unifyMeshNormals

Aligns adjacent faces in a triangulated mesh surface or volume

UNIFYMESHNORMALS Aligns mesh normals to all point in a consistent direction.

F_OUT = UNIFYMESHNORMALS(F,V) takes an N-by-3 array of faces F, and
returns an equivalent set of faces F_OUT with all adjacent faces in F_OUT
pointing in a consistent direction. Vertices V are also required in "in"
or "out" face alignment is specified (see below).

FV_OUT = UNIFYMESHNORMALS(FV) instead take a structure array with field
"faces" (and "vertices"), returning that structure with adjacent faces
aligned consistently as above.

[F_OUT, FLIPPED] = UNIFYMESHNORMALS(...) also returns FLIPPED, an N-by-1
logical mask showing which faces in F/FV were flipped during unification.

[...] = UNIFYMESHNORMALS(...,'alignTo','in')
[...] = UNIFYMESHNORMALS(...,'alignTo','out')
[...] = UNIFYMESHNORMALS(...,'alignTo',FACE) allows the user to specify a
single trusted FACE number which will remain unflipped, and all other
faces will be aligned to it. FACE may also be the string 'in' or 'out'.
'in' will result in all faces aligned, with direction towards the center
of the object. 'out' will result in directions pointing outwards.

Example:
tmpvol = zeros(20,20,20); % Empty voxel volume
tmpvol(5:15,8:12,8:12) = 1; % Turn some voxels on
tmpvol(8:12,5:15,8:12) = 1;
tmpvol(8:12,8:12,5:15) = 1;
fv = isosurface(tmpvol, 0.99); % Create the patch object
% Display patch object normal directions
facets = fv.vertices';
facets = permute(reshape(facets(:,fv.faces'), 3, 3, []),[2 1 3]);
edgeVecs = facets([2 3 1],:,:) - facets(:,:,:);
allFacNorms = bsxfun(@times, edgeVecs(1,[2 3 1],:), edgeVecs(2,[3 1 2],:)) - ...
bsxfun(@times, edgeVecs(2,[2 3 1],:), edgeVecs(1,[3 1 2],:));
allFacNorms = bsxfun(@rdivide, allFacNorms, sqrt(sum(allFacNorms.^2,2)));
facNorms = num2cell(squeeze(allFacNorms)',1);
facCents = num2cell(squeeze(mean(facets,1))',1);
facEdgeSize = mean(reshape(sqrt(sum(edgeVecs.^2,2)),[],1,1));
figure
patch(fv,'FaceColor','g','FaceAlpha',0.2), hold on, quiver3(facCents{:},facNorms{:},facEdgeSize), view(3), axis image
title('All normals point IN')
% Turn over some random faces to point the wrong way
flippedFaces = rand(size(fv.faces,1),1)>0.75;
fv_turned = fv;
fv_turned.faces(flippedFaces,:) = fv_turned.faces(flippedFaces,[2 1 3]);
figure, patch(fv_turned,'FaceColor','flat','FaceVertexCData',double(flippedFaces))
colormap(summer), caxis([0 1]), view(3), axis image
% Fix them to all point the same way
[fv_fixed, fixedFaces] = unifyMeshNormals(fv_turned);
figure, patch(fv_fixed,'FaceColor','flat','FaceVertexCData',double(xor(flippedFaces,fixedFaces)))
colormap(summer), caxis([0 1]), view(3), axis image

See also SPLITFV, INPOLYHEDRON, STLWRITE