Rotation angles to get an isometric projection?

Rui Maciel

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May 12, 2010, 5:07:25 AM5/12/10

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Let's say we have an orthographic projection. Does anyone know what rotation should I apply in
order to get an isometric projection angle?

Thanks in advance,
Rui Maciel

Frank Sullivan

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May 12, 2010, 10:56:42 AM5/12/10

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According to Wikipedia, you start with an x rotation of
arcsin( tan(30deg) ) followed by a y rotation of 45 deg (or a z
rotation, depending on which is vertical).

http://en.wikipedia.org/wiki/Isometric_projection#Mathematics

Rui Maciel

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May 12, 2010, 5:20:21 PM5/12/10

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Frank Sullivan wrote:

> According to Wikipedia, you start with an x rotation of
> arcsin( tan(30deg) ) followed by a y rotation of 45 deg (or a z
> rotation, depending on which is vertical).
>
> http://en.wikipedia.org/wiki/Isometric_projection#Mathematics

But surely it's possible to get the same transformation with a single rotation around a specific
axis.

As this must be a somewhat frequent task, does anyone have this info?

Rui Maciel

Wolfgang Draxinger

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May 12, 2010, 7:04:08 PM5/12/10

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Am Wed, 12 May 2010 22:20:21 +0100
schrieb Rui Maciel <rui.m...@gmail.com>:

Why not just calculate the eigenvectorvof the composedvrotation matrix
like given above? This gives you the axis.

Wolfgang

Andy V

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May 12, 2010, 7:28:34 PM5/12/10

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You can just use the 3x3 matrix given in the wikipedia article.
--
Andy V

fungus

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May 13, 2010, 2:35:32 AM5/13/10

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On May 12, 11:20 pm, Rui Maciel <rui.mac...@gmail.com> wrote:
>
> But surely it's possible to get the same transformation with
> a single rotation around a specific axis.
>

Not necessarily that's why quaternions have four
values, not three :-)

Dave Eberly

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May 13, 2010, 9:38:32 AM5/13/10

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"fungus" <opengl...@artlum.com> wrote in message
news:b63568a7-feeb-434f...@o8g2000yqo.googlegroups.com...

Quaternions that represent rotations are unit-length 4-tuples, so there are
only 3 degrees of freedom. The quaternion q and -q represent the same
rotation.

And it is possible to get the same transformation, as requested, and as
others have pointed out.

--
Dave Eberly
http://www.geometrictools.com

fungus

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May 13, 2010, 6:45:34 PM5/13/10

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On May 13, 3:38 pm, "Dave Eberly" <dNOSPAMebe...@usemydomain.com>
wrote:

>
> And it is possible to get the same transformation, as requested, and as
> others have pointed out.
>

For this transformation, yes because there's no "twist".

OTOH it's a micro-optimization which doesn't gain
much but makes the code less comprehensible.

I wouldn't do it.

--
<\___/>
/ O O \
\_____/ FTB.

Nobody

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May 14, 2010, 1:06:26 PM5/14/10

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On Wed, 12 May 2010 22:20:21 +0100, Rui Maciel wrote:

> But surely it's possible to get the same transformation with a single
> rotation around a specific axis.
>
> As this must be a somewhat frequent task, does anyone have this info?

This looks about right:

glRotatef(56.600269334224741,
0.5902844985873289,
0.76927373575385605,
-0.24450384497347222)