Re: Division of two complex numbers

On 1/21/2025 1:17 AM, Moebius wrote:

Am 21.01.2025 um 03:50 schrieb Chris M. Thomasson:

On 1/20/2025 3:15 PM, Moebius wrote:

Am 21.01.2025 um 00:03 schrieb Chris M. Thomasson:

On 1/20/2025 2:48 PM, Moebius wrote:

Am 20.01.2025 um 23:40 schrieb Chris M. Thomasson:
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[...] Fwiw, a fun part of GLSL is doing stuff like:
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vec3 a = vec3(.25, 1, .75);
vec2 b = a.xz;
vec2 c = b + vec2(.75, .25);
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c now equals (1, 1)

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Nice.
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In math:
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a := (.25, 1, .75) ,
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b := (a_1, a_3) ,
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c := b + (.75, .25) .
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Then c = (1, 1) .
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:-P
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Question. What if
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vec4 a = vec4(.25, 1, .75, .999);
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vec3 b = a.xz<?>;
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I'd like to get b == (.25, .75, .999). :-P
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That would be:
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vec4 a = vec4(.25, 1, .75, .999);
vec3 b = a.xzw;
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;^)

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C'mon... lol
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And then?

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vec4's in GLSL are (x, y, z, w) or
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vec4 a = vec4(1, 2, 3, 4);
a[1] = 3.f;
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now, a.y = 3   :^)
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xyzw ... uv ...
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I usually use the "series"
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      x, y, z, u, v, w
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in math/physics.

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GLSL has x, y, z, w or [0], [1], [2], [3]

 A useful convention, I guess, when doing graphics in (3D) space; for doing it in space-time I'd prefer t instead of w here. :-P
 

;^) well, shit happens. GLSL chose the symbol w for the 4d component of a vec4. Fwiw, in some of my work I use the 4'th dimension for plotting some of my fields. For instance, my cover of the AMS calendar used the 4'th dimension. In other words the w component was non-zero. It really casts an interesting "mutation" to the 3d components during iterations of field lines...