From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.org!.POSTED.blaine.gmane.org!not-for-mail From: Alp Aker Newsgroups: gmane.emacs.devel Subject: Re: Image transformations Date: Fri, 14 Jun 2019 06:45:41 -0400 Message-ID: References: <9A21DE14-BB5F-426E-BBB2-19C87930E733@gnu.org> <20190611200233.GA80199@breton.holly.idiocy.org> <83imta95z0.fsf@gnu.org> <20190612220746.GA89208@breton.holly.idiocy.org> <835zpa11qp.fsf@gnu.org> <83pnnhzlcp.fsf@gnu.org> <83imt9zcbr.fsf@gnu.org> Mime-Version: 1.0 Content-Type: multipart/alternative; boundary="000000000000b2e159058b465946" Injection-Info: blaine.gmane.org; posting-host="blaine.gmane.org:195.159.176.226"; logging-data="131765"; mail-complaints-to="usenet@blaine.gmane.org" Cc: Eli Zaretskii , Alan Third , Emacs Development To: Richard Copley Original-X-From: emacs-devel-bounces+ged-emacs-devel=m.gmane.org@gnu.org Fri Jun 14 12:52:50 2019 Return-path: Envelope-to: ged-emacs-devel@m.gmane.org Original-Received: from lists.gnu.org ([209.51.188.17]) by blaine.gmane.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.89) (envelope-from ) id 1hbjpB-000Y1P-8u for ged-emacs-devel@m.gmane.org; Fri, 14 Jun 2019 12:52:49 +0200 Original-Received: from localhost ([::1]:50114 helo=lists.gnu.org) by lists.gnu.org with esmtp (Exim 4.86_2) (envelope-from ) id 1hbjp8-0000Cp-CX for ged-emacs-devel@m.gmane.org; Fri, 14 Jun 2019 06:52:46 -0400 Original-Received: from eggs.gnu.org ([2001:470:142:3::10]:57885) by lists.gnu.org with esmtp (Exim 4.86_2) (envelope-from ) id 1hbjid-0008Jy-AO for emacs-devel@gnu.org; Fri, 14 Jun 2019 06:46:05 -0400 Original-Received: from Debian-exim by eggs.gnu.org with spam-scanned (Exim 4.71) (envelope-from ) id 1hbjiY-0008Rm-8F for emacs-devel@gnu.org; Fri, 14 Jun 2019 06:45:59 -0400 Original-Received: from mail-vs1-xe32.google.com ([2607:f8b0:4864:20::e32]:36382) by eggs.gnu.org with esmtps (TLS1.0:RSA_AES_128_CBC_SHA1:16) (Exim 4.71) (envelope-from ) id 1hbjiU-0008ED-Pj; Fri, 14 Jun 2019 06:45:55 -0400 Original-Received: by mail-vs1-xe32.google.com with SMTP id l20so1476593vsp.3; Fri, 14 Jun 2019 03:45:53 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:references:in-reply-to:from:date:message-id:subject:to :cc; bh=dT2SYZLiyCfvLk/d6Ry8x2zUBTVgCFoTVKn2zf0fK3c=; b=p4GeqqiOsoaryWP0skS5XRpXQIQhS+YAx08kMMknYhONoXTaG42EDGm8MPLsAg4cmy WqLSK+DQdHRPNk4xntZRX0i0vlOcGMc0wZ5RR0y0PQt3c+rHBerW9IJa7gOnu1elbkM1 Ca2wSzf2G5NWbWgynrpKUy0Ofqq4nkiXvrmX1nVMuiecdrzZhzAPMTBpV3nIEoI5S+qz xcQHFqiupcZLKv1RbgEfpBXiiNuMkhG3lVHzhtv1BM7YNSMEeHMjZJ6tQgqj7EuQWKqx pMIrULXd8Ew+0WQWAsp/BZsp4zQ9/qwJDuN5BazkzJiHtioDmBCxmxsLHCZjbC4CBQCZ R4+g== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:references:in-reply-to:from:date :message-id:subject:to:cc; bh=dT2SYZLiyCfvLk/d6Ry8x2zUBTVgCFoTVKn2zf0fK3c=; b=t19BbtL8ZtDY0BA5Clf166CGK0YipD83NDySBJiTnYMjv3jyOf/uxRjFZPiiL0Y/pp jecuw1TQ2J5PXuxvndhv6xM80ECAL1VynYTwJdh+cwSdO9ORHPH73JxUfmg7xIGl6SJj h7sBXj+YYb/3GSbcw08sGjkvB6UtCwkyvDBv1nBINnO25jftP/vedH5aQy5F1fNANlpz Y58krUTXhO1C7Lm3sLh3Un4T6bWv2gseQurS5WBzx0MTnv6XzF3GCbFs9qp3CnT4mH8W OTUY0iZbSRgX6gLBXExRYzJMCDSNzoGC4rqiaCgijKg+xAwUKAhJUAZu8OOpX9pdPLP0 NJtg== X-Gm-Message-State: APjAAAX4R81IiX/1qa2qsJmKxe2E+B1IUycsUh5Ou4QdloPF/YBGHjuO n0DoMDJaXqxcKaYRxDISZxPIg23raP4oFfAHp5k= X-Google-Smtp-Source: APXvYqxcq645Lcd6l8cBfkTXMttx5YNyUYe210ZvqianvNiMkGwf3Cp3BIain0SRNPj4E5TADRFTtil/ia7iHWMm4z0= X-Received: by 2002:a67:f518:: with SMTP id u24mr36369887vsn.87.1560509152418; Fri, 14 Jun 2019 03:45:52 -0700 (PDT) In-Reply-To: X-detected-operating-system: by eggs.gnu.org: Genre and OS details not recognized. X-Received-From: 2607:f8b0:4864:20::e32 X-BeenThere: emacs-devel@gnu.org X-Mailman-Version: 2.1.23 Precedence: list List-Id: "Emacs development discussions." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: emacs-devel-bounces+ged-emacs-devel=m.gmane.org@gnu.org Original-Sender: "Emacs-devel" Xref: news.gmane.org gmane.emacs.devel:237585 Archived-At: --000000000000b2e159058b465946 Content-Type: text/plain; charset="UTF-8" On Thu, Jun 13, 2019 at 3:01 PM Richard Copley wrote: > Yes, but our transformation includes translation, rotation, and > another translation. Not just one translation. IOW, it isn't the > transformation matrix that is given; it's the operation on the image. There's a miscommunication here. I was speaking to Alan's question about how to geometrically interpret the components of a transformation matrix. If the question is what translations to use in order to generate a rotation around an arbitrary point p, then there's no question: the sequence of operations is translation by -p, then rotation, then translation by p. > The origin is at the top left so a pure rotation clockwise about the origin > through angle a goes like this: > > [cos(a) -sin(a) 0] [X] [cos(a) * X - sin(a) * Y] > [sin(a) cos(a) 0] [Y] = [sin(a) * X + cos(a) * Y] > [ 0 0 1] [1] [ 1] That is a counter-clockwise rotation. --000000000000b2e159058b465946 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
On Thu, Jun 13, 2019 at 3:01 PM Richard Copley <rcopley@gmail.com> wrote:

> = =C2=A0 =C2=A0 Yes, but our transformation includes translation, rotation, a= nd
> =C2=A0 =C2=A0 another translation.=C2=A0 Not just one translatio= n.=C2=A0 IOW, it isn't the
> =C2=A0 =C2=A0 transformation matrix = that is given; it's the operation on the image.
=C2=A0
There'= s a miscommunication here.=C2=A0 I was speaking to Alan's question abou= t how
to geometrically interpret the components of a transformation matr= ix.

If the question is what translations to use in order to generate= a rotation
around an arbitrary point p, then there's no question: t= he sequence of
operations is translation by -p, then rotation, then tran= slation by p. =C2=A0

> The origin is at the top left so a pure ro= tation clockwise about the origin
> through angle a goes like this:>
> [cos(a) =C2=A0-sin(a) =C2=A00] [X] =C2=A0 [cos(a) * X - sin(= a) * Y]
> [sin(a) =C2=A0 cos(a) =C2=A00] [Y] =3D [sin(a) * X + cos(a)= * Y]
> [ =C2=A0 =C2=A0 0 =C2=A0 =C2=A0 =C2=A0 =C2=A00 =C2=A01] [1] = =C2=A0 [ =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2= =A0 =C2=A01]

That is a counter-clockwise rotation.
--000000000000b2e159058b465946--