🚀 go-pugleaf

In <7336@hub.ucsb.edu> 6600mage@ucsbuxa.ucsb.edu (Orion Wilson the Passable) writes:

>	.. Have you seen these hacker demos where
>the balls or whatever follow sinusoidal paths around
>the screen? And where there are HUNDREDS of balls
                                ^^^^^^^^^^
It depends on the size of the "balls", and how many planes. Most I've seen is
240 or so, 16*11(?)*2bp "balls".

>all going very smoothly through what appear to be
>complex hypo-cycloids and such?  
>My question is how these paths are computed. The
>number of objects and their speed incidates that
>they aren't being done by floating-point techniques,

Don't do it with FFP. It takes way too long. Since you have to recalculate every
frame and redraw(use the blitter), you can only calculate about 30 points.

>and i'm pretty sure the numbers are not
>pre-calculated, so it seems that smooth curves like
>the sin and cos can be done using integer (native
>MC68000) arithmatic.
>	
>	Is this so? Does anybody out there know what
>these algorythms are? Am i posting in the wrong
>area? And why hasn't my mouse come home?

>	For the answers to these questions and more,
>	 please write me so i may learn.

Do you want to start up a new newsgroup - "amiga.teachme68k" ?
Here's some code for a 3d rotation. The blitter line drawing routine can be 
found on pages 163-165 of Abacus' "Amiga System Programmer's Guide" or you could
easily find someone to tell you. I've used the code below for a filled vector
graphic demo(still not yet released though). I can't find many other ways to 
optimize the code(with respect to speed,not size). I assume you know about
swapping which planes are being displayed(eg.work on one, display other). Don't
use rubbish like the Taylor series to work out angles. People who recommend it
have been studying Mathematics too long and obviously don't code much. You don't
need to change the base positions. Just use pointers to places within the sine
table. Well, actually, this is untrue for some routines, and some other nice 
effects(of course), like merging from one shape to another. You'll need to do
a bit more work to get the nice hyperboloid effects, but we wouldn't want you to
get there too easily. Put some effort it. Anyway here's some text I wrote a 
while back:

ANGLETABLE:	360 Sine words stored multiplied by 32767. All cosine angles
		are sin(angle+90degrees).
		One pair for each angle stored here.
	eg.  0.8386 is [(8386*32767)/10000]  =  27478 ($6b56)
            -0.4324 is [(-4324*32767)/10000] = -14168 ($c8a8)

	They are thus used : (see rotation example at end)
	  A0: pointer to angle table
	  D1: offset of angle
	move.w	number,d0
	muls	(a0,d1.w),d0
	lsr.l	#8,d0
	lsr.l	#7,d0
	bclr	#16,d0		; often unnecessary
	  D0: now contains integer position

		Storage: blk.w	360,0
		Angles : 91 words (for sine angles 0-90 degrees). All other
			  angles in the angletable can be made from these, so
			  leave block storage at end.
	***** ***** ***** ***** ***** ***** ***** ***** ***** ***** 
	dc.l	$0000023b,$047706b2,$08ed0b27,$0d610f99 ;  0 -  7
	dc.l	$11d01405,$1639186c,$1a9c1cca,$1ef72120 ;  8 - 15
	dc.l	$2347256c,$278d29ab,$2bc62dde,$2ff23203 ; 16 - 23
	dc.l	$340f3617,$381c3a1b,$3c173e0d,$3fff41ec ; 24 - 31
	dc.l	$43d345b6,$4793496a,$4b3b4d07,$4ecd508c ; 32 - 39
	dc.l	$524653f9,$55a5574b,$58e95a81,$5c125d9c ; 40 - 47
	dc.l	$5f1e6099,$620c6378,$64dc6638,$678d68d9 ; 48 - 55
	dc.l	$6a1d6b58,$6c8b6db6,$6ed96ff2,$7103720b ; 56 - 63
	dc.l	$730a7400,$74ee75d2,$76ad777e,$78467905 ; 64 - 71
	dc.l	$79bb7a67,$7b097ba2,$7c317cb7,$7d327da4 ; 72 - 79
	dc.l	$7e0d7e6b,$7ec07f0a,$7f4b7f82,$7faf7fd2 ; 80 - 87
	dc.l	$7feb7ffa,$7fff0000			; 88 - 90
	***** ***** ***** ***** ***** ***** ***** ***** ***** ***** 

			  THREE DIMENSIONAL ROTATION
			  --------------------------
   (x,y,z)  must be rotated with matrices (in any order) :
	|cos -sin 0||x|		|cos 0 -sin||x|		|1  0	 0 ||x|
	|sin  cos 0||y|		| 0  1   0 ||y|		|0 cos -sin||y|
	| 0    0  1||z|		|sin 0  cos||z|		|0 sin  cos||z|
   however this can be done with the standard rotation matrix A :
     A =|cos -sin|	A|x|	A|x|	A|y|	NB. Make sure the correct
	|sin  cos|	 |y|	 |z|	 |z|	    angle is used each time.

	***** ***** ***** ***** ***** ***** ***** ***** ***** ***** 
	A0: pointer to angle table
	A1: x position
	A2: y position
	A3: z position
	D0-D2/D4-D7: work
ROTATION:	-getangle(d6,d7)	; D6: sine offset about Z axis
		move.w	a1,d4		; D7: cosine offset about Z axis
		move.w	a2,d5
		bsr.S	MATRIX
		move.w	d0,a1
		move.w	d1,a2
		-getangle(d6,d7)	; D6: sine offset about Y axis
		move.w	a1,d4		; D7: cosine offset about Y axis
		move.w	a3,d5
		bsr.S	MATRIX
		move.w	d0,a1
		move.w	d1,a3
		-getangle(d6,d7)	; D6: sine offset about X axis
		move.w	a2,d4		; D7: cosine offset about X axis
		move.w	a3,d5
		bsr.S	MATRIX
		move.w	d0,a2
		move.w	d0,a3
		......
		......
		rts

MATRIX:		move.w	d4,d0
		muls	(a0,d7.w),d0
		lsr.l	#8,d0
		add.l	#64,d0	(round off properly-remove if unnecessary)
		lsr.l	#7,d0
		move.w	d5,d1
		muls	(a0,d6.w),d1
		lsr.l	#8,d1
		add.l	#64,d1	(round off properly-remove if unnecessary)
		lsr.l	#7,d1
		sub.w	d1,d0
		move.w	d4,d1
		muls	(a0,d6.w),d1
		lsr.l	#8,d1
		add.l	#64,d1	(round off properly-remove if unnecessary)
		lsr.l	#7,d1
		move.w	d5,d2
		muls	(a0,d7.w),d2
		lsr.l	#8,d2
		add.l	#64,d2	(round off properly-remove if unnecessary)
		lsr.l	#7,d2
		add.w	d2,d1
		rts
	***** ***** ***** ***** ***** ***** ***** ***** ***** ***** 
-- 
	+---------------------------------+       _  _ _ _  __
	|	     Geoff		//|   /\  |\/|  |  / _   /\
	| static@phoenix.pub.uu.oz.au \X/ |  //\\ |  | _|_ \__| //\\
	+---------------------------------+