CODEWITHSUNDEEP
3dgeometry
thomthom
thomthom

Reputation: 2914

How do you compute the angle between two edges in a polygon in 3D space?

I want to compute the angle between two edges in a face in 3D space.

I thought I could used the solution in this question: Signed angle between two 3D vectors with same origin within the same plane

However, when I try it out on rectangle with all 90 degree angles I get one angle that's 90 degrees and three that's 270.

I have very little knowledge of math related to geometry, which is why I struggle with this and clearly made the wrong assumption.

So how do you calculate the angle between two edges in a face?

What I tried:

def self.full_angle_between( vector1, vector2, normal )
  angle = vector1.angle_between( vector2 )
  direction = normal % ( vector1 * vector2 )
  angle = 360.degrees - angle if direction < 0.0
  angle
end

normal is the face normal vector1 and vector2 both origins from the same vertex and each points towards the next vertex in either direction

vector1.angle_between( vector2 ) refer to a method in the SketchUp Rubu API: http://code.google.com/apis/sketchup/docs/ourdoc/vector3d.html#angle_between It return an angle between 0-180 in radians.

360.degrees yields the degrees in radians. Also an SketchUp API method.

When I iterate over all the vertices in a rectangle I get three angles reported as 270 degrees. Why?

Upvotes: 0

Views: 3461

Answers (4)

user3677092
user3677092

Reputation: 31

let's say we have two vectors called v1 and v2 (CV3 is a simple datatype with members x,y,z):

double VecAngle (CV3& v1, CV3& v2)
{
   double z = ScalarProd(v1, v2);
   double n = v1.Length() * v2.Length();
   return (acos(z/n));
}

with

const double ScalarProd (const CV3& argl, const CV3& argr)
{
   return (argl.x * argr.x + argl.y * argr.y + argl.z * argr.z);
}

Upvotes: 0

Yunfeng Bai
Yunfeng Bai

Reputation: 1

Since I can't add comments to the previous answer, I started a new answer just to point out that the dot product is only the cosine value of two vectors. To get the actual angle you need to call acos() after that.

Upvotes: 0

Rob Agar
Rob Agar

Reputation: 12447

I would say your problem lies in this line:

direction = normal % ( vector1 * vector2 )

It's not wrong in itself, but you might be passing in the wrong values.

If you're not fully up to speed on vector maths, the thing you may be missing is that the direction of the vector given by the cross product vector1 * vector2 depends on the order of the operands. If you swap them around you get the same vector pointing in the opposite direction.

So when you're iterating over the rectangle vertices, if you get the "next" and "previous" vertices mixed up you will get the bogus 270 degree results you describe.

Upvotes: 1

ChrisF
ChrisF

Reputation: 137128

You do just perform the dot product of the two vectors.

This will give you the angle. For 3d vectors it's:

product = (x1 * x2) + (y1 * y2) + (z1 * z2);

This assumes that the vectors are normalised (their length is one). So in the first instance you'll have to make sure this is so.

You'll have to make sure that you are choosing the right pair of edges each time:

edge1 * edge2
edge2 * edge3
edge3 * edge4
edge4 * edge1

Upvotes: 0

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