2d rotate by VLA
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;
; TITLE: 2d rotate text file
;WRITTEN BY: DRAEDEN
; DATE: 02/13/93
;
; NOTES: None.
;
;ASSOCIATED FILES:
;
; BWPRINT.ASM => Displays signed and unsigned bytes, words, or
; > double words
;
; SINCOS.DW => Contains data for the sine and cosine operations
;
; ROTATE.ASM => The asm file.
;
; MAKE.BAT => The file that'll put it all together into an .EXE
;
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Rotating a point around (0,0):
Rotating an object is really easier than it sounds. There is just a
simple formula for it, which is:
Xt = X*COS(φ) - Y*SIN(φ)
Yt = X*SIN(φ) + Y*COS(φ)
If you don't think this works, try a few values. For at instance φ = 0°,
Xt = X*1 - Y*0 = X
Yt = X*0 + Y*1 = Y
And at φ = 90°,
Xt = X*0 - Y*1 = -Y
Yt = X*1 + Y*0 = X
Both of which work. Also note that the rotation is counter-clockwise.
If you wanted it to rotate clockwise in stead, the formula would be:
Xt = X*COS(φ) + Y*SIN(φ)
Yt =-X*SIN(φ) + Y*COS(φ)
Or you could just negate the angle.
Now, if you wanted to rotate in 3 demensions (I hope this is obvious),
you would need 3 angles which I call Xan, Yan, and Zan. The formula would
be the same as above, but done 3 times.
1st, rotate on the X axis
Y = Y*COS(Xan) - Z*SIN(Xan)
Z = Y*SIN(Xan) + Z*COS(Xan)
Next, rotate on the Y axis
X = X*COS(Yan) - Z*SIN(Yan)
Z = X*SIN(Yan) + Z*COS(Yan)
And finally, the Z axis
Xt = X*COS(Zan) - Y*SIN(Zan)
Yt = X*SIN(Zan) + Y*COS(Zan)
You should notice that the order in which you rotate the object DOES
matter. To see the how, grab a disk and rotate it 90° along the X axis,
90° along the Y axis, and then 90° on the Z axis. Now try the rotations in
a different order. Different results, eh?
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And now an explaination of SINCOS.DW
SinCos.dw is a file which contians the sine of the 'angles' 0-255. I
used 256 angles because it is very convienent, and there just happens to
be a data structure that has a range of 0-255. It's called a BYTE, denoted
by 'DB'.
The bit of code (in BASIC) that would generate this sort of chart is:
────────
FOR i = 0 TO 255
an = i*2*pi/256
BYTE = INT( SIN( an )*256 +.5)
>> Store BYTE in a file <<
NEXT i
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Modifying the basic rotation formula for our data file would yield:
Xt = (X*COS(φ) - Y*SIN(φ)) /256
Yt = (X*SIN(φ) + Y*COS(φ)) /256
If you know your hexadecimal, you'd realise that dividing by 256 is
simply a "SAR XXX,8", where XXX is what you're dividing by 256.
I expanded this into assembler, that not only works, but is very fast.
To see it, examine the RotateXY procedure.
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BWPRINT.ASM
This file is just a little utility I put together many many years ago.
Ok, maybe not years, but It seems that long. I wrote it when I first got a
386. No more CAVEMAN computer! Oh well. The basic functions are:
PrintByte, PrintWord, and PrintBig.
They do this:
PrintByte: decodes a byte (in AL) and displays it as 3 digits plus a
an optional sign. If the carry is clear, it prints it as an
unsigned integer. If the carry is set, it prints it signed.
────
EXAMPLE:
mov al,-50
stc
call PrintByte
────
PrintWord: decodes and prints a WORD (in AX) in 5 digits.
────
EXAMPLE:
mov ax,50000
clc
call PrintWord
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PrintBig: decodes and prints a DOUBLEWORD (in EAX) in 10 digits.
NOTE: PrintBig requires a 386 to use.
────
EXAMPLE:
mov eax,-1234567890
stc
call PrintBig
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Well, that's it for now. See INFO.VLA for information on contacting us.
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