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Warp wrote:
> So the task is simple: Write a function f(m,n) which tells how many
> rectangles can be found in an m x n grid. (Explain how you came up
> with the function).
You mean just something like n*m*(n-1)*(m-1)/4? The derivation is
pretty direct from the one-dimensional case.
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On Wed, 16 Dec 2009 22:56:50 +0100, Orchid XP v8 <voi### [at] dev null> wrote:
>
> Also... Blender seems to incorrectly assume that Z is "up" and Y is
> "back". (It should obviously be the other way around.)
It is not incorrect; it is right-handed.
> Interesting how the amount of scaling is apparently completely unrelated
> to the mouse movement... (Seems to scale the cube by about 20% of the
> distance the mouse is moved.)
It depends on how far the mouse pointer is from the selection.
> OK, this one took me a while to figure out. You'd think you extrude it
> by dragging the face that you want to extrude... but no. You just click
> and Blender places faces at random for you.
Select faces/edges/vertices, press E to extrude. The newly formed
faces/edges/vertices are automatically selected, and by default you are
put in Grab mode; move the mouse to move them or right-click to keep them
where they are. You can also switch from Grab mode to Scale or Rotate by
pressing S or R.
> F9 doesn't appear to do anything.
F9 opens the Editing panel in the Buttons window. If the Editing panel was
already active, nothing will happen.
--
FE
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Kevin Wampler <wam### [at] uwashingtonedu> wrote:
> Warp wrote:
> > So the task is simple: Write a function f(m,n) which tells how many
> > rectangles can be found in an m x n grid. (Explain how you came up
> > with the function).
> You mean just something like n*m*(n-1)*(m-1)/4? The derivation is
> pretty direct from the one-dimensional case.
It would be interesting to see that derivation.
--
- Warp
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Warp wrote:
> Kevin Wampler <wam### [at] uwashingtonedu> wrote:
>> Warp wrote:
>>> So the task is simple: Write a function f(m,n) which tells how many
>>> rectangles can be found in an m x n grid. (Explain how you came up
>>> with the function).
>
>> You mean just something like n*m*(n-1)*(m-1)/4? The derivation is
>> pretty direct from the one-dimensional case.
>
> It would be interesting to see that derivation.
Let's consider the one-dimensional case (so set m=1). In this case we
have one rectangle of width n-1, two rectangles of width n-2, three of
width n-3, ..., and n-1 of width 1. We can express the total number of
rectangles as the sum:
sum_{i=1:n-1} i
Which as the solution n*(n-1)/2.
If we relax the restriction that m=1, then we instead get the double sum:
sum_{j=1:m-1} j * sum_{i=1:n-1} i
Intuitively you can think of this as follows: for each of the
one-dimensional rectangles along the m-axis, we have sum_{i=1:n-1}
rectangles along the n-axis. You can view this sum as expressing every
rectangle as being defined by two line segments along the n- and m-
axes. In any case, the value of the sum is easy to compute:
sum_{j=1:m-1} j * sum_{i=1:n-1} i
= sum_{j=1:m-1} j * n*(n-1)/2
= (n*(n-1)/2) * sum_{j=1:m-1} j
= (n*(n-1)/2) * (m*(m-1)/2)
= n*m*(n-1)*(m-1)/4
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Random statistic: A standard Go board has 38 lines, 361 intersections and
29241 rectangles.
--
- Warp
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On 12/16/09 13:21, Warp wrote:
>> that's what the mascot does all of the time - yet he gets chastized from
>> time to time ;-)
>
> He presents puzzles for people to think about?
His presence is a puzzle in itself.
--
Would the capacity of a Palaeozoic Hard Dive be measured in Trilobites?
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Warp wrote:
> Random statistic: A standard Go board has 38 lines, 361 intersections and
> 29241 rectangles.
And, rather surprisingly, 42 squares.
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Kevin Wampler <wam### [at] uwashingtonedu> wrote:
> Warp wrote:
> > Random statistic: A standard Go board has 38 lines, 361 intersections and
> > 29241 rectangles.
> And, rather surprisingly, 42 squares.
Since the lined grid of an official goban is 396 x 426.6 mm, does it form
any exact squares?
--
- Warp
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Warp wrote:
> Kevin Wampler <wam### [at] uwashingtonedu> wrote:
>> Warp wrote:
>>> Random statistic: A standard Go board has 38 lines, 361 intersections and
>>> 29241 rectangles.
>
>> And, rather surprisingly, 42 squares.
>
> Since the lined grid of an official goban is 396 x 426.6 mm, does it form
> any exact squares?
>
Hmm, no it doesn't. I was just getting my info from this page:
http://senseis.xmp.net/?path=GoHumour&page=HowManySquaresOnAGoBoard but
looking into it a bit more it seems that you're correct (at least for
Japanese boards). I don't about standard sizes in other countries
though (I think a Chinese board is somewhat larger, but I don't know
about Korea or other countries).
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> Has somebody invented a way of placing points in 3D space even though you
> only have a 2D edit area yet?
Most 3D modellers I've seen allow you to split the edit area into 4, 3
viewing orthogonally along each axis, and 1 perspective. This allows you to
place points accurately in 3D, and of course check the "real" look of the
outcome interactively (yes all views update together in real-time).
Like this:
http://www.nycresistor.com/wp-content/uploads/2009/07/blender-20080613-095701.jpg
Alternatively you just have 1 perspective view and slide the point along
each axis as you see fit (obviously rotating the model whilst you're doing
it to check the look).
Depends on personal preference I guess, and what exactly you're modelling.
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