Re: “We are doomed”

From	Malcolm McLean <malcolm.arthur.mclean@gmail.com>
Newsgroups	comp.lang.c++
Subject	Re: “We are doomed”
Date	2024-01-22 11:22 +0000
Organization	A noiseless patient Spider
Message-ID	<uolj5h$n00a$2@dont-email.me> (permalink)
References	<uo6ufu$1kle9$1@dont-email.me> <uoeebu$387sh$2@dont-email.me> <20240119103450.676@kylheku.com> <uogjjc$3mmvp$1@dont-email.me> <20240120134252.222@kylheku.com>

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On 21/01/2024 04:06, Kaz Kylheku wrote:
> On 2024-01-20, Malcolm McLean <malcolm.arthur.mclean@gmail.com> wrote:
>> On 19/01/2024 18:35, Kaz Kylheku wrote:
>>> On 2024-01-19, Malcolm McLean <malcolm.arthur.mclean@gmail.com> wrote:
>>>> One problem that could be very easily fixed is that there is no standard
>>>> representation of a point or a vector. Whilst generally it's just a POD
>>>> structure with x and y members, the name varies, and sometimes the
>>>
>>> For code working with 2D vectors, designers should consider complex numbers.
>>>
>> That's a nice idea.
>>
>> But I've never seen code where the horizontal axis is "real" and the
>> vertical "imaginary", except of course in code designed to demonstrate
>> complex numbers as such. Mandelbrot is my favourite test program when
>> getting a new system.
> 
> Complex numbers are used for expressing mappings that have geometric
> interpretations.
> 
> In 2D computer graphics, they are convenient. E.g. to rotate
> a vector that is a complex number z = a + ib, you just multiply by
> a complex number that is on the unit circle representing that
> angle   cos(theta) + i sin(theta) .
> 
> The multiplication math is exactly the same as
> 
>    [ cos -sin ] [ a ]
>    [ sin  cos ] [ b ]
> 
> Because when you multiply two complex nubmers (c + id)(a + ib),
> the FOIL rule produces
> 
>     ca + icb + ida + iidb
>     
>    = (ca - db) + i(cb + da).
> 
> And that's just
> 
>    [ c  -d ] [ a ]  =  [ ca - db ]
>    [ d   c ] [ b ]  =  [ da + cb ]
> 
Yes I know. I did complex numbers at high school.

But whilst you could use the Argand plane as your graphics surface and 
thus represent all points as complex numbers, I've never actually seen 
anyone do so, and the axes are always given different labels. Except of 
course in Mandelbrots or other programs concerned with complex numbers 
themselves.
-- 
Check out Basic Algorithms and my other books:
https://www.lulu.com/spotlight/bgy1mm

Thread

“We are doomed” Lynn McGuire <lynnmcguire5@gmail.com> - 2024-01-16 16:03 -0600
  Re: “We are doomed” Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-01-19 18:17 +0000
    Re: “We are doomed” Kaz Kylheku <433-929-6894@kylheku.com> - 2024-01-19 18:35 +0000
      Re: “We are doomed” Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-01-20 13:59 +0000
        Re: “We are doomed” "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-01-20 11:22 -0800
        Re: “We are doomed” Kaz Kylheku <433-929-6894@kylheku.com> - 2024-01-21 04:06 +0000
          Re: “We are doomed” Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-01-22 11:22 +0000
            Re: “We are doomed” "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-01-22 12:22 -0800
    Re: “We are doomed” "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-01-19 13:58 -0800
    Re: “We are doomed” immibis <news@immibis.com> - 2024-01-22 01:22 +0100
      Re: “We are doomed” Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-01-22 11:16 +0000
        Re: “We are doomed” "Fred. Zwarts" <F.Zwarts@HetNet.nl> - 2024-01-22 12:34 +0100
          Re: “We are doomed” Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-01-22 12:31 +0000
        Re: “We are doomed” "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-01-22 12:24 -0800
        Re: “We are doomed” MarioCCCP <NoliMihiFrangereMentulam@libero.it> - 2024-01-31 01:17 +0100

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