--- /dev/null
+function skl = nrbsurfderiveval (srf, uv, d)
+
+%
+% 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.
+
+% 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/>.
+
+ skl = zeros (3, d+1, d+1, size (uv, 2));
+
+ for iu = 1:size(uv, 2);
+ wders = squeeze (surfderiveval (srf.number(1)-1, srf.order(1)-1, ...
+ srf.knots{1}, srf.number(2)-1, ...
+ srf.order(2)-1, srf.knots{2}, ...
+ squeeze (srf.coefs(4, :, :)), uv(1,iu), ...
+ uv(2,iu), d));
+
+ for idim = 1:3
+ Aders = squeeze (surfderiveval (srf.number(1)-1, srf.order(1)-1, ...
+ srf.knots{1}, srf.number(2)-1, ...
+ srf.order(2)-1, srf.knots{2}, ...
+ squeeze (srf.coefs(idim, :, :)), uv(1,iu),...
+ uv(2,iu), d));
+
+ for k=0:d
+ for l=0:d-k
+ v = Aders(k+1, l+1);
+ for j=1:l
+ v = v - nchoosek(l,j)*wders(1,j+1)*skl(idim, k+1, l-j+1,iu);
+ end
+ for i=1:k
+ v = v - nchoosek(k,i)*wders(i+1,1)*skl(idim, k-i+1, l+1, iu);
+ v2 =0;
+ for j=1:l
+ v2 = v2 + nchoosek(l,j)*wders(i+1,j+1)*skl(idim, k-i+1, l-j+1, iu);
+ end
+ v = v - nchoosek(k,i)*v2;
+ end
+ skl(idim, k+1, l+1, iu) = v/wders(1,1);
+ end
+ end
+ end
+
+ end
+
+end
+
+%!test
+%! k = [0 0 1 1];
+%! c = [0 1];
+%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
+%! coef(3,:,:) = coef(1,:,:);
+%! srf = nrbmak (coef, {k, k});
+%! [u, v] = meshgrid (linspace(0,1,11));
+%! uv = [u(:)';v(:)'];
+%! skl = nrbsurfderiveval (srf, uv, 0);
+%! aux = nrbeval(srf,uv);
+%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
+
+
+%!test
+%! k = [0 0 1 1];
+%! c = [0 1];
+%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
+%! coef(3,:,:) = coef(1,:,:);
+%! srf = nrbmak (coef, {k, k});
+%! srf = nrbkntins (srf, {[], rand(2,1)});
+%! [u, v] = meshgrid (linspace(0,1,11));
+%! uv = [u(:)';v(:)'];
+%! skl = nrbsurfderiveval (srf, uv, 0);
+%! aux = nrbeval(srf,uv);
+%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
+
+%!shared srf, uv
+%!test
+%! k = [0 0 0 1 1 1];
+%! c = [0 1/2 1];
+%! [coef(1,:,:), coef(2,:,:)] = meshgrid (c, c);
+%! coef(3,:,:) = coef(1,:,:);
+%! srf = nrbmak (coef, {k, k});
+%! ders= nrbderiv (srf);
+%! [u, v] = meshgrid (linspace(0,1,11));
+%! uv = [u(:)';v(:)'];
+%! skl = nrbsurfderiveval (srf, uv, 1);
+%! [fun, der] = nrbdeval (srf, ders, uv);
+%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
+%!
+%!test
+%! srf = nrbdegelev (srf, [3, 1]);
+%! ders= nrbderiv (srf);
+%! [fun, der] = nrbdeval (srf, ders, uv);
+%! skl = nrbsurfderiveval (srf, uv, 1);
+%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
+
+%!shared uv
+%!test
+%! k = [0 0 0 1 1 1];
+%! c = [0 1/2 1];
+%! [coef(2,:,:), coef(1,:,:)] = meshgrid (c, c);
+%! coef(3,:,:) = coef(1,:,:);
+%! srf = nrbmak (coef, {k, k});
+%! ders= nrbderiv (srf);
+%! [u, v] = meshgrid (linspace(0,1,11));
+%! uv = [u(:)';v(:)'];
+%! skl = nrbsurfderiveval (srf, uv, 1);
+%! [fun, der] = nrbdeval (srf, ders, uv);
+%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
+%!
+%!test
+%! p = 3; q = 3;
+%! mcp = 5; ncp = 5;
+%! Lx = 10*rand(1); Ly = Lx;
+%! srf = nrbdegelev (nrb4surf ([0 0], [Lx, 0], [0 Ly], [Lx Ly]), [p-1, q-1]);
+%! %%srf = nrbkntins (srf, {linspace(0,1,mcp-p+2)(2:end-1), linspace(0,1,ncp-q+2)(2:end-1)});
+%! %%srf.coefs = permute (srf.coefs, [1 3 2]);
+%! ders= nrbderiv (srf);
+%! [fun, der] = nrbdeval (srf, ders, uv);
+%! skl = nrbsurfderiveval (srf, uv, 1);
+%! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
+%! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
+
+%!shared srf, uv, P, dPdx, d2Pdx2, c1, c2
+%!test
+%! [u, v] = meshgrid (linspace(0,1,10));
+%! uv = [u(:)';v(:)'];
+%! c1 = nrbmak([0 1/2 1; 0 1 0],[0 0 0 1 1 1]);
+%! c1 = nrbtform (c1, vecrotx (pi/2));
+%! c2 = nrbtform(c1, vectrans([0 1 0]));
+%! srf = nrbdegelev (nrbruled (c1, c2), [3, 1]);
+%! skl = nrbsurfderiveval (srf, uv, 2);
+%! P = squeeze(skl(:,1,1,:));
+%! dPdx = squeeze(skl(:,2,1,:));
+%! d2Pdx2 = squeeze(skl(:,3,1,:));
+%!assert(P(3,:), 2*(P(1,:)-P(1,:).^2),100*eps)
+%!assert(dPdx(3,:), 2-4*P(1,:), 100*eps)
+%!assert(d2Pdx2(3,:), -4+0*P(1,:), 100*eps)
+%! srf = nrbdegelev (nrbruled (c1, c2), [5, 6]);
+%! skl = nrbsurfderiveval (srf, uv, 2);
+%! P = squeeze(skl(:,1,1,:));
+%! dPdx = squeeze(skl(:,2,1,:));
+%! d2Pdx2 = squeeze(skl(:,3,1,:));
+%! aux = nrbeval(srf,uv);
+%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
+%!assert(P(3,:), 2*(P(1,:)-P(1,:).^2),100*eps)
+%!assert(dPdx(3,:), 2-4*P(1,:), 100*eps)
+%!assert(d2Pdx2(3,:), -4+0*P(1,:), 100*eps)
+%!
+%!test
+%! skl = nrbsurfderiveval (srf, uv, 0);
+%! aux = nrbeval (srf, uv);
+%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
+
+%!shared dPdu, d2Pdu2, P, srf, uv
+%!test
+%! [u, v] = meshgrid (linspace(0,1,10));
+%! uv = [u(:)';v(:)'];
+%! c1 = nrbmak([0 1/2 1; 0.1 1.6 1.1; 0 0 0],[0 0 0 1 1 1]);
+%! c2 = nrbmak([0 1/2 1; 0.1 1.6 1.1; 1 1 1],[0 0 0 1 1 1]);
+%! srf = nrbdegelev (nrbruled (c1, c2), [0, 1]);
+%! skl = nrbsurfderiveval (srf, uv, 2);
+%! P = squeeze(skl(:,1,1,:));
+%! dPdu = squeeze(skl(:,2,1,:));
+%! dPdv = squeeze(skl(:,1,2,:));
+%! d2Pdu2 = squeeze(skl(:,3,1,:));
+%! aux = nrbeval(srf,uv);
+%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
+%!assert(dPdu(2,:), 3-4*P(1,:),100*eps)
+%!assert(d2Pdu2(2,:), -4+0*P(1,:),100*eps)
+%!
+%!test
+%! skl = nrbsurfderiveval (srf, uv, 0);
+%! aux = nrbeval(srf,uv);
+%! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
+
+%!test
+%! srf = nrb4surf([0 0], [1 0], [0 1], [1 1]);
+%! geo = nrbdegelev (srf, [3 3]);
+%1 geo.coefs (4, 2:end-1, 2:end-1) = geo.coefs (4, 2:end-1, 2:end-1) + .1 * rand (1, geo.number(1)-2, geo.number(2)-2);
+%! geo = nrbkntins (geo, {[.1:.1:.9], [.2:.2:.8]});
+%! [u, v] = meshgrid (linspace(0,1,10));
+%! uv = [u(:)';v(:)'];
+%! skl = nrbsurfderiveval (geo, uv, 2);
+%! dgeo = nrbderiv (geo);
+%! [pnts, ders] = nrbdeval (geo, dgeo, uv);
+%! assert (ders{1}, squeeze(skl(:,2,1,:)), 1e-9)
+%! assert (ders{2}, squeeze(skl(:,1,2,:)), 1e-9)
+
+%!test
+%! crv = nrbline ([1 0], [2 0]);
+%! srf = nrbrevolve (crv, [0 0 0], [0 0 1], pi/2);
+%! srf = nrbtransp (srf);
+%! [v, u] = meshgrid (linspace (0, 1, 11));
+%! uv = [u(:)'; v(:)'];
+%! skl = nrbsurfderiveval (srf, uv, 2);
+%! c = sqrt(2);
+%! w = @(x, y) (2 - c)*y.^2 + (c-2)*y + 1;
+%! dwdy = @(x, y) 2*(2-c)*y + c - 2;
+%! d2wdy2 = @(x, y) 2*(2-c);
+%! F1 = @(x, y) (x+1) .* ((1-y).^2 + c*y.*(1-y)) ./ w(x,y);
+%! F2 = @(x, y) (x+1) .* (y.^2 + c*y.*(1-y)) ./ w(x,y);
+%! dF1dx = @(x, y) ((1-y).^2 + c*y.*(1-y)) ./ w(x,y);
+%! dF2dx = @(x, y) (y.^2 + c*y.*(1-y)) ./ w(x,y);
+%! dF1dy = @(x, y) (x+1) .* ((2 - 2*c)*y + c - 2) ./ w(x,y) - (x+1) .* ((1-y).^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
+%! dF2dy = @(x, y) (x+1) .* ((2 - 2*c)*y + c) ./ w(x,y) - (x+1) .* (y.^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
+%! d2F1dx2 = @(x, y) zeros (size (x));
+%! d2F2dx2 = @(x, y) zeros (size (x));
+%! d2F1dxdy = @(x, y) ((2 - 2*c)*y + c - 2) ./ w(x,y) - ((1-y).^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
+%! d2F2dxdy = @(x, y) ((2 - 2*c)*y + c) ./ w(x,y) - (y.^2 + c*y.*(1-y)) .* dwdy(x,y) ./ w(x,y).^2;
+%! d2F1dy2 = @(x, y) (x+1)*(2 - 2*c) ./ w(x,y) - 2*(x+1) .* ((2 - 2*c)*y + c - 2) .* dwdy(x,y) ./ w(x,y).^2 - ...
+%! (x+1) .* ((1-y).^2 + c*y.*(1-y)) * d2wdy2(x,y) ./ w(x,y).^2 + ...
+%! 2 * (x+1) .* ((1-y).^2 + c*y.*(1-y)) .* w(x,y) .*dwdy(x,y).^2 ./ w(x,y).^4;
+%! d2F2dy2 = @(x, y) (x+1)*(2 - 2*c) ./ w(x,y) - 2*(x+1) .* ((2 - 2*c)*y + c) .* dwdy(x,y) ./ w(x,y).^2 - ...
+%! (x+1) .* (y.^2 + c*y.*(1-y)) * d2wdy2(x,y) ./ w(x,y).^2 + ...
+%! 2 * (x+1) .* (y.^2 + c*y.*(1-y)) .* w(x,y) .*dwdy(x,y).^2 ./ w(x,y).^4;
+%! assert ([F1(u(:),v(:)), F2(u(:),v(:))], squeeze(skl(1:2,1,1,:))', 1e2*eps);
+%! assert ([dF1dx(u(:),v(:)), dF2dx(u(:),v(:))], squeeze(skl(1:2,2,1,:))', 1e2*eps);
+%! assert ([dF1dy(u(:),v(:)), dF2dy(u(:),v(:))], squeeze(skl(1:2,1,2,:))', 1e2*eps);
+%! assert ([d2F1dx2(u(:),v(:)), d2F2dx2(u(:),v(:))], squeeze(skl(1:2,3,1,:))', 1e2*eps);
+%! assert ([d2F1dxdy(u(:),v(:)), d2F2dxdy(u(:),v(:))], squeeze(skl(1:2,2,2,:))', 1e2*eps);
+%! assert ([d2F1dy2(u(:),v(:)), d2F2dy2(u(:),v(:))], squeeze(skl(1:2,1,3,:))', 1e2*eps);
+
+%!test
+%! knots = {[0 0 1 1] [0 0 1 1]};
+%! coefs(:,1,1) = [0;0;0;1];
+%! coefs(:,2,1) = [1;0;0;1];
+%! coefs(:,1,2) = [0;1;0;1];
+%! coefs(:,2,2) = [1;1;1;2];
+%! srf = nrbmak (coefs, knots);
+%! [v, u] = meshgrid (linspace (0, 1, 3));
+%! uv = [u(:)'; v(:)'];
+%! skl = nrbsurfderiveval (srf, uv, 2);
+%! w = @(x, y) x.*y + 1;
+%! F1 = @(x, y) x ./ w(x,y);
+%! F2 = @(x, y) y ./ w(x,y);
+%! F3 = @(x, y) x .* y ./ w(x,y);
+%! dF1dx = @(x, y) 1./w(x,y) - x.*y./w(x,y).^2;
+%! dF1dy = @(x, y) - x.^2./w(x,y).^2;
+%! dF2dx = @(x, y) - y.^2./w(x,y).^2;
+%! dF2dy = @(x, y) 1./w(x,y) - x.*y./w(x,y).^2;
+%! dF3dx = @(x, y) y./w(x,y) - x.*(y./w(x,y)).^2;
+%! dF3dy = @(x, y) x./w(x,y) - y.*(x./w(x,y)).^2;
+%! d2F1dx2 = @(x, y) -2*y./w(x,y).^2 + 2*x.*y.^2./w(x,y).^3;
+%! d2F1dy2 = @(x, y) 2*x.^3./w(x,y).^3;
+%! d2F1dxdy = @(x, y) -x./w(x,y).^2 - x./w(x,y).^2 + 2*x.^2.*y./w(x,y).^3;
+%! d2F2dx2 = @(x, y) 2*y.^3./w(x,y).^3;
+%! d2F2dy2 = @(x, y) -2*x./w(x,y).^2 + 2*y.*x.^2./w(x,y).^3;
+%! d2F2dxdy = @(x, y) -y./w(x,y).^2 - y./w(x,y).^2 + 2*y.^2.*x./w(x,y).^3;
+%! d2F3dx2 = @(x, y) -2*y.^2./w(x,y).^2 + 2*x.*y.^3./w(x,y).^3;
+%! d2F3dy2 = @(x, y) -2*x.^2./w(x,y).^2 + 2*y.*x.^3./w(x,y).^3;
+%! d2F3dxdy = @(x, y) 1./w(x,y) - 3*x.*y./w(x,y).^2 + 2*(x.*y).^2./w(x,y).^3;
+%! assert ([F1(u(:),v(:)), F2(u(:),v(:)), F3(u(:),v(:))], squeeze(skl(1:3,1,1,:))', 1e2*eps);
+%! assert ([dF1dx(u(:),v(:)), dF2dx(u(:),v(:)), dF3dx(u(:),v(:))], squeeze(skl(1:3,2,1,:))', 1e2*eps);
+%! assert ([dF1dy(u(:),v(:)), dF2dy(u(:),v(:)), dF3dy(u(:),v(:))], squeeze(skl(1:3,1,2,:))', 1e2*eps);
+%! assert ([d2F1dx2(u(:),v(:)), d2F2dx2(u(:),v(:)), d2F3dx2(u(:),v(:))], squeeze(skl(1:3,3,1,:))', 1e2*eps);
+%! assert ([d2F1dy2(u(:),v(:)), d2F2dy2(u(:),v(:)), d2F3dy2(u(:),v(:))], squeeze(skl(1:3,1,3,:))', 1e2*eps);
+%! assert ([d2F1dxdy(u(:),v(:)), d2F2dxdy(u(:),v(:)), d2F3dxdy(u(:),v(:))], squeeze(skl(1:3,2,2,:))', 1e2*eps);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff