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comp.lang.ruby

Is it me or Math::sqrt?

Phillip Gawlowski

3/31/2008 9:40:00 AM

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Hello list.

I'm a bit stupefied by the different results of this algorithm I
implemented (Euclidean distance for 3 dimensions):

# Calculates the relative distance_to an arbitrary
# Note: The algorithm is not yet optimized for speed.
# Hopefully, it is accurate, though.
def distance_to(actor)
~ # Stub, will use vector math or so to approximate the true distance
~ distance = (self.x - actor.x)^2 + (self.y - actor.y)^2 + (self.z -
actor.z)^2
~ Math::sqrt(distance.abs)
end

actor1 = Gondor::AI::Actor.new(:x => 0,:y => 0,:z => 0)
actor2 = Gondor::AI::Actor.new(:x => 16, :y => 16, :z => 16)
actor1.distance(actor2)
produces: 3.74165738677394

actor1 = Gondor::AI::Actor.new(:x => 1,:y => 1,:z => 1)
actor2 = Gondor::AI::Actor.new(:x => 15, :y => 15, :z => 15)
produces: 4.0

Why is that? From my understanding, these results should be identical
(The algebraic sign is eliminated by exponent 2, everything else is
addition).

Another thing that has me stumped is, that Math::sqrt requires the
absolute, but the result should be positive (addition of positive
algebraic signs).

Do I need to brush up my math more than I thought?

- -- Phillip Gawlowski
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8 Answers

Robert Klemme

3/31/2008 9:48:00 AM

0

2008/3/31, Phillip Gawlowski <cmdjackryan@googlemail.com>:
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> Hello list.
>
> I'm a bit stupefied by the different results of this algorithm I
> implemented (Euclidean distance for 3 dimensions):
>
> # Calculates the relative distance_to an arbitrary
> # Note: The algorithm is not yet optimized for speed.
> # Hopefully, it is accurate, though.
> def distance_to(actor)
> ~ # Stub, will use vector math or so to approximate the true distance
> ~ distance = (self.x - actor.x)^2 + (self.y - actor.y)^2 + (self.z -
> actor.z)^2
> ~ Math::sqrt(distance.abs)
> end
>
> actor1 = Gondor::AI::Actor.new(:x => 0,:y => 0,:z => 0)
> actor2 = Gondor::AI::Actor.new(:x => 16, :y => 16, :z => 16)
> actor1.distance(actor2)
> produces: 3.74165738677394
>
> actor1 = Gondor::AI::Actor.new(:x => 1,:y => 1,:z => 1)
> actor2 = Gondor::AI::Actor.new(:x => 15, :y => 15, :z => 15)
> produces: 4.0
>
> Why is that? From my understanding, these results should be identical
> (The algebraic sign is eliminated by exponent 2, everything else is
> addition).
>
> Another thing that has me stumped is, that Math::sqrt requires the
> absolute, but the result should be positive (addition of positive
> algebraic signs).
>
> Do I need to brush up my math more than I thought?
>
> - -- Phillip Gawlowski
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- without words -

irb(main):002:0> (0-16)^2
=> -14
irb(main):003:0> (0-16) ** 2
=> 256

:-)

Kind regards

robert

--
use.inject do |as, often| as.you_can - without end

Peter Hickman

3/31/2008 9:51:00 AM

0

Phillip Gawlowski wrote:
> actor1 = Gondor::AI::Actor.new(:x => 0,:y => 0,:z => 0)
> actor2 = Gondor::AI::Actor.new(:x => 16, :y => 16, :z => 16)
> actor1.distance(actor2)
> produces: 3.74165738677394
>
> actor1 = Gondor::AI::Actor.new(:x => 1,:y => 1,:z => 1)
> actor2 = Gondor::AI::Actor.new(:x => 15, :y => 15, :z => 15)
> produces: 4.0
>
> Why is that? From my understanding, these results should be identical
> (The algebraic sign is eliminated by exponent 2, everything else is
> addition).

If my reading is correct the distances should be different. I am not
saying that the reported distances are correct only that they should be
different. Take the x axis for example:

(0 - 16) * (0 - 16) = 256
(1 - 15) * (1 - 15) = 196

What you probably meant was:

actor1 = Gondor::AI::Actor.new(:x => 0,:y => 0,:z => 0)
actor2 = Gondor::AI::Actor.new(:x => 15, :y => 15, :z => 15)

should be the same distance as:

actor1 = Gondor::AI::Actor.new(:x => 1,:y => 1,:z => 1)
actor2 = Gondor::AI::Actor.new(:x => 16, :y => 16, :z => 16)

Phillip Gawlowski

3/31/2008 9:59:00 AM

0

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Robert Klemme wrote:
| 2008/3/31, Phillip Gawlowski <cmdjackryan@googlemail.com>:
|> # Calculates the relative distance_to an arbitrary
|> # Note: The algorithm is not yet optimized for speed.
|> # Hopefully, it is accurate, though.
|> def distance_to(actor)
|> # Stub, will use vector math or so to approximate the true distance
|> distance = (self.x - actor.x)^2 + (self.y - actor.y)^2 + (self.z -
|> actor.z)^2
|> Math::sqrt(distance.abs)
|> end
|>
|> actor1 = Gondor::AI::Actor.new(:x => 0,:y => 0,:z => 0)
|> actor2 = Gondor::AI::Actor.new(:x => 16, :y => 16, :z => 16)
|> actor1.distance(actor2)
|> produces: 3.74165738677394
|>
|> actor1 = Gondor::AI::Actor.new(:x => 1,:y => 1,:z => 1)
|> actor2 = Gondor::AI::Actor.new(:x => 15, :y => 15, :z => 15)
|> produces: 4.0
|>
|> Why is that? From my understanding, these results should be identical
|> (The algebraic sign is eliminated by exponent 2, everything else is
|> addition).
|>
|> Another thing that has me stumped is, that Math::sqrt requires the
|> absolute, but the result should be positive (addition of positive
|> algebraic signs).
|>
|> Do I need to brush up my math more than I thought?
|
| - without words -
|
| irb(main):002:0> (0-16)^2
| => -14
| irb(main):003:0> (0-16) ** 2
| => 256
|
| :-)
|
| Kind regards
|
| robert
|

I've replaced ^2 with ** 2, but that doesn't seem to change the
magnitude of the error (Though, the results "feels" more correct now, so
thanks for that).

The results are still different, as you can see:
24.2487113059643 for actor1's x,y,z = 1, and actor2's x,y,z = 15
27.712812921102 for actor1's x,y,z = 0, and actor2's x,y,z = 16

However, since the coordinates are subtracted on their respective
axises, I guess that my assumption on the "error" is incorrect, and that
I do get the correct value. However, intuitively, the distance between
these two points should be the same. Hmmmm..

- -- Phillip Gawlowski
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Phillip Gawlowski

3/31/2008 10:03:00 AM

0

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Peter Hickman wrote:

|
| If my reading is correct the distances should be different. I am not
| saying that the reported distances are correct only that they should be
| different. Take the x axis for example:
|
| (0 - 16) * (0 - 16) = 256
| (1 - 15) * (1 - 15) = 196
|
| What you probably meant was:
|
| actor1 = Gondor::AI::Actor.new(:x => 0,:y => 0,:z => 0)
| actor2 = Gondor::AI::Actor.new(:x => 15, :y => 15, :z => 15)
|
| should be the same distance as:
|
| actor1 = Gondor::AI::Actor.new(:x => 1,:y => 1,:z => 1)
| actor2 = Gondor::AI::Actor.new(:x => 16, :y => 16, :z => 16)


D'oh. Forrest, meet trees. Yes, that is what I should check on, and
nothing else. Thank you for that reality check.

- --Phillip Gawlowski
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Robert Klemme

3/31/2008 10:50:00 AM

0

2008/3/31, Phillip Gawlowski <cmdjackryan@googlemail.com>:
> I've replaced ^2 with ** 2, but that doesn't seem to change the
> magnitude of the error (Though, the results "feels" more correct now, so
> thanks for that).

Is this really true after Peter's response? Looks ok to me:

irb(main):001:0> Math.sqrt(3 * (16-1)**2)
=> 25.9807621135332
irb(main):002:0> Math.sqrt(3 * (15-0)**2)
=> 25.9807621135332

Cheers

robert

--
use.inject do |as, often| as.you_can - without end

Phillip Gawlowski

3/31/2008 12:31:00 PM

0

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Robert Klemme wrote:
| 2008/3/31, Phillip Gawlowski <cmdjackryan@googlemail.com>:
|> I've replaced ^2 with ** 2, but that doesn't seem to change the
|> magnitude of the error (Though, the results "feels" more correct now, so
|> thanks for that).
|
| Is this really true after Peter's response? Looks ok to me:
|
| irb(main):001:0> Math.sqrt(3 * (16-1)**2)
| => 25.9807621135332
| irb(main):002:0> Math.sqrt(3 * (15-0)**2)
| => 25.9807621135332

Yeah, the mistake was clearly mine. Fixing my assumption helped with
fixing the bug. Though, this time the bug was a PBKAC.

A hint should've been that I needed Fixnum#abs to properly calculate the
square root required by the algorithm.

Which shows that flying solo has its dangers.

Thanks for correcting me. :)

- -- Phillip Gawlowski
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Robert Klemme

3/31/2008 12:35:00 PM

0

2008/3/31, Phillip Gawlowski <cmdjackryan@googlemail.com>:
> Yeah, the mistake was clearly mine. Fixing my assumption helped with
> fixing the bug. Though, this time the bug was a PBKAC.
>
> A hint should've been that I needed Fixnum#abs to properly calculate the
> square root required by the algorithm.

Yes, that was what got me wondering.

> Which shows that flying solo has its dangers.

Often it's helpful to try parts of an algorithm in IRB. That way you
easily find bugs as this one. :-)

Kind regards

robert

--
use.inject do |as, often| as.you_can - without end

Phillip Gawlowski

3/31/2008 12:51:00 PM

0

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Robert Klemme wrote:
| 2008/3/31, Phillip Gawlowski <cmdjackryan@googlemail.com>:
|
| Often it's helpful to try parts of an algorithm in IRB. That way you
| easily find bugs as this one. :-)

The difficulty is, that my assumptions were broken. And even with irb,
the assumptions *I* make aren't checked. Neither would unit tests or
similar things: If my assumptions are incorrect, and I don't know it,
I'll write tests and code that validate my assumptions.

The difficulty, if one is working alone, to find a way to check
assumptions (and looking up the math formula for calculating the
Euclidean distance between two points helped my catch another assumption
I made, fortunately), which co-workers or so could provide.

Ah, well, this just shows that I have to check my assumptions, too, and
perform due diligence when working on something. Which is blatantly
obvious, of course, but I needed that reminder, obviously.

I'm just glad that I only write code in a vacuum, but don't exist in one. :P


- -- Phillip Gawlowski
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