VE Perl Script

[RChung]

( crr, cda )= ( 0.005014958, 0.384314348) RESID: ( 0.0000002056)

Ah. So the trigonometric refinements don't make much difference after all. That's a relief.

[AndyF]

( crr, cda )= ( 0.005014958, 0.384314348) RESID: ( 0.0000002056)

Ah. So the trigonometric refinements don't make much difference after all. That's a relief.

I'm not sure you can say that, here. It's a question of there existing at least one cow that is brown on at least one side.

For your point-wise matching algorithm ( matching a single ve elevation point to another) the tolerance-stacking arising from the small-angle approximation might be significant. And for the added computational cost, I think coding the exact equation is justified. It's one less thing to worry about.

[RChung]

( crr, cda )= ( 0.005014958, 0.384314348) RESID: ( 0.0000002056)

Ah. So the trigonometric refinements don't make much difference after all. That's a relief.

I'm not sure you can say that, here. It's a question of there existing at least one cow that is brown on at least one side.

For your point-wise matching algorithm ( matching a single ve elevation point to another) the tolerance-stacking arising from the small-angle approximation might be significant. And for the added computational cost, I think coding the exact equation is justified. It's one less thing to worry about.

Dude, don't harsh my mellow.

We know that the profile you were matching was constructed using the "naive" slope calculation with (Crr, CdA) = (.005, .3840). Your first script, using the exact trigonometric calculation, gave (.0047, .3888), while your new script which also uses the exact trig produces ...drumroll ... (.005, .3843).

[AndyF]

Dude, don't harsh my mellow.

No mellow-harshing intended, Robert. Honest. I just want to get to the bottom of it, just like you do, I'm sure. I offer my code and results up "warts-and-all".

We know that the profile you were matching was constructed using the "naive" slope calculation with (Crr, CdA) = (.005, .3840). Your first script, using the exact trigonometric calculation, gave (.0047, .3888), while your new script which also uses the exact trig produces ...drumroll ... (.005, .3843).

I hurried up and hacked together a comparison here: http://andyfroncioni.com/2009/12/ve-a-test-of-the-small-angle-approximation/. Anyone can draw their own conclusions as to whether it's worth coding the exact equations or not. It's probably safe to say that the accumulated elevation differences are very small for short rides, but grow with ride length.

Enjoy!

[RChung]

I hurried up and hacked together a comparison here: http://andyfroncioni.com/2009/12/ve-a-test-of-the-small-angle-approximation/. Anyone can draw their own conclusions as to whether it's worth coding the exact equations or not. It's probably safe to say that the accumulated elevation differences are very small for short rides, but grow with ride length.
Enjoy!

[AndyF]

It's probably safe to say that the accumulated elevation differences are very small for short rides, but grow with ride length.
Enjoy!

Oops, sorry -- I meant the absolute value of the accumulated elevation differences grow with ride length.