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All these years, I thought the correct way to compute the cross product
of two vectors is
x3 = y1 z2 - z1 y2
y3 = x1 z2 - z1 x2
z3 = x1 y2 - y1 x2
But, apparently, I was wrong. The correct way is in fact
x3 = y1 z2 - z1 y2
y3 = z1 x2 - x1 z2
z3 = x1 y2 - y1 x2
In particular, this results in y3 having the opposite sign. No wonder my
program can't construct an orthogonal vector basis! >_<
FAIL.
The best part? I got this wrong in a library I released. Yes, my program
is failing due to a bug in my own damned library... :'{
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On 17-1-2010 21:42, Orchid XP v8 wrote:
> All these years, I thought the correct way to compute the cross product
> of two vectors is
>
> x3 = y1 z2 - z1 y2
> y3 = x1 z2 - z1 x2
> z3 = x1 y2 - y1 x2
>
> But, apparently, I was wrong. The correct way is in fact
>
> x3 = y1 z2 - z1 y2
> y3 = z1 x2 - x1 z2
> z3 = x1 y2 - y1 x2
>
You should have caught that based on symmetry.
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>> All these years, I thought the correct way to compute the cross
>> product of two vectors is
>>
>> x3 = y1 z2 - z1 y2
>> y3 = x1 z2 - z1 x2
>> z3 = x1 y2 - y1 x2
>>
>> But, apparently, I was wrong. The correct way is in fact
>>
>> x3 = y1 z2 - z1 y2
>> y3 = z1 x2 - x1 z2
>> z3 = x1 y2 - y1 x2
>>
>
> You should have caught that based on symmetry.
Well, the rule seems clear: the expression for (say) Y involves every
coordinate except Y itself. I never realised it actually matters which
order you put them in...
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> Well, the rule seems clear: the expression for (say) Y involves every
> coordinate except Y itself. I never realised it actually matters which
> order you put them in...
Your initial algorithm would fail even the most basic test of the cross
product:
x cross y = z
y cross z = x
z cross x = y
where x = (1,0,0), y = (0,1,0), z = (0,0,1)
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Invisible a écrit :
>>> All these years, I thought the correct way to compute the cross
>>> product of two vectors is
>>>
>>> x3 = y1 z2 - z1 y2
>>> y3 = x1 z2 - z1 x2
>>> z3 = x1 y2 - y1 x2
>>>
>>> But, apparently, I was wrong. The correct way is in fact
>>>
>>> x3 = y1 z2 - z1 y2
>>> y3 = z1 x2 - x1 z2
>>> z3 = x1 y2 - y1 x2
>>>
>>
>> You should have caught that based on symmetry.
>
> Well, the rule seems clear: the expression for (say) Y involves every
> coordinate except Y itself. I never realised it actually matters which
> order you put them in...
My rule is rather a rotation (X->Y->Z->X) and yes, order matter.
You can write the first line as you want, but for the next lines, the
rotation must be applied on it strictly.
Basic check: X.Y gives Z, Y.Z gives X, Z.X gives Y, it's always a XYZ
sequence in loop. (X Y Z X Y Z...)
--
Real software engineers work from 9 to 5, because that is<br/>
the way the job is described in the formal spec. Working<br/>
late would feel like using an undocumented external procedure.
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>> Well, the rule seems clear: the expression for (say) Y involves every
>> coordinate except Y itself. I never realised it actually matters which
>> order you put them in...
>
> My rule is rather a rotation (X->Y->Z->X) and yes, order matter.
Yes, that does appear to be the correct method...
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On 01/17/10 12:42, Orchid XP v8 wrote:
> All these years, I thought the correct way to compute the cross product
> of two vectors is
>
> x3 = y1 z2 - z1 y2
> y3 = x1 z2 - z1 x2
> z3 = x1 y2 - y1 x2
Oh dear. Use the determinant form - easiest to remember:
http://en.wikipedia.org/wiki/Cross_product#Matrix_notation
--
I'm addicted to placebos. I'd give them up, but it wouldn't make any
difference. - Steven Wright
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Neeum Zawan wrote:
> Oh dear. Use the determinant form - easiest to remember:
>
> http://en.wikipedia.org/wiki/Cross_product#Matrix_notation
...except that then I'd have to somehow remember the correct way to do
matrix multiplication. (Something which I never get right with more than
50% probability...)
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Invisible <voi### [at] dev null> wrote:
> Neeum Zawan wrote:
> > Oh dear. Use the determinant form - easiest to remember:
> >
> > http://en.wikipedia.org/wiki/Cross_product#Matrix_notation
> ...except that then I'd have to somehow remember the correct way to do
> matrix multiplication. (Something which I never get right with more than
> 50% probability...)
Then you just end up using left-handed coordinates for your cross product
rather than right-handed. In other words, it only affects the sign of the
result.
--
- Warp
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>> ...except that then I'd have to somehow remember the correct way to do
>> matrix multiplication. (Something which I never get right with more than
>> 50% probability...)
>
> Then you just end up using left-handed coordinates for your cross product
> rather than right-handed. In other words, it only affects the sign of the
> result.
Oh, does it?
With general matrix multiplication, getting it wrong tends to really
mess things up. But in the specific case of a cross product, maybe it
doesn't...
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