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circle with no sines

   Author:       Pawel Niejadlik - Laffik of Dreamolers CAPS
   Uploader:     laffik laffik com
   Type:         dev/amos
   Version:      2.1.1.6
   Architecture: generic
   Distribution: Aminet
   Date:         2024-06-26
   Readme:       http://aminet.net/dev/amos/no_sine_circle.readme
   Downloads:    4

http://aminet.net/dev/amos/no_sine_circle.lha

New civilisation has happen - invoked by the discovery of a circle drawn

with no trigonometric functions.

Program draws a circle using Euler method of solving differential equations.

Program sets initial conditions of velocity for x coordinate and position

fory. Simulates spring resilience setting acceleration of a drawing point.

In case of x's initial conditions, method draws sine and cosine in case of

initial conditions of y. Constants required for drawing the circle

proportionally, were gained of empiric methods of linear approximation in

double logarythmic scale. There these constants become linear and supereasy

for approximating.

Circle gets of shape a bit, for amount of steps of iteration close to 1.

Upper limit of steps is set by precision of calculations. For not sufficient

precision of calculations at superhigh amounts of steps, program falls into

multiple drawing, limited by accidental fall into full cycle's detection.

Computer arythmetic's low precision reduces probability of proper detection

of finished drawing. Keep amount of steps below 1.000.000 for usual Amos

precision.

Similar algorythm was presented in early 90's in Polish magazine Amigowiec.

I didn't recall it good enough to write it today, much enough it had been

coming to my mind while reading control theory, filter design, numeric

methods of maths and differential equations scripts. Basing on these,

I reproduiced this original solution nowadays.

Contents of dev/amos/no_sine_circle.lha

PERMISSION  UID  GID    PACKED    SIZE  RATIO METHOD CRC     STAMP     NAME
---------- ----------- ------- ------- ------ ---------- ------------ ----------
[generic]                  565    1372  41.2% -lh5- dc53 Jun 26  1980 no sine circle.amos
[generic]                  867    1660  52.2% -lh5- e859 Jun 26  1980 no sine circle.readme
---------- ----------- ------- ------- ------ ---------- ------------ ----------
 Total         2 files    1432    3032  47.2%            Jun 27 03:27