subtract two angle

[thomthom]

Hi all,

I have a strange result when I subtract two angle in radians!!!!

example :

Code: Select all

axe = Geom::Vector3d.new(-0.999782867743517, -0.0208378829670674, 0.0)
up = Geom::Vector3d.new(0.00335712544250249, -0.161071856847676, 0.98693697196954)
axe.normalize!
up.normalize!
# (90 deg) = 1.5707963267948966 in rad
#(Math::PI/2.0) = 90.0 in degrees, 1.5707963267949 in radians

# angle between up-axe = 90.0 in degrees, 1.5707963267949 in radians
angle = (Math::PI/2.0) + (up.angle_between axe)
puts angle.radians  #=> 180 degrees, 3.14159265358979 radians GOOD !!!

angle = (Math::PI/2.0) - (up.angle_between axe)
puts angle.radians  #=> 1.27222187258541e-014 BAD,  2.22044604925031e-016 in radians BAD  

can you help me ?

[Dan Rathbun]

What version Sketchup and build number, are you running ???

The angle_between method was bugged in early v7 releases.

But it was later fixed.

[macgile]

thank's Dan Rathbun


i have sketchup 8 !!!

it's not angle between, but the subtraction.
because the calculation of the angle is good.

[TIG]

Why not use 90.degrees etc and return the angle.radians to see what it is in degrees too... skip all of the PI and radian confusion...
Why are you making your axe/up vectors so complex ?
Your figures are off too...

Code: Select all

axe = Geom::Vector3d.new(-0.999782867743517, -0.0208378829670674, 0.0)
Vector3d(-0.999783, -0.0208379, 0)
axe.normalize!
Vector3d(-0.999783, -0.0208379, 0)
up = Geom::Vector3d.new(0.00335712544250249, -0.161071856847676, 0.98693697196954)
Vector3d(0.00335713, -0.161072, 0.986937)
up.normalize!
Vector3d(0.00335713, -0.161072, 0.986937)
90.degrees
1.5707963267949
Math::PI/2.0
1.5707963267949
up.angle_between(axe)
1.5707963267949
### So far ALL the same ???
angle = (Math::PI/2.0) - (up.angle_between(axe))
2.22044604925031e-016
### Which is a very tiny number that's ALMOST zero
This is a a simple tolerance issue...
angle==0
false
### BUT to test for tiny values use something like:
### a 'rounding' method - here to 6dp.
angle=(angle*10**6).round.to_f/10**6
angle==0
true
### This will then trap for these tiny inaccuracies...  

...

[Dan Rathbun]

It's a tiny tiny wee little smidgen Floating Point Error.

Round your numbers off to a reasonable number of decimal places.

Your inputting double precision numbers, but Sketchup's internal tolerance for geometry is 0.001 inch.

You can use the Length class to test if two numbers are equal within Sketchup's tolerance, even though they are angles: (your not changing the objects, your creating two new Length objects for comparison.)

(Math::PI/2.0).to_l == up.angle_between(axe).to_l
>> true

[macgile]

Why not use 90.degrees etc and return the angle.radians to see what it is in degrees too... skip all of the PI and radian confusion...

=====> I tested with 90.degrees, but I thought it was the conversion that was bad


Why are you making your axe/up vectors so complex ?
Your figures are off too...
axe = Geom::Vector3d.new(-0.999782867743517, -0.0208378829670674, 0.0)

=====> because it is real vectors returned with axe.inspect
I was given a real example.


### Which is a very tiny number that's ALMOST zero
This is a a simple tolerance issue...

======>Tolerance has importance here because it is cumulative.

### BUT to test for tiny values use something like:
### a 'rounding' method - here to 6dp.
angle=(angle*10**6).round.to_f/10**6
angle==0
true
### This will then trap for these tiny inaccuracies...
...

[Dan Rathbun]

Wikipedia: Floating_point : Accuracy_problems

[thomthom]

What Every Programmer Should Know About Floating-Point Arithmetic
A.K.A. "Why don’t my numbers add up?"