Concept

The idea is to reposition verticles so your mesh ends up nice and smooth. Of course there is already a function in Blender that does it, but that doesn’t take the actual “surface” of the mesh into account. So say you have a part of a perfect sphere selected, and you run the current internal function, it would flatten that selection, or even make it concave (hollow). That’s what we don’t want. In stead if you try to smooth a perfect sphere, it should not change anything. You can’t get smoother than a sphere!

See below here… that’s not nicely smoothed!

Smoothing the normal way

I’ll explain the concept in 2D. Lets say we want to smooth the position of vertex A and it’s connected to vertex B and C. Then we get the vertex normals for B and C. We then rotate those normal vectors 90 degrees towards A and make them half the length of the distance between that specific vert (B or C) and A. Once we have those, we find the points at the ends of those two vectors and place vert A at the midpoint between them.

But let me explain with a picture, which should help.

That’s just the basics

Of course there is a lot more that you can do with a script. Like looking further along the surface and using more normals. Also in 3d at times you have quads and you need to figure out what you want to do with the vert at the far end of the quad. Having non manifold meshes can be tricky too.

At least I hope this explains the idea a bit, and as ideas go…. it’s not too bad

Dolf

I’m working on some physics things for my swarm AI… tricky since I haven’t done any of this for ehm… 15 years or so.

Second law of Newton

F = m * a
a = F/m
m = F/a

F is force in newtons
m is mass in kilograms
a is acceleration in meters per second

This method can for instance be used to create effects like with the ma baker or ma self scripts;

Finding the angle between two faces in Blender

Now this isn’t really complicated.

Lets say you retrieve two faces from Blender’s python API that are connected by an edge.

Lets call them face1 and face2 and face1.no retrieves the face normal of face1.

Then we can simply do the following to find the angle:

myAngle = Mathutils.AngleBetweenVecs(face1.no, face2.no)

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myAngle = Mathutils.AngleBetweenVecs(face1.no, face2.no)

The result though is only an angle between 0 and 90 degrees, to find out if that is positive or negative continue reading below.

Finding out whether the angle between two faces is convex or concave

A lot of the time you also want to know whether the angle is concave or convex (positive or negative).

To get that we get the vector from the midpoint of face1 to the midpoint of face2.

The midpoint of a face is retrieved by getting face1.cent.

Then we get the dot product of the face normal of face1 and the vector we just retrieved.

In python that could be:

dotProduct = Mathutils.DotVecs(face1.no, (face2.cent - face1.cent))

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dotProduct = Mathutils.DotVecs(face1.no, (face2.cent - face1.cent))

The resulting dot product will be either positive or negative depending on whether the angle is concave or convex.

(small characters here refer to angles, capitals to lengths of sides)

An oblique triangle

A triangle without a 90 degree angle

Python equivalents of the above math are for instance (untested):

A = math.sin(a) / (math.sin(b)/B)

B = math.sin(b) / (math.sin(c)/C)

C = math.sin(c) / (math.sin(a)/A)

A right angle triangle

A triangle with a single 90 degree angle (a in this case)

Python equivalents of the above math are for instance:

c = math.asin(C/A)

c = math.acos(A/C)

c = math.atan(C/B)

A = math.sqrt(B*B+C*C)

Remember soscastoa!