW(ones(3,1), :, :, :);
+
+dX{1} = one_div_W .* (dP - X .* dW);
+
+clear dP;
+
+d2X = []; d3X = []; d4X = [];
+
+if (max_der < 2)
+ return;
end
-if (nargout >= 4)
- varargout{4} = third_der;
+
+[d2P, d2W] = nrbeval(dnurbs2, tt);
+d2W = d2W(ones(3,1), :, :, :);
+
+d2X{1} = one_div_W .* (d2P - dX{1} .* dW - dX{1} .* dW - X .* d2W);
+
+if (max_der < 3)
+ return;
+end
+
+clear d2P;
+
+
+[d3P, d3W] = nrbeval(dnurbs3, tt);
+d3W = d3W(ones(3,1), :, :, :);
+
+d3X{1} = one_div_W .* (d3P - 3 * d2X{1} .* dW - 3 * dX{1} .* d2W - X .* d3W);
+
+
+if (max_der < 4)
+ return;
+end
+
+
+[d4P, d4W] = nrbeval(dnurbs4, tt);
+d4W = d4W(ones(3,1), :, :, :);
+
+d4X{1} = one_div_W .* (d4P - 4 * d3X{1} .* dW - 6 * d2X{1} .* d2W - 4 * dX{1}
.* d3W - X .* d4W);
+
+
+end
+
+function [X, dX, d2X, d3X, d4X] = nrbdeval_srf_rational (nurbs, dnurbs,
dnurbs2, dnurbs3, dnurbs4, tt, max_der)
+
+[P, W] = nrbeval(nurbs, tt);
+W = W(ones(3,1), :, :, :);
+one_div_W = 1.0 ./ W;
+
+X = one_div_W .* P;
+
+clear P;
+
+dP = cell(1, 2); dW = cell(1, 2);
+[dP{1}, dW{1}] = nrbeval(dnurbs{1}, tt);
+[dP{2}, dW{2}] = nrbeval(dnurbs{2}, tt);
+dW{1} = dW{1}(ones(3,1), :, :, :);
+dW{2} = dW{2}(ones(3,1), :, :, :);
+
+dX{1} = one_div_W .* (dP{1} - X .* dW{1});
+dX{2} = one_div_W .* (dP{2} - X .* dW{2});
+
+d2X = []; d3X = []; d4X = [];
+
+if (max_der < 2)
+ return;
+end
+
+clear dP;
+
+d2P = cell(2, 2); d2W = cell(2, 2);
+[d2P{1,1}, d2W{1,1}] = nrbeval(dnurbs2{1,1}, tt);
+[d2P{1,2}, d2W{1,2}] = nrbeval(dnurbs2{1,2}, tt);
+[d2P{2,2}, d2W{2,2}] = nrbeval(dnurbs2{2,2}, tt);
+d2W{1,1} = d2W{1,1}(ones(3,1), :, :, :);
+d2W{1,2} = d2W{1,2}(ones(3,1), :, :, :);
+d2W{2,2} = d2W{2,2}(ones(3,1), :, :, :);
+
+d2X{1, 1} = one_div_W .* (d2P{1, 1} - dX{1} .* dW{1} - dX{1} .* dW{1} - X .*
d2W{1, 1});
+d2X{1, 2} = one_div_W .* (d2P{1, 2} - dX{1} .* dW{2} - dX{2} .* dW{1} - X .*
d2W{1, 2});
+d2X{2, 2} = one_div_W .* (d2P{2, 2} - dX{2} .* dW{2} - dX{2} .* dW{2} - X .*
d2W{2, 2});
+
+d2X{2, 1} = d2X{1, 2};
+
+if (max_der < 3)
+ return;
+end
+
+clear d2P;
+
+d3P = cell(2, 2, 2); d3W = cell(2, 2, 2);
+[d3P{1,1,1}, d3W{1,1,1}] = nrbeval(dnurbs3{1,1,1}, tt);
+[d3P{1,1,2}, d3W{1,1,2}] = nrbeval(dnurbs3{1,1,2}, tt);
+[d3P{1,2,2}, d3W{1,2,2}] = nrbeval(dnurbs3{1,2,2}, tt);
+[d3P{2,2,2}, d3W{2,2,2}] = nrbeval(dnurbs3{2,2,2}, tt);
+d3W{1,1,1} = d3W{1,1,1}(ones(3,1), :, :, :);
+d3W{1,1,2} = d3W{1,1,2}(ones(3,1), :, :, :);
+d3W{1,2,2} = d3W{1,2,2}(ones(3,1), :, :, :);
+d3W{2,2,2} = d3W{2,2,2}(ones(3,1), :, :, :);
+
+d3X{1, 1, 1} = one_div_W .* (d3P{1, 1, 1} - 3 * d2X{1, 1} .* dW{1} - 3 * dX{1}
.* d2W{1, 1} - X .* d3W{1, 1, 1});
+d3X{1, 1, 2} = one_div_W .* (d3P{1, 1, 2} - d2X{1, 1} .* dW{2} - 2 * d2X{1, 2}
.* dW{1} - 2 * dX{1} .* d2W{1, 2} - dX{2} .* d2W{1, 1} - X .* d3W{1, 1, 2});
+d3X{1, 2, 2} = one_div_W .* (d3P{1, 2, 2} - 2 * d2X{1, 2} .* dW{2} - d2X{2, 2}
.* dW{1} - dX{1} .* d2W{2, 2} - 2 * dX{2} .* d2W{1, 2} - X .* d3W{1, 2, 2});
+d3X{2, 2, 2} = one_div_W .* (d3P{2, 2, 2} - 3 * d2X{2, 2} .* dW{2} - 3 * dX{2}
.* d2W{2, 2} - X .* d3W{2, 2, 2});
+
+d3X{2, 1, 1} = d3X{1, 1, 2};
+d3X{1, 2, 1} = d3X{1, 1, 2};
+d3X{2, 2, 1} = d3X{1, 2, 2};
+d3X{2, 1, 2} = d3X{1, 2, 2};
+
+if (max_der < 4)
+ return;
end
-if (nargout == 5)
- varargout{5} = fourth_der;
+
+clear d3P;
+
+
+d4P = cell(2, 2, 2, 2); d4W = cell(2, 2, 2, 2);
+[d4P{1,1,1,1}, d4W{1,1,1,1}] = nrbeval(dnurbs4{1,1,1,1}, tt);
+[d4P{1,1,1,2}, d4W{1,1,1,2}] = nrbeval(dnurbs4{1,1,1,2}, tt);
+[d4P{1,1,2,2}, d4W{1,1,2,2}] = nrbeval(dnurbs4{1,1,2,2}, tt);
+[d4P{1,2,2,2}, d4W{1,2,2,2}] = nrbeval(dnurbs4{1,2,2,2}, tt);
+[d4P{2,2,2,2}, d4W{2,2,2,2}] = nrbeval(dnurbs4{2,2,2,2}, tt);
+d4W{1,1,1,1} = d4W{1,1,1,1}(ones(3,1), :, :, :);
+d4W{1,1,1,2} = d4W{1,1,1,2}(ones(3,1), :, :, :);
+d4W{1,1,2,2} = d4W{1,1,2,2}(ones(3,1), :, :, :);
+d4W{1,2,2,2} = d4W{1,2,2,2}(ones(3,1), :, :, :);
+d4W{2,2,2,2} = d4W{2,2,2,2}(ones(3,1), :, :, :);
+
+d4X{1, 1, 1, 1} = one_div_W .* (d4P{1, 1, 1, 1} - 4 * d3X{1, 1, 1} .* dW{1} -
6 * d2X{1, 1} .* d2W{1, 1} - 4 * dX{1} .* d3W{1, 1, 1} - X .* d4W{1, 1, 1, 1});
+d4X{1, 1, 1, 2} = one_div_W .* (d4P{1, 1, 1, 2} - d3X{1, 1, 1} .* dW{2} - 3 *
d3X{1, 1, 2} .* dW{1} - 3 * d2X{1, 1} .* d2W{1, 2} - 3 * d2X{1, 2} .* d2W{1, 1}
- 3 * dX{1} .* d3W{1, 1, 2} - dX{2} .* d3W{1, 1, 1} - X .* d4W{1, 1, 1, 2});
+d4X{1, 1, 2, 2} = one_div_W .* (d4P{1, 1, 2, 2} - 2 * d3X{1, 1, 2} .* dW{2} -
2 * d3X{1, 2, 2} .* dW{1} - d2X{1, 1} .* d2W{2, 2} - 4 * d2X{1, 2} .* d2W{1, 2}
- d2X{2, 2} .* d2W{1, 1} - 2 * dX{1} .* d3W{1, 2, 2} - 2 * dX{2} .* d3W{1, 1,
2} - X .* d4W{1, 1, 2, 2});
+d4X{1, 2, 2, 2} = one_div_W .* (d4P{1, 2, 2, 2} - 3 * d3X{1, 2, 2} .* dW{2} -
d3X{2, 2, 2} .* dW{1} - 3 * d2X{1, 2} .* d2W{2, 2} - 3 * d2X{2, 2} .* d2W{1, 2}
- dX{1} .* d3W{2, 2, 2} - 3 * dX{2} .* d3W{1, 2, 2} - X .* d4W{1, 2, 2, 2});
+d4X{2, 2, 2, 2} = one_div_W .* (d4P{2, 2, 2, 2} - 4 * d3X{2, 2, 2} .* dW{2} -
6 * d2X{2, 2} .* d2W{2, 2} - 4 * dX{2} .* d3W{2, 2, 2} - X .* d4W{2, 2, 2, 2});
+
+d4X{2, 1, 1, 1} = d4X{1, 1, 1, 2};
+d4X{1, 2, 1, 1} = d4X{1, 1, 1, 2};
+d4X{2, 2, 1, 1} = d4X{1, 1, 2, 2};
+d4X{1, 1, 2, 1} = d4X{1, 1, 1, 2};
+d4X{2, 1, 2, 1} = d4X{1, 1, 2, 2};
+d4X{1, 2, 2, 1} = d4X{1, 1, 2, 2};
+d4X{2, 2, 2, 1} = d4X{1, 2, 2, 2};
+d4X{2, 1, 1, 2} = d4X{1, 1, 2, 2};
+d4X{1, 2, 1, 2} = d4X{1, 1, 2, 2};
+d4X{2, 2, 1, 2} = d4X{1, 2, 2, 2};
+d4X{2, 1, 2, 2} = d4X{1, 2, 2, 2};
+
+end
+
+function [X, dX, d2X, d3X, d4X] = nrbdeval_vol_rational (nurbs, dnurbs,
dnurbs2, dnurbs3, dnurbs4, tt, max_der)
+
+[P, W] = nrbeval(nurbs, tt);
+W = W(ones(3,1), :, :, :);
+one_div_W = 1.0 ./ W;
+
+X = one_div_W .* P;
+
+
+dP = cell(1, 3); dW = cell(1, 3);
+[dP{1}, dW{1}] = nrbeval(dnurbs{1}, tt);
+[dP{2}, dW{2}] = nrbeval(dnurbs{2}, tt);
+[dP{3}, dW{3}] = nrbeval(dnurbs{3}, tt);
+dW{1} = dW{1}(ones(3,1), :, :, :);
+dW{2} = dW{2}(ones(3,1), :, :, :);
+dW{3} = dW{3}(ones(3,1), :, :, :);
+
+dX{1} = one_div_W .* (dP{1} - X .* dW{1});
+dX{2} = one_div_W .* (dP{2} - X .* dW{2});
+dX{3} = one_div_W .* (dP{3} - X .* dW{3});
+
+
+d2X = []; d3X = []; d4X = [];
+
+if (max_der < 2)
+ return;
end
+clear dP;
+
+d2P = cell(3, 3); d2W = cell(3, 3);
+[d2P{1,1}, d2W{1,1}] = nrbeval(dnurbs2{1,1}, tt);
+[d2P{1,2}, d2W{1,2}] = nrbeval(dnurbs2{1,2}, tt);
+[d2P{1,3}, d2W{1,3}] = nrbeval(dnurbs2{1,3}, tt);
+[d2P{2,2}, d2W{2,2}] = nrbeval(dnurbs2{2,2}, tt);
+[d2P{2,3}, d2W{2,3}] = nrbeval(dnurbs2{2,3}, tt);
+[d2P{3,3}, d2W{3,3}] = nrbeval(dnurbs2{3,3}, tt);
+d2W{1,1} = d2W{1,1}(ones(3,1), :, :, :);
+d2W{1,2} = d2W{1,2}(ones(3,1), :, :, :);
+d2W{1,3} = d2W{1,3}(ones(3,1), :, :, :);
+d2W{2,2} = d2W{2,2}(ones(3,1), :, :, :);
+d2W{2,3} = d2W{2,3}(ones(3,1), :, :, :);
+d2W{3,3} = d2W{3,3}(ones(3,1), :, :, :);
+
+d2X{1, 1} = one_div_W .* (d2P{1, 1} - dX{1} .* dW{1} - dX{1} .* dW{1} - X .*
d2W{1, 1});
+d2X{1, 2} = one_div_W .* (d2P{1, 2} - dX{1} .* dW{2} - dX{2} .* dW{1} - X .*
d2W{1, 2});
+d2X{1, 3} = one_div_W .* (d2P{1, 3} - dX{1} .* dW{3} - dX{3} .* dW{1} - X .*
d2W{1, 3});
+d2X{2, 2} = one_div_W .* (d2P{2, 2} - dX{2} .* dW{2} - dX{2} .* dW{2} - X .*
d2W{2, 2});
+d2X{2, 3} = one_div_W .* (d2P{2, 3} - dX{2} .* dW{3} - dX{3} .* dW{2} - X .*
d2W{2, 3});
+d2X{3, 3} = one_div_W .* (d2P{3, 3} - dX{3} .* dW{3} - dX{3} .* dW{3} - X .*
d2W{3, 3});
+
+d2X{2, 1} = d2X{1, 2};
+d2X{3, 1} = d2X{1, 3};
+d2X{3, 2} = d2X{2, 3};
+
+if (max_der < 3)
+ return;
+end
+
+clear d2P;
+
+
+d3P = cell(3, 3, 3); d3W = cell(3, 3, 3);
+[d3P{1,1,1}, d3W{1,1,1}] = nrbeval(dnurbs3{1,1,1}, tt);
+[d3P{1,1,2}, d3W{1,1,2}] = nrbeval(dnurbs3{1,1,2}, tt);
+[d3P{1,1,3}, d3W{1,1,3}] = nrbeval(dnurbs3{1,1,3}, tt);
+[d3P{1,2,2}, d3W{1,2,2}] = nrbeval(dnurbs3{1,2,2}, tt);
+[d3P{1,2,3}, d3W{1,2,3}] = nrbeval(dnurbs3{1,2,3}, tt);
+[d3P{1,3,3}, d3W{1,3,3}] = nrbeval(dnurbs3{1,3,3}, tt);
+[d3P{2,2,2}, d3W{2,2,2}] = nrbeval(dnurbs3{2,2,2}, tt);
+[d3P{2,2,3}, d3W{2,2,3}] = nrbeval(dnurbs3{2,2,3}, tt);
+[d3P{2,3,3}, d3W{2,3,3}] = nrbeval(dnurbs3{2,3,3}, tt);
+[d3P{3,3,3}, d3W{3,3,3}] = nrbeval(dnurbs3{3,3,3}, tt);
+d3W{1,1,1} = d3W{1,1,1}(ones(3,1), :, :, :);
+d3W{1,1,2} = d3W{1,1,2}(ones(3,1), :, :, :);
+d3W{1,1,3} = d3W{1,1,3}(ones(3,1), :, :, :);
+d3W{1,2,2} = d3W{1,2,2}(ones(3,1), :, :, :);
+d3W{1,2,3} = d3W{1,2,3}(ones(3,1), :, :, :);
+d3W{1,3,3} = d3W{1,3,3}(ones(3,1), :, :, :);
+d3W{2,2,2} = d3W{2,2,2}(ones(3,1), :, :, :);
+d3W{2,2,3} = d3W{2,2,3}(ones(3,1), :, :, :);
+d3W{2,3,3} = d3W{2,3,3}(ones(3,1), :, :, :);
+d3W{3,3,3} = d3W{3,3,3}(ones(3,1), :, :, :);
+
+d3X{1, 1, 1} = one_div_W .* (d3P{1, 1, 1} - 3 * d2X{1, 1} .* dW{1} - 3 * dX{1}
.* d2W{1, 1} - X .* d3W{1, 1, 1});
+d3X{1, 1, 2} = one_div_W .* (d3P{1, 1, 2} - d2X{1, 1} .* dW{2} - 2 * d2X{1, 2}
.* dW{1} - 2 * dX{1} .* d2W{1, 2} - dX{2} .* d2W{1, 1} - X .* d3W{1, 1, 2});
+d3X{1, 1, 3} = one_div_W .* (d3P{1, 1, 3} - d2X{1, 1} .* dW{3} - 2 * d2X{1, 3}
.* dW{1} - 2 * dX{1} .* d2W{1, 3} - dX{3} .* d2W{1, 1} - X .* d3W{1, 1, 3});
+d3X{1, 2, 2} = one_div_W .* (d3P{1, 2, 2} - 2 * d2X{1, 2} .* dW{2} - d2X{2, 2}
.* dW{1} - dX{1} .* d2W{2, 2} - 2 * dX{2} .* d2W{1, 2} - X .* d3W{1, 2, 2});
+d3X{1, 2, 3} = one_div_W .* (d3P{1, 2, 3} - d2X{1, 2} .* dW{3} - d2X{1, 3} .*
dW{2} - d2X{2, 3} .* dW{1} - dX{1} .* d2W{2, 3} - dX{2} .* d2W{1, 3} - dX{3} .*
d2W{1, 2} - X .* d3W{1, 2, 3});
+d3X{1, 3, 3} = one_div_W .* (d3P{1, 3, 3} - 2 * d2X{1, 3} .* dW{3} - d2X{3, 3}
.* dW{1} - dX{1} .* d2W{3, 3} - 2 * dX{3} .* d2W{1, 3} - X .* d3W{1, 3, 3});
+d3X{2, 2, 2} = one_div_W .* (d3P{2, 2, 2} - 3 * d2X{2, 2} .* dW{2} - 3 * dX{2}
.* d2W{2, 2} - X .* d3W{2, 2, 2});
+d3X{2, 2, 3} = one_div_W .* (d3P{2, 2, 3} - d2X{2, 2} .* dW{3} - 2 * d2X{2, 3}
.* dW{2} - 2 * dX{2} .* d2W{2, 3} - dX{3} .* d2W{2, 2} - X .* d3W{2, 2, 3});
+d3X{2, 3, 3} = one_div_W .* (d3P{2, 3, 3} - 2 * d2X{2, 3} .* dW{3} - d2X{3, 3}
.* dW{2} - dX{2} .* d2W{3, 3} - 2 * dX{3} .* d2W{2, 3} - X .* d3W{2, 3, 3});
+d3X{3, 3, 3} = one_div_W .* (d3P{3, 3, 3} - 3 * d2X{3, 3} .* dW{3} - 3 * dX{3}
.* d2W{3, 3} - X .* d3W{3, 3, 3});
+
+d3X{2, 1, 1} = d3X{1, 1, 2};
+d3X{3, 1, 1} = d3X{1, 1, 3};
+d3X{1, 2, 1} = d3X{1, 1, 2};
+d3X{2, 2, 1} = d3X{1, 2, 2};
+d3X{3, 2, 1} = d3X{1, 2, 3};
+d3X{1, 3, 1} = d3X{1, 1, 3};
+d3X{2, 3, 1} = d3X{1, 2, 3};
+d3X{3, 3, 1} = d3X{1, 3, 3};
+d3X{2, 1, 2} = d3X{1, 2, 2};
+d3X{3, 1, 2} = d3X{1, 2, 3};
+d3X{3, 2, 2} = d3X{2, 2, 3};
+d3X{1, 3, 2} = d3X{1, 2, 3};
+d3X{2, 3, 2} = d3X{2, 2, 3};
+d3X{3, 3, 2} = d3X{2, 3, 3};
+d3X{2, 1, 3} = d3X{1, 2, 3};
+d3X{3, 1, 3} = d3X{1, 3, 3};
+d3X{3, 2, 3} = d3X{2, 3, 3};
+
+if (max_der < 4)
+ return;
+end
+
+
+clear d3P;
+
+
+d4P = cell(3, 3, 3, 3); d4W = cell(3, 3, 3, 3);
+[d4P{1,1,1,1}, d4W{1,1,1,1}] = nrbeval(dnurbs4{1,1,1,1}, tt);
+[d4P{1,1,1,2}, d4W{1,1,1,2}] = nrbeval(dnurbs4{1,1,1,2}, tt);
+[d4P{1,1,1,3}, d4W{1,1,1,3}] = nrbeval(dnurbs4{1,1,1,3}, tt);
+[d4P{1,1,2,2}, d4W{1,1,2,2}] = nrbeval(dnurbs4{1,1,2,2}, tt);
+[d4P{1,1,2,3}, d4W{1,1,2,3}] = nrbeval(dnurbs4{1,1,2,3}, tt);
+[d4P{1,1,3,3}, d4W{1,1,3,3}] = nrbeval(dnurbs4{1,1,3,3}, tt);
+[d4P{1,2,2,2}, d4W{1,2,2,2}] = nrbeval(dnurbs4{1,2,2,2}, tt);
+[d4P{1,2,2,3}, d4W{1,2,2,3}] = nrbeval(dnurbs4{1,2,2,3}, tt);
+[d4P{1,2,3,3}, d4W{1,2,3,3}] = nrbeval(dnurbs4{1,2,3,3}, tt);
+[d4P{1,3,3,3}, d4W{1,3,3,3}] = nrbeval(dnurbs4{1,3,3,3}, tt);
+[d4P{2,2,2,2}, d4W{2,2,2,2}] = nrbeval(dnurbs4{2,2,2,2}, tt);
+[d4P{2,2,2,3}, d4W{2,2,2,3}] = nrbeval(dnurbs4{2,2,2,3}, tt);
+[d4P{2,2,3,3}, d4W{2,2,3,3}] = nrbeval(dnurbs4{2,2,3,3}, tt);
+[d4P{2,3,3,3}, d4W{2,3,3,3}] = nrbeval(dnurbs4{2,3,3,3}, tt);
+[d4P{3,3,3,3}, d4W{3,3,3,3}] = nrbeval(dnurbs4{3,3,3,3}, tt);
+d4W{1,1,1,1} = d4W{1,1,1,1}(ones(3,1), :, :, :);
+d4W{1,1,1,2} = d4W{1,1,1,2}(ones(3,1), :, :, :);
+d4W{1,1,1,3} = d4W{1,1,1,3}(ones(3,1), :, :, :);
+d4W{1,1,2,2} = d4W{1,1,2,2}(ones(3,1), :, :, :);
+d4W{1,1,2,3} = d4W{1,1,2,3}(ones(3,1), :, :, :);
+d4W{1,1,3,3} = d4W{1,1,3,3}(ones(3,1), :, :, :);
+d4W{1,2,2,2} = d4W{1,2,2,2}(ones(3,1), :, :, :);
+d4W{1,2,2,3} = d4W{1,2,2,3}(ones(3,1), :, :, :);
+d4W{1,2,3,3} = d4W{1,2,3,3}(ones(3,1), :, :, :);
+d4W{1,3,3,3} = d4W{1,3,3,3}(ones(3,1), :, :, :);
+d4W{2,2,2,2} = d4W{2,2,2,2}(ones(3,1), :, :, :);
+d4W{2,2,2,3} = d4W{2,2,2,3}(ones(3,1), :, :, :);
+d4W{2,2,3,3} = d4W{2,2,3,3}(ones(3,1), :, :, :);
+d4W{2,3,3,3} = d4W{2,3,3,3}(ones(3,1), :, :, :);
+d4W{3,3,3,3} = d4W{3,3,3,3}(ones(3,1), :, :, :);
+
+d4X{1, 1, 1, 1} = one_div_W .* (d4P{1, 1, 1, 1} - 4 * d3X{1, 1, 1} .* dW{1} -
6 * d2X{1, 1} .* d2W{1, 1} - 4 * dX{1} .* d3W{1, 1, 1} - X .* d4W{1, 1, 1, 1});
+d4X{1, 1, 1, 2} = one_div_W .* (d4P{1, 1, 1, 2} - d3X{1, 1, 1} .* dW{2} - 3 *
d3X{1, 1, 2} .* dW{1} - 3 * d2X{1, 1} .* d2W{1, 2} - 3 * d2X{1, 2} .* d2W{1, 1}
- 3 * dX{1} .* d3W{1, 1, 2} - dX{2} .* d3W{1, 1, 1} - X .* d4W{1, 1, 1, 2});
+d4X{1, 1, 1, 3} = one_div_W .* (d4P{1, 1, 1, 3} - d3X{1, 1, 1} .* dW{3} - 3 *
d3X{1, 1, 3} .* dW{1} - 3 * d2X{1, 1} .* d2W{1, 3} - 3 * d2X{1, 3} .* d2W{1, 1}
- 3 * dX{1} .* d3W{1, 1, 3} - dX{3} .* d3W{1, 1, 1} - X .* d4W{1, 1, 1, 3});
+d4X{1, 1, 2, 2} = one_div_W .* (d4P{1, 1, 2, 2} - 2 * d3X{1, 1, 2} .* dW{2} -
2 * d3X{1, 2, 2} .* dW{1} - d2X{1, 1} .* d2W{2, 2} - 4 * d2X{1, 2} .* d2W{1, 2}
- d2X{2, 2} .* d2W{1, 1} - 2 * dX{1} .* d3W{1, 2, 2} - 2 * dX{2} .* d3W{1, 1,
2} - X .* d4W{1, 1, 2, 2});
+d4X{1, 1, 2, 3} = one_div_W .* (d4P{1, 1, 2, 3} - d3X{1, 1, 2} .* dW{3} -
d3X{1, 1, 3} .* dW{2} - 2 * d3X{1, 2, 3} .* dW{1} - d2X{1, 1} .* d2W{2, 3} - 2
* d2X{1, 2} .* d2W{1, 3} - 2 * d2X{1, 3} .* d2W{1, 2} - d2X{2, 3} .* d2W{1, 1}
- 2 * dX{1} .* d3W{1, 2, 3} - dX{2} .* d3W{1, 1, 3} - dX{3} .* d3W{1, 1, 2} - X
.* d4W{1, 1, 2, 3});
+d4X{1, 1, 3, 3} = one_div_W .* (d4P{1, 1, 3, 3} - 2 * d3X{1, 1, 3} .* dW{3} -
2 * d3X{1, 3, 3} .* dW{1} - d2X{1, 1} .* d2W{3, 3} - 4 * d2X{1, 3} .* d2W{1, 3}
- d2X{3, 3} .* d2W{1, 1} - 2 * dX{1} .* d3W{1, 3, 3} - 2 * dX{3} .* d3W{1, 1,
3} - X .* d4W{1, 1, 3, 3});
+d4X{1, 2, 2, 2} = one_div_W .* (d4P{1, 2, 2, 2} - 3 * d3X{1, 2, 2} .* dW{2} -
d3X{2, 2, 2} .* dW{1} - 3 * d2X{1, 2} .* d2W{2, 2} - 3 * d2X{2, 2} .* d2W{1, 2}
- dX{1} .* d3W{2, 2, 2} - 3 * dX{2} .* d3W{1, 2, 2} - X .* d4W{1, 2, 2, 2});
+d4X{1, 2, 2, 3} = one_div_W .* (d4P{1, 2, 2, 3} - d3X{1, 2, 2} .* dW{3} - 2 *
d3X{1, 2, 3} .* dW{2} - d3X{2, 2, 3} .* dW{1} - 2 * d2X{1, 2} .* d2W{2, 3} -
d2X{1, 3} .* d2W{2, 2} - d2X{2, 2} .* d2W{1, 3} - 2 * d2X{2, 3} .* d2W{1, 2} -
dX{1} .* d3W{2, 2, 3} - 2 * dX{2} .* d3W{1, 2, 3} - dX{3} .* d3W{1, 2, 2} - X
.* d4W{1, 2, 2, 3});
+d4X{1, 2, 3, 3} = one_div_W .* (d4P{1, 2, 3, 3} - 2 * d3X{1, 2, 3} .* dW{3} -
d3X{1, 3, 3} .* dW{2} - d3X{2, 3, 3} .* dW{1} - d2X{1, 2} .* d2W{3, 3} - 2 *
d2X{1, 3} .* d2W{2, 3} - 2 * d2X{2, 3} .* d2W{1, 3} - d2X{3, 3} .* d2W{1, 2} -
dX{1} .* d3W{2, 3, 3} - dX{2} .* d3W{1, 3, 3} - 2 * dX{3} .* d3W{1, 2, 3} - X
.* d4W{1, 2, 3, 3});
+d4X{1, 3, 3, 3} = one_div_W .* (d4P{1, 3, 3, 3} - 3 * d3X{1, 3, 3} .* dW{3} -
d3X{3, 3, 3} .* dW{1} - 3 * d2X{1, 3} .* d2W{3, 3} - 3 * d2X{3, 3} .* d2W{1, 3}
- dX{1} .* d3W{3, 3, 3} - 3 * dX{3} .* d3W{1, 3, 3} - X .* d4W{1, 3, 3, 3});
+d4X{2, 2, 2, 2} = one_div_W .* (d4P{2, 2, 2, 2} - 4 * d3X{2, 2, 2} .* dW{2} -
6 * d2X{2, 2} .* d2W{2, 2} - 4 * dX{2} .* d3W{2, 2, 2} - X .* d4W{2, 2, 2, 2});
+d4X{2, 2, 2, 3} = one_div_W .* (d4P{2, 2, 2, 3} - d3X{2, 2, 2} .* dW{3} - 3 *
d3X{2, 2, 3} .* dW{2} - 3 * d2X{2, 2} .* d2W{2, 3} - 3 * d2X{2, 3} .* d2W{2, 2}
- 3 * dX{2} .* d3W{2, 2, 3} - dX{3} .* d3W{2, 2, 2} - X .* d4W{2, 2, 2, 3});
+d4X{2, 2, 3, 3} = one_div_W .* (d4P{2, 2, 3, 3} - 2 * d3X{2, 2, 3} .* dW{3} -
2 * d3X{2, 3, 3} .* dW{2} - d2X{2, 2} .* d2W{3, 3} - 4 * d2X{2, 3} .* d2W{2, 3}
- d2X{3, 3} .* d2W{2, 2} - 2 * dX{2} .* d3W{2, 3, 3} - 2 * dX{3} .* d3W{2, 2,
3} - X .* d4W{2, 2, 3, 3});
+d4X{2, 3, 3, 3} = one_div_W .* (d4P{2, 3, 3, 3} - 3 * d3X{2, 3, 3} .* dW{3} -
d3X{3, 3, 3} .* dW{2} - 3 * d2X{2, 3} .* d2W{3, 3} - 3 * d2X{3, 3} .* d2W{2, 3}
- dX{2} .* d3W{3, 3, 3} - 3 * dX{3} .* d3W{2, 3, 3} - X .* d4W{2, 3, 3, 3});
+d4X{3, 3, 3, 3} = one_div_W .* (d4P{3, 3, 3, 3} - 4 * d3X{3, 3, 3} .* dW{3} -
6 * d2X{3, 3} .* d2W{3, 3} - 4 * dX{3} .* d3W{3, 3, 3} - X .* d4W{3, 3, 3, 3});
+
+d4X{2, 1, 1, 1} = d4X{1, 1, 1, 2};
+d4X{3, 1, 1, 1} = d4X{1, 1, 1, 3};
+d4X{1, 2, 1, 1} = d4X{1, 1, 1, 2};
+d4X{2, 2, 1, 1} = d4X{1, 1, 2, 2};
+d4X{3, 2, 1, 1} = d4X{1, 1, 2, 3};
+d4X{1, 3, 1, 1} = d4X{1, 1, 1, 3};
+d4X{2, 3, 1, 1} = d4X{1, 1, 2, 3};
+d4X{3, 3, 1, 1} = d4X{1, 1, 3, 3};
+d4X{1, 1, 2, 1} = d4X{1, 1, 1, 2};
+d4X{2, 1, 2, 1} = d4X{1, 1, 2, 2};
+d4X{3, 1, 2, 1} = d4X{1, 1, 2, 3};
+d4X{1, 2, 2, 1} = d4X{1, 1, 2, 2};
+d4X{2, 2, 2, 1} = d4X{1, 2, 2, 2};
+d4X{3, 2, 2, 1} = d4X{1, 2, 2, 3};
+d4X{1, 3, 2, 1} = d4X{1, 1, 2, 3};
+d4X{2, 3, 2, 1} = d4X{1, 2, 2, 3};
+d4X{3, 3, 2, 1} = d4X{1, 2, 3, 3};
+d4X{1, 1, 3, 1} = d4X{1, 1, 1, 3};
+d4X{2, 1, 3, 1} = d4X{1, 1, 2, 3};
+d4X{3, 1, 3, 1} = d4X{1, 1, 3, 3};
+d4X{1, 2, 3, 1} = d4X{1, 1, 2, 3};
+d4X{2, 2, 3, 1} = d4X{1, 2, 2, 3};
+d4X{3, 2, 3, 1} = d4X{1, 2, 3, 3};
+d4X{1, 3, 3, 1} = d4X{1, 1, 3, 3};
+d4X{2, 3, 3, 1} = d4X{1, 2, 3, 3};
+d4X{3, 3, 3, 1} = d4X{1, 3, 3, 3};
+d4X{2, 1, 1, 2} = d4X{1, 1, 2, 2};
+d4X{3, 1, 1, 2} = d4X{1, 1, 2, 3};
+d4X{1, 2, 1, 2} = d4X{1, 1, 2, 2};
+d4X{2, 2, 1, 2} = d4X{1, 2, 2, 2};
+d4X{3, 2, 1, 2} = d4X{1, 2, 2, 3};
+d4X{1, 3, 1, 2} = d4X{1, 1, 2, 3};
+d4X{2, 3, 1, 2} = d4X{1, 2, 2, 3};
+d4X{3, 3, 1, 2} = d4X{1, 2, 3, 3};
+d4X{2, 1, 2, 2} = d4X{1, 2, 2, 2};
+d4X{3, 1, 2, 2} = d4X{1, 2, 2, 3};
+d4X{3, 2, 2, 2} = d4X{2, 2, 2, 3};
+d4X{1, 3, 2, 2} = d4X{1, 2, 2, 3};
+d4X{2, 3, 2, 2} = d4X{2, 2, 2, 3};
+d4X{3, 3, 2, 2} = d4X{2, 2, 3, 3};
+d4X{1, 1, 3, 2} = d4X{1, 1, 2, 3};
+d4X{2, 1, 3, 2} = d4X{1, 2, 2, 3};
+d4X{3, 1, 3, 2} = d4X{1, 2, 3, 3};
+d4X{1, 2, 3, 2} = d4X{1, 2, 2, 3};
+d4X{2, 2, 3, 2} = d4X{2, 2, 2, 3};
+d4X{3, 2, 3, 2} = d4X{2, 2, 3, 3};
+d4X{1, 3, 3, 2} = d4X{1, 2, 3, 3};
+d4X{2, 3, 3, 2} = d4X{2, 2, 3, 3};
+d4X{3, 3, 3, 2} = d4X{2, 3, 3, 3};
+d4X{2, 1, 1, 3} = d4X{1, 1, 2, 3};
+d4X{3, 1, 1, 3} = d4X{1, 1, 3, 3};
+d4X{1, 2, 1, 3} = d4X{1, 1, 2, 3};
+d4X{2, 2, 1, 3} = d4X{1, 2, 2, 3};
+d4X{3, 2, 1, 3} = d4X{1, 2, 3, 3};
+d4X{1, 3, 1, 3} = d4X{1, 1, 3, 3};
+d4X{2, 3, 1, 3} = d4X{1, 2, 3, 3};
+d4X{3, 3, 1, 3} = d4X{1, 3, 3, 3};
+d4X{2, 1, 2, 3} = d4X{1, 2, 2, 3};
+d4X{3, 1, 2, 3} = d4X{1, 2, 3, 3};
+d4X{3, 2, 2, 3} = d4X{2, 2, 3, 3};
+d4X{1, 3, 2, 3} = d4X{1, 2, 3, 3};
+d4X{2, 3, 2, 3} = d4X{2, 2, 3, 3};
+d4X{3, 3, 2, 3} = d4X{2, 3, 3, 3};
+d4X{2, 1, 3, 3} = d4X{1, 2, 3, 3};
+d4X{3, 1, 3, 3} = d4X{1, 3, 3, 3};
+d4X{3, 2, 3, 3} = d4X{2, 3, 3, 3};
+
+
+end
+
+function rational = is_rational(nurbs)
+if (size(nurbs.coefs, 1) < 4)
+ rational = false;
+else
+ tolerance = 1.0e-15;
+ rational = any(abs(nurbs.coefs(4, :) - 1) > tolerance);
+end
end
%!demo
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/inst/nrbinverse.m
new/nurbs-1.4.4/inst/nrbinverse.m
--- old/nurbs-1.4.3/inst/nrbinverse.m 2021-03-29 12:11:45.795919320 +0200
+++ new/nurbs-1.4.4/inst/nrbinverse.m 2025-02-10 14:35:08.000000000 +0100
@@ -59,7 +59,7 @@
% Default options
options = struct ('u0' , .5*ones (ndim, 1), ...
'MaxIter' , 10, ...
- 'Display' , true, ...
+ 'Display' , false, ...
'TolX', 1e-8, ...
'TolFun', 1e-8);
@@ -85,8 +85,9 @@
x = x(:);
% Define functions for Newton iteration
+ ders = nrbderiv (nrb);
f = @(U) nrbeval (nrb, num2cell (U)) - x;
- jac = @(U) nrbjacobian (nrb, num2cell (U));
+ jac = @(U) nrbjacobian (nrb, ders, num2cell (U));
% Newton cycle
u_old = options.u0(:);
@@ -128,9 +129,9 @@
end
-function jac = nrbjacobian (nrb, u)
+function jac = nrbjacobian (nrb, ders, u)
- ders = nrbderiv (nrb);
+% ders = nrbderiv (nrb);
[~, jac] = nrbdeval (nrb, ders, u);
jac = [jac{:}];
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/inst/nrbmeasure.m
new/nurbs-1.4.4/inst/nrbmeasure.m
--- old/nurbs-1.4.3/inst/nrbmeasure.m 2021-03-29 12:11:45.795919320 +0200
+++ new/nurbs-1.4.4/inst/nrbmeasure.m 2025-02-10 14:35:08.000000000 +0100
@@ -84,9 +84,9 @@
function l = len (u, nrb, ders)
[~, d] = nrbdeval (nrb, ders, u);
- f = d(1, :);
- g = d(2, :);
- h = d(3, :);
+ f = d{1}(1, :);
+ g = d{1}(2, :);
+ h = d{1}(3, :);
l = sqrt (f.^2 + g.^2 + h.^2);
end
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/src/low_level_functions.cc
new/nurbs-1.4.4/src/low_level_functions.cc
--- old/nurbs-1.4.3/src/low_level_functions.cc 2021-03-29 12:11:45.811919565
+0200
+++ new/nurbs-1.4.4/src/low_level_functions.cc 2025-02-10 14:35:08.000000000
+0100
@@ -17,6 +17,8 @@
*/
+#include <cassert>
+
#include <octave/oct.h>
#include "low_level_functions.h"
#include <iostream>
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/src/nrbsurfderiveval.cc
new/nurbs-1.4.4/src/nrbsurfderiveval.cc
--- old/nurbs-1.4.3/src/nrbsurfderiveval.cc 2021-03-29 12:11:45.815919627
+0200
+++ new/nurbs-1.4.4/src/nrbsurfderiveval.cc 2025-02-10 14:35:08.000000000
+0100
@@ -14,6 +14,7 @@
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
+#include <cassert>
#include <iostream>
#include <octave/oct.h>
#include <octave/oct-map.h>
diff -urN '--exclude=CVS' '--exclude=.cvsignore' '--exclude=.svn'
'--exclude=.svnignore' old/nurbs-1.4.3/src/tbasisfun.cc
new/nurbs-1.4.4/src/tbasisfun.cc
--- old/nurbs-1.4.3/src/tbasisfun.cc 2021-03-29 12:11:45.815919627 +0200
+++ new/nurbs-1.4.4/src/tbasisfun.cc 2025-02-10 14:35:08.000000000 +0100
@@ -15,6 +15,8 @@
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
+#include <cassert>
+
#include <octave/oct.h>
#include <iostream>
