Re: [Jmol-developers] question about how planes are defined...

[Robert H. <ha...@st...>]

http://mathworld.wolfram.com/Point-PlaneDistance.html

On Thu, Jun 10, 2010 at 10:32 AM, Robert Hanson <ha...@st...> wrote:

>
>
> On Tue, Jun 8, 2010 at 5:03 PM, Jonathan Gutow <gu...@uw...> wrote:
>
>> I'm working on a slicer tool and want to make sure I'm clear about how
>> planes are defined within the transform manager as I want to adjust the slab
>> and depth planes in real time based on user input.  Here's my understanding.
>>
>> 1) Planes are defined by point4f's where the x, y, z coordinates define a
>> vector from the origin that is perpendicular to the plane.
>> 2) I assume the plane includes the point at the end of the vector.
>> 3) I'm most confused about the meaning of w (the fourth coordinate) for
>> planes that are not parallel to the screen surface, but fixed in the
>> molecule coordinate system.
>>
>> Can anybody clarify?
>>
>>
> plane:   ax + by + cz + d = 0
>
> "w" is "d". Then the distance to the origin of the plane is
>
> d / sqrt(a^2 + b^2 + c^2)
>
> and
>
> d is the length of the vector (a, b, c) times the directed distance of the
> plane to the origin.
>
> So in xyzw notation,
>
> w is the length of the vector (x,y,z) times the directed distance of the
> plane to the origin.
>
> BOb
>
>
> Thanks,
>> Jonathan
>>                         Dr. Jonathan H. Gutow
>> Chemistry Department                                gu...@uw...
>> UW-Oshkosh                                          Office: 920-424-1326
>> 800 Algoma Boulevard                                FAX:920-424-2042
>> Oshkosh, WI 54901
>>                http://www.uwosh.edu/facstaff/gutow
>>
>>
>>
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>
>
>
> --
> Robert M. Hanson
> Professor of Chemistry
> St. Olaf College
> 1520 St. Olaf Ave.
> Northfield, MN 55057
> http://www.stolaf.edu/people/hansonr
> phone: 507-786-3107
>
>
> If nature does not answer first what we want,
> it is better to take what answer we get.
>
> -- Josiah Willard Gibbs, Lecture XXX, Monday, February 5, 1900
>



-- 
Robert M. Hanson
Professor of Chemistry
St. Olaf College
1520 St. Olaf Ave.
Northfield, MN 55057
http://www.stolaf.edu/people/hansonr
phone: 507-786-3107


If nature does not answer first what we want,
it is better to take what answer we get.

-- Josiah Willard Gibbs, Lecture XXX, Monday, February 5, 1900