Is there one way to make the normals of one mesh consistent?

Question

Recently I get a triangle mesh, but the normal directions of triangles on the mesh is not consistent. Is there any algorithm to convert the normals consistent? From one book，it says "Usually the orientation of the normals is propagated along a minimum spanning tree between neighboring patches either in a preprocessing step or implicitly during traversal of the input [Hoppe et al. 92].

Does it mean that making the normals consistent is not easy?

Regards Jogging

Answer 1

It is not easy business indeed. There are numerous papers on the subject. The original paper from which it all began is this:

H. Hoppe, T. DeRose, T. Duchamp, J. McDonald and W. Stuetzle, "Suface reconstruction from unorganized points," in SIGGRAPH, 1992. The method itself is realized in VCG (Meshlab) and PCL libraries.

One of the more recent papers: J. Liu, J. Cao, X. Liu, J. Wang, X. Wang and X. Shi, "Mendable consistent orientation of point clouds," Computer-Aided Design, vol. 55, pp. 26-36, 2014 http://jjcao.weebly.com/uploads/4/5/3/4/4534726/cad14.pdf

The authors of the paper provide a Matlab code: http://jjcao-orientation.googlecode.com/svn/trunk/Code/ The code is much slower than the original Hoppe algorithm but gives much nicer results, especially in hard cases when the mesh contains sharp corners and non-smooth edges.

Also, a good review of general ideas is this one: http://vmv09.tu-bs.de/downloads/papers/koe09.pdf

If you know that the point cloud was obtained from a particular point (say, from a Kinect or a laser scanner), you can make the direction of the normals to be consistent with the viewpoint by flipping them if needed. But if you deal with a model of an entire object which, then some normal propagation algorithm is required.