[Oberon] Oberon-7 - Circle Segments

John R. Strohm strohm at airmail.net
Wed Feb 20 01:49:08 CET 2019

You can do an iterative approximation using multiply and add/subtract.

I don't guarantee the following.  You'll need to recheck the trig and the derivation.

Recall from basic trigonometry:

   cos u+du = cos u cos du - sin u sin du
   sin u+du = sin u cos du + cos u sin du

Set du to your step size in radians, and precalculate cos du and sin du.  Call them c and s, respectively.

Set u to 0, precalculate initial x = cos 0 = 1.0 and y = sin 0 = 0.0.

Then the iteration becomes something along the lines of:

   x_new := x * c - y * s;
   y_new := y * c + x * s;
   x := x_new;
   y := y_new;

The catch is that you will need a wide, precise multiply and add. 

You may have to synthesize this from single-precision integer multiplication if you don't have a stable double-precision floating-point system.

Consider using rounding bits in the two iteration addition steps, to control rounding error.

--- schierlm at gmx.de wrote:

From: Michael Schierl <schierlm at gmx.de>
To: ETH Oberon and related systems <oberon at lists.inf.ethz.ch>
Subject: Re: [Oberon] Oberon-7 - Circle Segments
Date: Tue, 19 Feb 2019 22:52:14 +0100

Hello Tomas,

Am 19.02.2019 um 18:23 schrieb Tomas Kral:

> I probably cannot do without trigonometry, right?

sine and cosine of 30°/60°/90° are all nice values (0, 0.5, sqrt(0.75),
1), so you can hardcode the values. For the square root you can use an
approximation if you want to avoid calculating it.


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