Surface ops

matlab/@surfer/lap_n_op.m

@@ -0,0 +1,18 @@
+function lapn = lap_n_op(obj)
+%  lapn = shape_op(S,p)
+%     This subroutine evaluates the surface Laplacian of the surface normal
+%     vector
+%
+%  Input arguments:
+%    * obj: surfer object
+%
+%  Output arguments:
+%    * lapn: double (3,S.npts) 
+%
+    n = obj.n;
+    [lapnx] = get_surface_laplacian(obj,n(1,:));
+    [lapny] = get_surface_laplacian(obj,n(2,:));
+    [lapnz] = get_surface_laplacian(obj,n(3,:));
+
+    lapn = [lapnx;lapny;lapnz];
+end

matlab/@surfer/shape_op.m

@@ -0,0 +1,38 @@
+function shape = shape_op(obj)
+%  shape = shape_op(S)
+%     This subroutine evaluates the shape operator of a surface in
+%     cartesian coordinates.
+%
+%     The shape operator is defined to be surface gradient of the surface
+%     normal.
+%
+%  Input arguments:
+%    * obj: surfer object
+%
+%  Output arguments:
+%    * shape: double (3,3,S.npts) 
+%
+    ffrm2 = cell2mat(obj.sfform);
+    ffrm2 = reshape(ffrm2, 2, obj.npatches, 2,[]); 
+    ffrm2 = permute(ffrm2,[1,3,4,2]); ffrm2= ffrm2(:,:,:);
+
+    iffrm = cell2mat(obj.ffforminv);
+    iffrm = reshape(iffrm,  2, obj.npatches, 2,[]);
+    iffrm = permute(iffrm,[1,3,4,2]); iffrm= iffrm(:,:,:);
+
+    shape_red = pagemtimes(iffrm,ffrm2);
+    shape_red = pagemtimes(shape_red,iffrm);
+
+    du = obj.du;
+    dv = obj.dv;
+
+    X = zeros(3,2,obj.npts);
+    XT= zeros(2,3,obj.npts);
+
+    X(:,1,:) = du;
+    X(:,2,:) = dv;
+    XT(1,:,:) = du;
+    XT(2,:,:) = dv;
+
+    shape = pagemtimes(pagemtimes(X,shape_red),XT);
+end

matlab/@surfer/surfer.m

@@ -92,6 +92,7 @@
         mean_curv     % mean curvatures at nodes (npts*1)
         ffform        % cell array of first fundamental forms at nodes (2,2,npts)
         ffforminv     % cell array of inverses of ffforms at nodes (2,2,npts)
+        sfform        % cell array of second fundamental forms at nodes (2,2,npts)
         aspect_ratio  % measure of local aspect ratio of patch, (npts,1);
         patch_distortion % integral of aspect ratio
         cms           % centroid location of patches (3,npatches)
@@ -223,6 +224,7 @@
             obj.mean_curv = zeros(obj.npts,1);
             obj.ffforminv = cell(npatches,1);
             obj.ffform = cell(npatches,1);
+            obj.sfform = cell(npatches,1);
             obj.aspect_ratio = zeros(obj.npts,1);
             obj.patch_distortion = zeros(obj.npatches,1);
             obj.cms = zeros(3,obj.npatches);
@@ -282,6 +284,7 @@
                 sfform(2,1,iind) = M;
                 sfform(2,2,iind) = N;
 
+                obj.sfform{i} = sfform(:,:,iind);
                 % Mean curvature (LG-2MF+NE)/2(EG-F^2):
                 obj.mean_curv(iind) = -0.5*(L.*dvnormsq - ...
                                        2*M.*duv + dunormsq.*N).*ddinv;

matlab/src/get_oversampling_parameters.m

@@ -1,4 +1,4 @@
-function [novers, varargout] = get_oversampling_parameters(S, Q, eps)
+function [novers,varargout] = get_oversampling_parameters(S,Q,eps)
 %
 %  get_oversampling_parameters
 %     subroutine to estimate the oversampling paramters for a given