Alternative to angle_between?

Dan Rathbun · 23 Sept 2011, 22:20

atan2() is one of the methods in the standard Ruby Math module.

Somewhere TIG posted an example method of using it with Sketchup API units.

bentleykfrog · 24 Sept 2011, 04:10

wow, major oversight! I should probably be using edge.reversed_in? to reliably find the edge normal direction relative to the face.

Just to double-check my logic: on outer loops edge.reversed_in? will return true if the start and end vertex of the edge is running clockwise (if your looking against the normal of the face [the negative face normal vector is the vector for determining clockwise or anti-clockwise]). On inner loops (face.loops - face.outer_loop) edge.reversed_in will return true if the start and end vertex of the edge is running counter-clockwise?

mac1 · 24 Sept 2011, 04:33

Once one determines the angle value the inverse trig functions calculate the principal value. Therefore to determine the actual angle logic must be use either in the method or in the program its self to determine the correct quadrant. Give one can get the cos from the dot product, sine from the cross and even tangent from tan( theta) = |V1xV2|/ (V1 dot V2) then it is possible to establish the quadrant??

thomthom · 26 Sept 2011, 07:34

@bentleykfrog said:

wow, major oversight! I should probably be using edge.reversed_in? to reliably find the edge normal direction relative to the face.

Just to double-check my logic: on outer loops edge.reversed_in? will return true if the start and end vertex of the edge is running clockwise (if your looking against the normal of the face [the negative face normal vector is the vector for determining clockwise or anti-clockwise]). On inner loops (face.loops - face.outer_loop) edge.reversed_in will return true if the start and end vertex of the edge is running counter-clockwise?

Aye. Loop and EdgeUse objects can be very useful.

bentleykfrog · 26 Sept 2011, 14:53

@bentleykfrog said:

Just to double-check my logic: on outer loops edge.reversed_in? will return true if the start and end vertex of the edge is running clockwise (if your looking against the normal of the face [the negative face normal vector is the vector for determining clockwise or anti-clockwise]). On inner loops (face.loops - face.outer_loop) edge.reversed_in will return true if the start and end vertex of the edge is running counter-clockwise?

I'm probably getting a bit off topic here, so to sum up, when you're looking against the normal of the face edge.reversed_in? returns true when the face is on the left hand side of the edge, and false when on the right hand side of the face (irrespective of inner and outer loops, so disregard my previous assumption).

@mac1 said:

Once one determines the angle value the inverse trig functions calculate the principal value. Therefore to determine the actual angle logic must be use either in the method or in the program its self to determine the correct quadrant. Give one can get the cos from the dot product, sine from the cross and even tangent from tan( theta) = |V1xV2|/ (V1 dot V2) then it is possible to establish the quadrant??

I agree, the problem I had in Sketchup (I think) is determining a consistent cross and dot product vectors. Once you've established consistent methods for determining these, you should be good to go.

In my case I'm trying to define a 2d manifold. What's important in a 2d manifold is the angle between two faces (complex polygons) at a common edge. Given this angle, we can establish 2d manifold errors (like an edge sharing 3 or more faces).

To establish this angle we need three vectors: 'the edge vector normal on the first face', 'the face normal' & the 'the edge vector normal on the second face'. edge.reversed_in? seems to be a very consistent way to get the right edge vector normals. Also, to eliminate errors with faces that are reversed, we need to define a 'dominant' face. This dominant face is the origin of the 2d manifold, so all other connected faces should be oriented in the same direction as the dominant face (ie. all looking into the 2d manifold, or all looking out of the 2d manifold), if not, their normal vector is reversed (not the face itself) so the angle between two faces remains consistent. In my code, the dominant face is the face the user hovers over with their cursor.

@thomthom said:

Aye. Loop and EdgeUse objects can be very useful.

Normalize Toolkit Work In Progress 2

mac1 · 27 Sept 2011, 03:50

Not ruby programmer so leave that up to you, but for 3d vectors and using the general approach the angle is the shortest great circle path between the two. The angle is atan2( Norm( cross(a,b)), dot( a,b)). This means the angle is 0 to pi()
FYI http://www.euclideanspace.com/maths/algebra/vectors/angleBetween/index.htm and http://www.mathworks.com/matlabcentral/newsreader/view_thread/151925