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2017-08-20 16:28

Trap

Registered: Jul 2010
Posts: 223

How to make efficient double-sine calculations

Hi,

I am trying to improve a little on my effect animation skills. To that purpose I'd like to hear how you guys solve the issue of double-sine table calculations. As I am by no means a math-guru - not even close, try to keep it at a practical level :)
Sure, there has to be some clever way around this. Usually I'd do something like the following mock-up code:

lda Counter1 // Copy counters to indexes
sta Index1
lda Counter2
sta Index2
ldx #TableSize
!CalcAnim: ldy Index1
lda SineWave1,y // Get first value
iny // Index1 Delta + 1
sty Index1
ldy Index2
clc
adc SineWave2,y // Add second value
iny // Index2 Delta + 1
sty Index2
tay
lda Lookuptable,y // Find the value and store it
sta Destinationtable,x
dex
bne CalcAnim-
lda Counter1
clc
adc #1 // Velocity 1
sta Counter1
lda Counter2
clc
adc #1 // Velocity 2
sta Counter2

Apart from unrolling the loop, I am short of good ideas on how to make this efficient. Use of ZP for the indexes saves a few cycles as well.
How do you guys approach this in your demos?

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2017-08-22 14:59

Dano

Registered: Jul 2004
Posts: 234

Me doing it mostly the Oswald-way these days. With ROR if needed..

2017-08-22 15:10

lft

Registered: Jul 2007
Posts: 369

Quoting Trap

Lft, that's an interesting thought - could you elaborate?

Well, it depends on what you need the values for, of course. The simplest case would be an 8x8 plasma, where you just use sin(x)+sin(y) as the character value, and put a gradient pattern in the chars. With ECM you can have many colours in the gradient. To animate, you just modify the scale and origin of the coordinate system (x and y independently), and recompute.

Now suppose you want to render f(sin(x) + sin(y)) all over the screen (1x1 plasma), and let's say you limit yourself to sixteen different values of sin(y) and sixteen different values of sin(x). Then you can precalc full lines (wider than the screen) of graphics for each possible sin(y) inside each half of each font bank. Based on your desired scale and offset for the x axis, you compute char references into the first row of each of two video matrices -- one that picks chars from the first half of the font, and one that picks from the second half. Then you fetch that into the VIC chip with a badline, and repeat the same line over the entire screen, while switching banks according to sin(y) on each line.

2017-08-22 15:36

Oswald

Registered: Apr 2002
Posts: 5094

lft, that sounds excitingly cool, but your description is impossible to follow for me. 1x1 pixels? how ? :D

one way of 8x8 (char reso) plasma I can imagine is having charsets like:

cset0 char0: picks gradient 0+0
cset1 char0: picks gradient 0+1
cset2 char0: picks gradient 0+2

cset0 char1: picks gradient 1+0
cset1 char1: picks gradient 1+1
cset2 char1: picks gradient 1+2

that way by switching charsets one can do the +sin(y) with the VICII. The beauty of this is, it is enough to render only one line compared to usual "raster plasma" (my terminology) routines, which need to precompute all lines for the possible sin(Y) values per frame. the downside is only 8 different charsets, maybe thats why you talk about half fonts and 2 screens, to have 16 virtual charsets.

2017-08-23 06:29

lft

Registered: Jul 2007
Posts: 369

Sorry for my confusing description. It was a bit hurried. The last part is quite wrong too, because if we use two video matrices in that way, we have to trigger badlines on every line.

Anyway, here is an example of what I mean. A single VIC-bank is used. In the Y direction, it's normal FPP with 16 choices. In the X direction, by rewriting the video matrices, we are looking at a 40-chars-wide subsection of a complete cyclic pattern of 123 chars (leaving 5 chars = 40 bytes for the first video matrix row). The animation (x-wobble and colour cycle) is built into the pattern.

2017-08-23 13:26

Oswald

Registered: Apr 2002
Posts: 5094

thanks, that makes it clear :)

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