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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 ; ──────────────────────────────────────────────────────────────────────────── 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? ──────────────────────────────────────────────────────────────────────────── 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 ──────── 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. ──────────────────────────────────────────────────────────────────────────── 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 ──── 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 ──────────────────────────────────────────────────────────────────────────── Well, that's it for now. See INFO.VLA for information on contacting us.
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