nurbs-1.4.3/inst/nrbsurfderiveval.m

1 function skl = nrbsurfderiveval (srf, uv, d)
6 % usage: skl = nrbsurfderiveval (srf, [u; v], d)
20 %   skl (i, j, k, l) = i-th component derived j-1,k-1 times at the
40  skl = zeros (3, d+1, d+1, size (uv, 2));  variable
60 	    v = v - nchoosek(l,j)*wders(1,j+1)*skl(idim, k+1, l-j+1,iu);
63 	    v = v - nchoosek(k,i)*wders(i+1,1)*skl(idim, k-i+1, l+1, iu);
66 	      v2 = v2 + nchoosek(l,j)*wders(i+1,j+1)*skl(idim, k-i+1, l-j+1, iu);
70 	  skl(idim, k+1, l+1, iu) = v/wders(1,1);
87 %! skl = nrbsurfderiveval (srf, uv, 0);
89 %! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
101 %! skl = nrbsurfderiveval (srf, uv, 0);
103 %! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
115 %! skl = nrbsurfderiveval (srf, uv, 1);
117 %! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
118 %! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
119 %! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
125 %! skl = nrbsurfderiveval (srf, uv, 1);
126 %! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
127 %! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
128 %! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
140 %! skl = nrbsurfderiveval (srf, uv, 1);
142 %! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
143 %! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
144 %! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
155 %! skl = nrbsurfderiveval (srf, uv, 1);
156 %! assert (squeeze (skl (1:2,1,1,:)), fun(1:2,:), 1e3*eps)
157 %! assert (squeeze (skl (1:2,2,1,:)), der{1}(1:2,:), 1e3*eps)
158 %! assert (squeeze (skl (1:2,1,2,:)), der{2}(1:2,:), 1e3*eps)
168 %! skl = nrbsurfderiveval (srf, uv, 2);
169 %! P = squeeze(skl(:,1,1,:));
170 %! dPdx = squeeze(skl(:,2,1,:));
171 %! d2Pdx2 = squeeze(skl(:,3,1,:));
176 %! skl = nrbsurfderiveval (srf, uv, 2);
177 %! P = squeeze(skl(:,1,1,:));
178 %! dPdx = squeeze(skl(:,2,1,:));
179 %! d2Pdx2 = squeeze(skl(:,3,1,:));
181 %! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
187 %! skl = nrbsurfderiveval (srf, uv, 0);
189 %! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
198 %! skl = nrbsurfderiveval (srf, uv, 2);
199 %! P = squeeze(skl(:,1,1,:));
200 %! dPdu = squeeze(skl(:,2,1,:));
201 %! dPdv = squeeze(skl(:,1,2,:));
202 %! d2Pdu2 = squeeze(skl(:,3,1,:));
204 %! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
209 %! skl = nrbsurfderiveval (srf, uv, 0);
211 %! assert (squeeze (skl (1:2,1,1,:)), aux(1:2,:), 1e3*eps)
220 %! skl = nrbsurfderiveval (geo, uv, 2);
223 %! assert (ders{1}, squeeze(skl(:,2,1,:)), 1e-9)
224 %! assert (ders{2}, squeeze(skl(:,1,2,:)), 1e-9)
232 %! skl = nrbsurfderiveval (srf, uv, 2);
253 %! assert ([F1(u(:),v(:)), F2(u(:),v(:))], squeeze(skl(1:2,1,1,:))', 1e2*eps);
254 %! assert ([dF1dx(u(:),v(:)), dF2dx(u(:),v(:))], squeeze(skl(1:2,2,1,:))', 1e2*eps);
255 %! assert ([dF1dy(u(:),v(:)), dF2dy(u(:),v(:))], squeeze(skl(1:2,1,2,:))', 1e2*eps);
256 %! assert ([d2F1dx2(u(:),v(:)), d2F2dx2(u(:),v(:))], squeeze(skl(1:2,3,1,:))', 1e2*eps);
257 %! assert ([d2F1dxdy(u(:),v(:)), d2F2dxdy(u(:),v(:))], squeeze(skl(1:2,2,2,:))', 1e2*eps);
258 %! assert ([d2F1dy2(u(:),v(:)), d2F2dy2(u(:),v(:))], squeeze(skl(1:2,1,3,:))', 1e2*eps);
269 %! skl = nrbsurfderiveval (srf, uv, 2);
289 %! assert ([F1(u(:),v(:)), F2(u(:),v(:)), F3(u(:),v(:))], squeeze(skl(1:3,1,1,:))', 1e2*eps);
290 %! assert ([dF1dx(u(:),v(:)), dF2dx(u(:),v(:)), dF3dx(u(:),v(:))], squeeze(skl(1:3,2,1,:))', 1e2*ep…
291 %! assert ([dF1dy(u(:),v(:)), dF2dy(u(:),v(:)), dF3dy(u(:),v(:))], squeeze(skl(1:3,1,2,:))', 1e2*ep…
292 %! assert ([d2F1dx2(u(:),v(:)), d2F2dx2(u(:),v(:)), d2F3dx2(u(:),v(:))], squeeze(skl(1:3,3,1,:))', …
293 %! assert ([d2F1dy2(u(:),v(:)), d2F2dy2(u(:),v(:)), d2F3dy2(u(:),v(:))], squeeze(skl(1:3,1,3,:))', …
294 %! assert ([d2F1dxdy(u(:),v(:)), d2F2dxdy(u(:),v(:)), d2F3dxdy(u(:),v(:))], squeeze(skl(1:3,2,2,:))…