Fixed rounding error angle calculation of parallel and anti-parallel vec...

[mschoeler]

This fixes angle convexity calculation for parallel and anti-parallel normals, where a rounding error occasionally caused NaN angles.
This solves issue #1033.

[mschoeler]

There actually exists a function in common doing something similar:
getAngle3D (const Eigen::Vector4f &v1, const Eigen::Vector4f &v2)
but it takes Vector4f and returns an angle in rad.
Since I'm using cross products (not defined on Vector4f) and angles in degrees using this function would make the code look ugly. This is why I implemented it as a static member function.

[taketwo]

What about adding a new overload in common?

getAngle3D (const Eigen::Vector3f &v1, const Eigen::Vector3f &v2)

As for the radians to degree conversion, there is rad2deg() in "common/angles.h". So inside LCCP this would look something like:

float intersection_angle =  rad2deg (getAngle3D (ncross, vec_t_to_s));

(Does not look too ugly to me, what do you think? :))

[mschoeler]

I thought about the the same. I guess if it is ok to add a new overloaded function to common, I would just change it to that.

[mschoeler]

what about a boolean flag in the function
getAngle3D (const Eigen::Vector3f &v1, const Eigen::Vector3f &v2, const bool in_degree = false)

[VictorLamoine]

I'm using cross products (not defined on Vector4f)

Cross Dot product is defined between two Eigen::Vector4f: (why would it not?)

  Eigen::Vector4f v1, v2;
  v1 << 1, 0, 0, 0;
  v2 << 1, 1, 1, 1;
  double test = v1.dot(v2);

Just make sure the last coordinates are zero.

[mschoeler]

dot product yes, but not cross product? At least I don't know a definition ouside of three dimensions.

[VictorLamoine]

Oh sorry I misread; you should be able to do these computations without a cross product though.
http://stackoverflow.com/questions/14066933/direct-way-of-computing-clockwise-angle-between-2-vectors

[mschoeler]

Implementing cross functions was actually what I had in the code in the first place, but it was confusing and redundent. In my oppinion an overloaded function in common makes most sense.
I also added an optional flag to the function, which determines if an angle in radians or degrees is prefered. This should not affect any existing code.

[mschoeler]

i also made the code for getAngle3D a little easier (Removed / sqrt (sqNorm...) )

[mschoeler]

oh, forgot to change the if to else if.
Will do that, too.

[taketwo]

We can make this a reference to avoid copying.

[mschoeler]

good point