[Code] How do you compute weighted vertex normals?

[thomthom]

Reference:
http://www.bytehazard.com/code/vertnorm.html
http://meshlabstuff.blogspot.com/2009/0 ... rmals.html

How can you compute weighted vertex normals for vertices in SketchUp?

Vertex Normal.png

Compute vertex normals so these two boxes produces similar normals.
Adding up all connected face normals results in a normal that lean towards the triangulated side - which not what I want.

---

Current Solution
The current solution that appear to yield the best results:

Code: Select all


  def self.vertex_normal( vertex )
    faces = vertex.faces
    edges = vertex.edges
    point = vertex.position
    normal = Geom::Vector3d.new( 0, 0, 0 )
    until faces.empty?
      face = faces.shift
      e1, e2 = face.edges & edges
      # Ensure the vectors are in the order of the loop.
      test_vertex = e1.reversed_in?( face ) ? e1.start : e1.end
      if test_vertex == vertex
        e1, e2 = [ e2, e1 ]
      end
      # Now the full angle can be calculated.
      pt1 = e1.other_vertex( vertex ).position
      pt2 = e2.other_vertex( vertex ).position
      v1 = point.vector_to( pt1 )
      v2 = point.vector_to( pt2 )
      angle = self.full_angle_between( v1, v2, face.normal )
      face_normal = face.normal
      face_normal.length = angle
      normal += face_normal
    end
    normal.normalize!
  end
  
  def self.full_angle_between( vector1, vector2, normal )
    cross = vector1 * vector2
    direction = cross % normal
    angle = vector1.angle_between( vector2 )
    angle = 360.degrees - angle if direction > 0.0
    angle
  end


[TIG]

Perhaps something like
faces = vertex.faces
return nil if not faces[0]
norm = faces[0].normal
faces.shift
faces.each{|face| norm = norm + face.normal }
return norm
???
EDIT: Fixed typo * >>> + TIG.

[thomthom]

That's the naive version I used. But it doesn't always produce the normal one want. The linked articles describe the issues that method has, and further explains one has to weigh the contribution of the faces.

[TIG]

Well then try perhaps 'weight' by each face's surface area...
faces = vertex.faces
return nil if not faces[0]
norm = faces[0].normal
norm.length = faces[0].area
faces.shift
faces.each{|face|
fnor = face.normal
fnor.length = face.area
norm = norm + fnor
}
norm.normalize!
return norm
OR get relative angles between the normals and make adjustments ???
EDIT: typo fixed * >>> + TIG.

[thomthom]

That snippet gave me zero length vectors for a vertex with three connected faces at an corner.

[Chris Fullmer]

Wouldn't it have something to do with the angle between the 2 edges of the face at that vertex * that face's normal. Something so that a small sliver of a face - only 5 degrees for example, would get its normal * 5. Then a face with 90 degrees would get its normal weight * 90. Then combine all those normals, and the vector will be greater than 1, so normalize it to scale it back down.

Would that give an appropriate weight to each face in the overall vertex normal?

[thomthom]

Wouldn't it have something to do with the angle between the 2 edges of the face at that vertex * that face's normal. Something so that a small sliver of a face - only 5 degrees for example, would get its normal * 5. Then a face with 90 degrees would get its normal weight * 90. Then combine all those normals, and the vector will be greater than 1, so normalize it to scale it back down.

Would that give an appropriate weight to each face in the overall vertex normal?

What you describe is one of the methods in the links in my OP. The problem is that I don't fully understand how to implement the weighting...

[thomthom]

This appear to work:

Code: Select all


def self.vertex_normal( vertex )
    faces = vertex.faces
    edges = vertex.edges
    point = vertex.position
    return nil if faces.empty?
    normal = Geom::Vector3d.new( 0, 0, 0 )
    until faces.empty?
      face = faces.shift
      e1, e2 = face.edges & edges
      pt1 = e1.other_vertex( vertex ).position
      pt2 = e2.other_vertex( vertex ).position
      v1 = point.vector_to( pt1 )
      v2 = point.vector_to( pt2 )
      angle = v1.angle_between( v2 )
      face_normal = face.normal
      face_normal.length = angle
      normal += face_normal
    end
    normal.normalize!
  end


[thomthom]

Though, the linked article seem to also take into account the face area... wonder what importance that has...

[thomthom]

hmm... it must be flawed. if a face is connected to the vertex then vector1.angle_between( vector2 ) won't give the correct angle, as it only return angles between 0 - 180 degrees. Either I need to deal with each triangle in each face, or I calculate the full angle.

[TIG]

Stupid typo is my code should be norm + fnor not '*'... I've corrected the original - it should now work as expected - weighting vertex-normals dependent on the face's areas!

[thomthom]

This seem to account for wide angle corners:

Code: Select all


  def self.vertex_normal( vertex )
    faces = vertex.faces
    edges = vertex.edges
    point = vertex.position
    normal = Geom::Vector3d.new( 0, 0, 0 )
    until faces.empty?
      face = faces.shift
      e1, e2 = face.edges & edges
      pt1 = e1.other_vertex( vertex ).position
      pt2 = e2.other_vertex( vertex ).position
      v1 = point.vector_to( pt1 )
      v2 = point.vector_to( pt2 )
      angle = self.full_angle_between( v1, v2, face.normal )
      face_normal = face.normal
      face_normal.length = angle
      normal += face_normal
    end
    normal.normalize!
  end
  
  def self.full_angle_between( vector1, vector2, normal )
    cross = vector1 * vector2
    direction = cross % normal
    angle = vector1.angle_between( vector2 )
    angle = 360.degrees - angle if direction > 0.0
    angle
  end


[thomthom]

Stupid typo is my code should be norm + fnorm not '*'... I've corrected the original - it should now work as expected !!!!

I'll revisit your code again. http://www.bytehazard.com/code/vertnorm.html mentions that using the area still makes some faces weigh too much, but that it's not that notable. But since it looks to require less computing that checking the angles then it might be preferable.

[thomthom]

hm... I added face area to the equations, but that yielded deviating normals depending how I divided the large face.
removing the face area appear to yield the exact same result.

VertexNormals.png

Weighted by angle:

1. Vector3d(0.419345, 0.0772543, 0.904534)
2. Vector3d(0.419345, 0.0772543, 0.904534)
3. Vector3d(0.419345, 0.0772543, 0.904534)

Weighted by area * angle:

1. Vector3d(0.324298, 0.116468, 0.938758)
2. Vector3d(0.706956, 0.253896, 0.660114)
3. Vector3d(0.770689, 0.276785, 0.573959)

[thomthom]

I wonder if the linked article uses the face area because they computer the normals for lighting...

[TIG]

Several coplanar faces at a vertex are the same as one face of the same area as the bits? So the both area-weight-adjusted vertex-normals will be the same.
I think it is more for lighting...

[thomthom]

Several coplanar faces at a vertex are the same as one face of the same area as the bits? So the both area-weight-adjusted vertex-normals will be the same.

But if a vertex is connected to three sides, one large and two small, then using the area would make the normal lean toward the large area, would it not?

[TIG]

Not if the two small areas were equivalent to the large one... then it'd be 'balanced'...
The large area pulls it over then the 1st small are pulls it back and then the 2nd small area pulls it back again.
IF there's a large and a small area the large one 'wins'.

[voljanko]

By computer you mean compute?

[TIG]

By computer you mean compute?

A simple typo by tt in the original title - but we understood what he meant...

[voljanko]

I'm trying to follow your conversation,but not sure to understand what are you trying to do.
Do you want to align faces that are nearly aligned?

[thomthom]

Not if the two small areas were equivalent to the large one... then it'd be 'balanced'...
The large area pulls it over then the 1st small are pulls it back and then the 2nd small area pulls it back again.
IF there's a large and a small area the large one 'wins'.

Yes, but when they are not, which would be in any non-regular mesh. So I still wonder why one would use area to weigh the normals.

[thomthom]

By computer you mean compute?

A simple typo by tt in the original title - but we understood what he meant...

Fixed!

[thomthom]

I'm trying to follow your conversation,but not sure to understand what are you trying to do.
Do you want to align faces that are nearly aligned?

No, I just want to compute the vertex normals.
In this particular case I need it to be able to calculate some of the topographical characteristic of the mesh.

[thomthom]

My full_angle_between code seem to not work in all scenarios... back to the drawing table...

[thomthom]

Now I seemed to have corrected it. I had to ensure the vectors I used came in the same direction as the edge loop.