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Re: Quaternions (was Re: Default signedness of 'plain' char.)

From Lawrence D’Oliveiro <ldo@nz.invalid>
Newsgroups comp.lang.c
Subject Re: Quaternions (was Re: Default signedness of 'plain' char.)
Date 2026-08-12 03:36 +0000
Organization A noiseless patient Spider
Message-ID <115gpod$gl9f$1@dont-email.me> (permalink)
References (14 earlier) <115djoi$3h06u$1@dont-email.me> <115dot7$3ihmr$1@dont-email.me> <115dv3d$3k3jl$1@dont-email.me> <115feen$3msd$1@dont-email.me> <115fuu3$93db$1@dont-email.me>

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On Tue, 11 Aug 2026 14:54:11 -0500, BGB wrote:

> Partly, this goes back to my more 3D engine programming days, where
> I had ended up using [quaternions] for 3D skeletal animation math
> (though my first versions worked by interpolating 3x3 matrices,
> which was another pain, and inefficient, *).
>
> *1: Doesn't flow at uniform speed or maintain scale or
> orthogonality. This means, to interpolate between dissimilar 3D
> rotation matrices it was necessary to subdivide the interpolation
> and then re-normalize and fix-up orthogonality at each step.

Also prone to accumulated rounding errors.

There was an item in one of the “Graphics Gems” books about a
numerical technique for fixing this up every N rotation steps, for a
suitable choice of N. You need to renormalize the matrix so its
determinant becomes 1. There is a cost to this, which is why you might
not want to do it after every rotation step.

> I ended up switching mostly to quaternions here; which interpolate
> more nicely. Though still need to subdivide and renormalize for
> larger movements, and hack around the "720 degrees for a full
> rotation" quirk.

I think that 720° range is not considered a bug, it’s a feature ;).

Basically, it eases the job of interpolating full-circle rotations,
since you have the leeway to start at any point without a
discontinuity.

> Annoyingly though, SCAD lacks any ways to express texture-mapping or
> skeletal animation. I had debated adding these as informal
> extensions (but, then this breaks the ability to preview models in
> OpenSCAD, unless I were to essentially write a clone of this as
> well).

The big 3D studios (Pixar etc) have gone through a number of different
standard interchange formats for expressing this sort of information.
The current darling seems to be “Universal Scene Description” or USD.

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Default signedness of 'plain' char. gazelle@shell.xmission.com (Kenny McCormack) - 2026-08-02 14:17 +0000
  Re: Default signedness of 'plain' char. Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-03 02:45 +0800
    Re: Default signedness of 'plain' char. gazelle@shell.xmission.com (Kenny McCormack) - 2026-08-03 01:47 +0000
      Re: Default signedness of 'plain' char. Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-03 23:14 +0800
        Re: Default signedness of 'plain' char. bart <bc@freeuk.com> - 2026-08-03 17:04 +0100
          The Spanish Inquisition (was: Re: Default signedness of 'plain' char.) Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-04 00:23 +0800
            Re: The Spanish Inquisition bart <bc@freeuk.com> - 2026-08-03 18:03 +0100
              Re: The Spanish Inquisition Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-04 01:26 +0800
        Re: Default signedness of 'plain' char. Theo <theom+news@chiark.greenend.org.uk> - 2026-08-04 13:13 +0100
          Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 07:30 +0000
            Re: Default signedness of 'plain' char. Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-05 18:18 +0800
              Re: Default signedness of 'plain' char. bart <bc@freeuk.com> - 2026-08-05 17:20 +0100
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 21:57 +0000
                Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-05 15:29 -0700
  Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-03 09:56 +0200
    Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-03 13:56 -0500
  Re: Default signedness of 'plain' char. antispam@fricas.org (Waldek Hebisch) - 2026-08-03 13:48 +0000
  Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-03 14:47 +0000
  Re: Default signedness of 'plain' char. Lew Pitcher <lew.pitcher@digitalfreehold.ca> - 2026-08-03 14:47 +0000
    Re: Default signedness of 'plain' char. Lew Pitcher <lew.pitcher@digitalfreehold.ca> - 2026-08-03 15:04 +0000
      Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-03 16:58 -0700
        Re: Default signedness of 'plain' char. Lew Pitcher <lew.pitcher@digitalfreehold.ca> - 2026-08-04 15:10 +0000
          Re: Default signedness of 'plain' char. scott@slp53.sl.home (Scott Lurndal) - 2026-08-04 15:50 +0000
          Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 03:00 +0000
          Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-05 09:01 +0200
      Re: Default signedness of 'plain' char. antispam@fricas.org (Waldek Hebisch) - 2026-08-04 18:10 +0000
        Compilers targetting the C64 (was: Re: Default signedness of 'plain' char.) Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-05 03:17 +0800
        Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-04 16:25 -0500
        Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 02:57 +0000
          Re: Default signedness of 'plain' char. Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-05 00:19 -0500
            Re: Default signedness of 'plain' char. Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-05 18:57 +0800
            Re: Default signedness of 'plain' char. scott@slp53.sl.home (Scott Lurndal) - 2026-08-05 14:33 +0000
            Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-05 22:38 +0000
        Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-04 21:36 -0700
          Re: Default signedness of 'plain' char. antispam@fricas.org (Waldek Hebisch) - 2026-08-06 00:21 +0000
  Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-03 13:20 -0700
    Re: Default signedness of 'plain' char. bart <bc@freeuk.com> - 2026-08-03 22:06 +0100
      Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-03 14:25 -0700
        Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-03 18:38 -0500
          Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-03 19:34 -0700
            Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-05 04:40 -0500
          Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 07:22 +0000
            Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-05 04:02 -0500
              Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-05 12:35 +0200
              Re: Default signedness of 'plain' char. Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-05 18:49 +0800
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-05 12:39 -0700
                Dear Chris (was: Re: Default signedness of 'plain' char.) Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-06 20:15 +0800
                Re: Dear Chris bart <bc@freeuk.com> - 2026-08-06 15:05 +0100
                Re: Dear Chris Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-06 23:16 +0800
                Re: Dear Chris David Brown <david.brown@hesbynett.no> - 2026-08-06 20:10 +0200
              Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 21:54 +0000
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-06 04:49 -0500
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-07 00:10 +0000
                Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-07 09:56 +0200
            Re: Default signedness of 'plain' char. James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-08-05 13:33 -0400
              Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 21:50 +0000
                Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-06 10:34 +0200
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-09 15:19 -0500
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-09 20:33 +0000
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-09 18:04 -0700
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-10 02:45 +0000
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-10 02:24 -0700
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-09 18:03 -0700
                Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-10 08:58 +0200
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-10 15:17 -0500
                Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-10 15:19 -0700
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-10 17:31 -0500
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-10 23:48 +0000
                Re: Default signedness of 'plain' char. James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-08-10 20:03 -0400
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-10 20:44 -0500
                Re: Default signedness of 'plain' char. James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-08-11 11:17 -0400
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-11 14:54 -0500
                Re: Quaternions (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-12 03:36 +0000
                Re: Quaternions (was Re: Default signedness of 'plain' char.) BGB <cr88192@gmail.com> - 2026-08-12 01:24 -0500
                Re: Quaternions (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-12 07:47 +0000
                Re: Quaternions (was Re: Default signedness of 'plain' char.) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-12 12:52 -0700
                Re: Quaternions (was Re: Default signedness of 'plain' char.) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-12 12:56 -0700
                Re: Quaternions (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-13 02:16 +0000
                Re: Quaternions (was Re: Default signedness of 'plain' char.) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-12 21:04 -0700
                Re: Quaternions (was Re: Default signedness of 'plain' char.) BGB <cr88192@gmail.com> - 2026-08-12 23:07 -0500
                Re: Quaternions (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-13 05:00 +0000
                Re: Quaternions (was Re: Default signedness of 'plain' char.) BGB <cr88192@gmail.com> - 2026-08-13 04:37 -0500
                Re: Quaternions (was Re: Default signedness of 'plain' char.) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-13 14:36 -0700
                Re: Quaternions (was Re: Default signedness of 'plain' char.) BGB <cr88192@gmail.com> - 2026-08-13 23:07 -0500
                Re: Quaternions (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-13 23:44 +0000
                Re: Quaternions (was Re: Default signedness of 'plain' char.) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-13 18:50 -0700
                Re: Quaternions (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-14 02:41 +0000
                Re: Quaternions (was Re: Default signedness of 'plain' char.) BGB <cr88192@gmail.com> - 2026-08-13 23:47 -0500
                Re: Quaternions (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-14 04:59 +0000
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-11 13:47 -0700
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-13 23:50 -0500
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-14 05:59 +0000
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-14 03:16 -0500
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-14 08:32 +0000
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:36 -0700
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-15 03:16 +0000
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 22:38 -0700
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-16 00:08 +0000
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:17 -0700
                Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-11 13:46 +0000
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-11 13:49 -0700
                Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-11 08:58 +0200
                Re: Default signedness of 'plain' char. BGB <cr88192@gmail.com> - 2026-08-11 04:03 -0500
                Re: Default signedness of 'plain' char. steve g <Sgonedes1977@gmail.com> - 2026-08-10 20:29 -0400
                Re: Vectors! Quaternions! (was Re: Default signedness of 'plain' char.) Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-11 03:58 +0000
                Re: Default signedness of 'plain' char. David Brown <david.brown@hesbynett.no> - 2026-08-11 09:06 +0200
                Re: Default signedness of 'plain' char. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-10 21:15 -0700
                Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-11 04:52 +0000
                Re: Default signedness of 'plain' char. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-11 06:45 -0700
                Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-11 14:01 -0700
            Re: Default signedness of 'plain' char. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-05 12:36 -0700
    Re: Default signedness of 'plain' char. Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-05 07:18 +0000
  Re: Default signedness of 'plain' char. Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-05 18:30 -0500
    Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-05 16:41 -0700
      Re: Default signedness of 'plain' char. bart <bc@freeuk.com> - 2026-08-06 01:24 +0100
        Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-05 17:46 -0700
        Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-06 22:59 +0000
          Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-06 19:54 -0700
            Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-07 11:02 +0000
              Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-07 10:35 -0700
                Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-07 18:32 +0000
                Re: Default signedness of 'plain' char. Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-07 20:55 +0200
              Use of isascii() back in early days (was Re: Default signedness of 'plain' char.) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-07 20:51 +0200
                Re: Use of isascii() back in early days (was Re: Default signedness of 'plain' char.) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-07 13:03 -0700
                Re: Use of isascii() back in early days (was Re: Default signedness of 'plain' char.) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-07 13:32 -0700
                Re: Use of isascii() back in early days (was Re: Default signedness of 'plain' char.) cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-07 21:44 +0000
                Re: Use of isascii() back in early days (was Re: Default signedness of 'plain' char.) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-07 23:47 +0200
                Re: Use of isascii() back in early days (was Re: Default signedness of 'plain' char.) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-07 15:26 -0700
      Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-06 22:57 +0000
        Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-06 18:23 -0700
          Re: Default signedness of 'plain' char. cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-07 11:47 +0000
    Re: Default signedness of 'plain' char. scott@slp53.sl.home (Scott Lurndal) - 2026-08-06 14:40 +0000
      Re: Default signedness of 'plain' char. Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-06 15:33 -0700

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