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!AWMay93/Goodies/2dWaves/!2DWaves/!help

This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.

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Filename: !AWMay93/Goodies/2dWaves/!2DWaves/!help
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Exec address: 0000
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File contents
                        ____________________________________

                        !2DWave by Jan Vlietinck (8-12-1992)
                        ____________________________________


1. Introduction
===============

2DWave is simulation program for two dimensional waves. The program is both educative and entertaining. The idea is to simulate waves exactly as they would behave in real live. Such waves are waves on a water surface, acoustic waves produced by a speaker and even electro magnetical waves.
The waves are calculated according to the correct physical rules described by the Laplace differential equation, resulting in a smooth colourful animation.
On an Arm2 machine, 12.5 full screen frames per second can be displayed. Those frames are at the full 320x256 resolution of the 256 colours mode 13. Special hand optimised Arm machine code had to be written to achieve this speed.


2. Workings
===========

Internally the wave plane is represented by a two dimensional array with each point having two states : height and velocity of a cell. On the screen each pixel is coloured according to the height of a point on the wave surface. The calculations resembles those of a cellular automat. The new height is the old one added with a number proportionally to the velocity. The new velocity is the previous one multiplied by a viscous damping factor and incremented proportional to the difference between the average height of the four surrounding cells and the current height of the cell.
Thus :
  h'(x,y) =   h(x,y)+a*v(x,y)
  v'(x,y) = b*v(x,y)+c*(h(x-1,y)+h(x+1,y)+h(x,y-1)+h(x,y+1)-4*h(x,y))/4

Where h(x,y) and v(x,y) are the height and velocity of a cell on position (x,y). In the program : a=1, b=1-2^-n, c= 2^-m.
To speed up calculations, interpolation is used. For a full screen 320x256 display, only a 80x64 mesh is calculated. The other points are found by interpolation.


3. The menu
===========

After starting the program you are presented with the menu screen. The menu which is surrounded by a rectangle is divided in three submenus : 'actions', 'options' and 'settings'. A selection in this menu can be made by moving the mouse on one of the entries and clicking the left mouse button.


3.1 Actions submenu
-------------------
The actions submenu is used to enter wave sources in a number of ways before starting a simulation. The excitation of a source is either generated by the computer or you can control it with the mouse. The computer controlled sources produce a sinusoidal excitation of which the amplitude, frequency, phase and position can be entered.

When selecting 'automatic' a number of random sources are configured and the wave simulation starts.

Selecting the second entry in the menu leads to the 'semi-automatic' control screen. On the left top of this screen, the amplitude, frequency, phase and position of the current source are displayed.
A source is represented by a solid circle, the current source is surrounded by a white circle. Also the current wave is graphically represented by a sinusoid. By moving the mouse you can alter the position of the source, clicking the left button enters the source.
Holding down the right mouse button and moving the mouse allows you to change the amplitude and frequency of the current source. Horizontal movements control the frequency while vertical movements alter the amplitude. The parameters of a source can also be configured by pressing the '1 2 3' and 'Q W E' keys to increase and decrease the amplitude, frequency and phase. When you have entered all the required sources the simulation is started after clicking the middle button.

The third, 'manual', entry in the actions submenu allows you to control a source with the mouse whilst simulation. Moving the mouse up and down controls the amplitude of the source. Moving the mouse and clicking the right button repositions the source. Holding down the left button and moving the mouse produces an effect similar to that of a boat sailing through the sea.

The 'continue' entry allows you to continue simulation after suspension.

At any time during simulation the action can be frozen by holding down the right button. Returning to the menu screen is done by clicking the middle button.


3.2 Options submenu
-------------------
The 'options' submenu allows you to switch on and off various options.
Clicking on one of the three option switches the option on, another click switches it back off. The on state is depicted with a mark to the left of the option.

Setting on the 'projection' option gives you a three dimensional, perspective, projection of the simulation.

The 'loose edges' option allows you to choose between fixed or loose edges of the simulated surface. Fixed edges is like the film of a tambour while loose edges resembles water in a pool.

When the 'colour lookup' option is on, the colour of every pixel is translated via a lookup table before display, to give a more pretty colour display of the waves. When this option is off and projection is chosen then all the points are coloured white to give a look more reminiscent of water waves.

At any time during simulation the three options can be toggled on and off with a key to give instant change. To toggle the projection, edge and colour effect, press the 'P','E' and 'C' key.


3.3 Settings submenu
--------------------
With the 'settings' submenu some physical parameters of the simulated plane can be reconfigured. To alter the default value click on one of the five entries, enter a chosen number and press return. Out of range
numbers are automatically constrained to the maximum or minimum value.

With the 'width' and 'height' parameters the physical extent of the plane may be set. The width may be varied between 10 and 80 while the height is variable between 10 and 64.

The 'viscosity' and 'time step' value determine the behaviour of the simulated plane. The viscosity factor may be varied between 1 and 10. A value of 1 gives a very watery appearance. Entering the maximum of 10 gives a very viscous, syrupy, simulation.
Also the time step factor can be varied between 1 and 10. 10 is the default, a lower number allows you to slow down the action by reducing the elapsed simulation time between successive frames.

Finally the 'base colour' option allows you to shift through the colour pallet.


4. Saving the screen
====================     

At any time during simulation the current frame can be saved. Pressing the 'S' key causes the current screen to be saved. There is no need to enter a file name; all screens saved are automatically named as Dump0, Dump1,... Ensure that sufficient space is available on discs before saving!


5. Hints and tips
==================

- Projection is more attractive with loose edges.
- Colour lookup is prettier but it slow down the simulation considerably.
- Simulation with small width and height may execute too fast, therefore you should reduce the time step.
- When you find that the waves decay to slowly then increase the viscosity factor.
- Dipole sources are constructed with two very close sources with the same amplitude and frequency but with a phase difference of pi. To avoid reflections at the edges which would spoil the effect increase the viscosity to 7.
- Analogous a swirl may be generated by four sources with the same amplitude and frequency but with phases 0, 0.5, 1 and  1.5 pi, positioned in a close cross formation.
- Also watch some sources with low amplitude and high frequency superimposed on a source with a high amplitude and low frequency.
- Base colour 140 also gives nice colours.


Enjoy the program !




Any comments welcome at :

Jan vlietinck
Essendreef 15
8300 Knokke-Heist
Belgium


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00000050  20 20 20 20 20 20 20 21  32 44 57 61 76 65 20 62  |       !2DWave b|
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00001a20  48 69 6e 74 73 20 61 6e  64 20 74 69 70 73 0a 3d  |Hints and tips.=|
00001a30  3d 3d 3d 3d 3d 3d 3d 3d  3d 3d 3d 3d 3d 3d 3d 3d  |================|
00001a40  3d 0a 0a 2d 20 50 72 6f  6a 65 63 74 69 6f 6e 20  |=..- Projection |
00001a50  69 73 20 6d 6f 72 65 20  61 74 74 72 61 63 74 69  |is more attracti|
00001a60  76 65 20 77 69 74 68 20  6c 6f 6f 73 65 20 65 64  |ve with loose ed|
00001a70  67 65 73 2e 0a 2d 20 43  6f 6c 6f 75 72 20 6c 6f  |ges..- Colour lo|
00001a80  6f 6b 75 70 20 69 73 20  70 72 65 74 74 69 65 72  |okup is prettier|
00001a90  20 62 75 74 20 69 74 20  73 6c 6f 77 20 64 6f 77  | but it slow dow|
00001aa0  6e 20 74 68 65 20 73 69  6d 75 6c 61 74 69 6f 6e  |n the simulation|
00001ab0  20 63 6f 6e 73 69 64 65  72 61 62 6c 79 2e 0a 2d  | considerably..-|
00001ac0  20 53 69 6d 75 6c 61 74  69 6f 6e 20 77 69 74 68  | Simulation with|
00001ad0  20 73 6d 61 6c 6c 20 77  69 64 74 68 20 61 6e 64  | small width and|
00001ae0  20 68 65 69 67 68 74 20  6d 61 79 20 65 78 65 63  | height may exec|
00001af0  75 74 65 20 74 6f 6f 20  66 61 73 74 2c 20 74 68  |ute too fast, th|
00001b00  65 72 65 66 6f 72 65 20  79 6f 75 20 73 68 6f 75  |erefore you shou|
00001b10  6c 64 20 72 65 64 75 63  65 20 74 68 65 20 74 69  |ld reduce the ti|
00001b20  6d 65 20 73 74 65 70 2e  0a 2d 20 57 68 65 6e 20  |me step..- When |
00001b30  79 6f 75 20 66 69 6e 64  20 74 68 61 74 20 74 68  |you find that th|
00001b40  65 20 77 61 76 65 73 20  64 65 63 61 79 20 74 6f  |e waves decay to|
00001b50  20 73 6c 6f 77 6c 79 20  74 68 65 6e 20 69 6e 63  | slowly then inc|
00001b60  72 65 61 73 65 20 74 68  65 20 76 69 73 63 6f 73  |rease the viscos|
00001b70  69 74 79 20 66 61 63 74  6f 72 2e 0a 2d 20 44 69  |ity factor..- Di|
00001b80  70 6f 6c 65 20 73 6f 75  72 63 65 73 20 61 72 65  |pole sources are|
00001b90  20 63 6f 6e 73 74 72 75  63 74 65 64 20 77 69 74  | constructed wit|
00001ba0  68 20 74 77 6f 20 76 65  72 79 20 63 6c 6f 73 65  |h two very close|
00001bb0  20 73 6f 75 72 63 65 73  20 77 69 74 68 20 74 68  | sources with th|
00001bc0  65 20 73 61 6d 65 20 61  6d 70 6c 69 74 75 64 65  |e same amplitude|
00001bd0  20 61 6e 64 20 66 72 65  71 75 65 6e 63 79 20 62  | and frequency b|
00001be0  75 74 20 77 69 74 68 20  61 20 70 68 61 73 65 20  |ut with a phase |
00001bf0  64 69 66 66 65 72 65 6e  63 65 20 6f 66 20 70 69  |difference of pi|
00001c00  2e 20 54 6f 20 61 76 6f  69 64 20 72 65 66 6c 65  |. To avoid refle|
00001c10  63 74 69 6f 6e 73 20 61  74 20 74 68 65 20 65 64  |ctions at the ed|
00001c20  67 65 73 20 77 68 69 63  68 20 77 6f 75 6c 64 20  |ges which would |
00001c30  73 70 6f 69 6c 20 74 68  65 20 65 66 66 65 63 74  |spoil the effect|
00001c40  20 69 6e 63 72 65 61 73  65 20 74 68 65 20 76 69  | increase the vi|
00001c50  73 63 6f 73 69 74 79 20  74 6f 20 37 2e 0a 2d 20  |scosity to 7..- |
00001c60  41 6e 61 6c 6f 67 6f 75  73 20 61 20 73 77 69 72  |Analogous a swir|
00001c70  6c 20 6d 61 79 20 62 65  20 67 65 6e 65 72 61 74  |l may be generat|
00001c80  65 64 20 62 79 20 66 6f  75 72 20 73 6f 75 72 63  |ed by four sourc|
00001c90  65 73 20 77 69 74 68 20  74 68 65 20 73 61 6d 65  |es with the same|
00001ca0  20 61 6d 70 6c 69 74 75  64 65 20 61 6e 64 20 66  | amplitude and f|
00001cb0  72 65 71 75 65 6e 63 79  20 62 75 74 20 77 69 74  |requency but wit|
00001cc0  68 20 70 68 61 73 65 73  20 30 2c 20 30 2e 35 2c  |h phases 0, 0.5,|
00001cd0  20 31 20 61 6e 64 20 20  31 2e 35 20 70 69 2c 20  | 1 and  1.5 pi, |
00001ce0  70 6f 73 69 74 69 6f 6e  65 64 20 69 6e 20 61 20  |positioned in a |
00001cf0  63 6c 6f 73 65 20 63 72  6f 73 73 20 66 6f 72 6d  |close cross form|
00001d00  61 74 69 6f 6e 2e 0a 2d  20 41 6c 73 6f 20 77 61  |ation..- Also wa|
00001d10  74 63 68 20 73 6f 6d 65  20 73 6f 75 72 63 65 73  |tch some sources|
00001d20  20 77 69 74 68 20 6c 6f  77 20 61 6d 70 6c 69 74  | with low amplit|
00001d30  75 64 65 20 61 6e 64 20  68 69 67 68 20 66 72 65  |ude and high fre|
00001d40  71 75 65 6e 63 79 20 73  75 70 65 72 69 6d 70 6f  |quency superimpo|
00001d50  73 65 64 20 6f 6e 20 61  20 73 6f 75 72 63 65 20  |sed on a source |
00001d60  77 69 74 68 20 61 20 68  69 67 68 20 61 6d 70 6c  |with a high ampl|
00001d70  69 74 75 64 65 20 61 6e  64 20 6c 6f 77 20 66 72  |itude and low fr|
00001d80  65 71 75 65 6e 63 79 2e  0a 2d 20 42 61 73 65 20  |equency..- Base |
00001d90  63 6f 6c 6f 75 72 20 31  34 30 20 61 6c 73 6f 20  |colour 140 also |
00001da0  67 69 76 65 73 20 6e 69  63 65 20 63 6f 6c 6f 75  |gives nice colou|
00001db0  72 73 2e 0a 0a 0a 45 6e  6a 6f 79 20 74 68 65 20  |rs....Enjoy the |
00001dc0  70 72 6f 67 72 61 6d 20  21 0a 0a 0a 0a 0a 41 6e  |program !.....An|
00001dd0  79 20 63 6f 6d 6d 65 6e  74 73 20 77 65 6c 63 6f  |y comments welco|
00001de0  6d 65 20 61 74 20 3a 0a  0a 4a 61 6e 20 76 6c 69  |me at :..Jan vli|
00001df0  65 74 69 6e 63 6b 0a 45  73 73 65 6e 64 72 65 65  |etinck.Essendree|
00001e00  66 20 31 35 0a 38 33 30  30 20 4b 6e 6f 6b 6b 65  |f 15.8300 Knokke|
00001e10  2d 48 65 69 73 74 0a 42  65 6c 67 69 75 6d 0a 0a  |-Heist.Belgium..|
00001e20

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