| |
Oswald
Registered: Apr 2002
Posts: 5094 |
accurate 3d rotation
some silly questions & a lot of text here, its been ages I have done this routine and I am wondering where could I find more accuracy.
I am using the additive method to get the rotation matrix, working with 16 bit sines.
first, I wonder why have I choosen the sinetable max value to be +/- $1fff, there's no consecutive 4 adc's to have overflow over +/- $8000, still an adc / sbc pair may turn into adc/adc because of the case when substracting a negative number? :/ not sure if sine lookups may align this way. also should I round the 16 bit table or those bits will go bad anyway? (dont remember if I have rounded it, boy its been precalculated in basic in the stone ages:)
secondly, I keep adding #$40 to rotation angles in many places before looking them up in sincos tables. I suspect I am doing something wrong here, trying to turn the lookup value into cosine, while still having a label for the cosine offset. sin+$40= cosine, cosine+(angle+#$40)= ??? why ? :D or does this thing come from the sin*cos to addition theoremes?
third: if I recall right each adc/sbc introduces 1 bit error, is this true? so after 2 adc lowmost 2 bits in the 16 bit result is unusable?
fourth: flipping sign of a 2 complement 16 bit number is this correct?:
lda yxl ;*-1
eor #$ff
clc
adc #$01
sta yxl
lda yxh
eor #$ff
adc #$00
sta yxh
finally, getting a cube coordinate out of the rotation matrix, only using the HI bytes:
lda xzh ;mpp
clc
adc xyh
sec
sbc xxh
sta vertexes+0
should I rewrite this to gain accuracy including the low 8 bits?:
lda xzl
clc
adc xyl
sta templ
lda xzh
adc xyh
sta temph
...
etc
finally, rounding the final8 bits by looking at the low8 is a good idea? ie, if low8 (signless) msb is high, inc high8 bits? |
|
| |
JackAsser
Registered: Jun 2002
Posts: 2014 |
1. You want your input sines to be as accurate as possible, i.e. as many bits as possible and correctly rounded.
2. Sounds weird, but can be part of some older optimizations you did.
3. Since the input sines where rounded in the first place you really can't trust the least significant bit. So adding two untrusted bits will give you a really untrustworthy bit. :)
4. It is correct, but slow. See http://codebase64.org/doku.php?id=base:seriously_fast_multiplic..
5. Depends on what you wanna do. If you only place vector bobs or plots you only need HSB. But if you wanna to subpixel accurate bresenham you will init it with the LSB.
Hope that clarified some.... :P |
| |
Oswald
Registered: Apr 2002
Posts: 5094 |
#1 I will try to write a new sine gen, btw I am never sure, one should _ALWAYS_ correct with adc #$01 after eor #$ff ?:) (ie even when storing to table)
I dont get what you mean in #4, btw I have utilised your mul routine, but accuracy didnt change, I hoped you did it more accurate than me, but its "only" faster ;) probably I can get rid of sign flipping by better ordering tho.
#5, so you say using only HSB results in rock solid vertex movement?
also I have a problem with backface culling, I am calculating Z of the normal and it is of in about 5% of the frames, in edgy cases. is there a better method, somehow determine winding (order of vertices) with additive formulas or tables? In the past I got rid of this problem by some trial and error asl/lsr of the result, but I'd like a perfect solution. |
| |
JackAsser
Registered: Jun 2002
Posts: 2014 |
Quote: #1 I will try to write a new sine gen, btw I am never sure, one should _ALWAYS_ correct with adc #$01 after eor #$ff ?:) (ie even when storing to table)
I dont get what you mean in #4, btw I have utilised your mul routine, but accuracy didnt change, I hoped you did it more accurate than me, but its "only" faster ;) probably I can get rid of sign flipping by better ordering tho.
#5, so you say using only HSB results in rock solid vertex movement?
also I have a problem with backface culling, I am calculating Z of the normal and it is of in about 5% of the frames, in edgy cases. is there a better method, somehow determine winding (order of vertices) with additive formulas or tables? In the past I got rid of this problem by some trial and error asl/lsr of the result, but I'd like a perfect solution.
#4 i mean for sign-handling...
#5 yes. 8 bits result in 256 rocksolid positions. :)
Backface culling: determine which side of the poly the cam is. For a cube it's very simple. Theory:
Plane equation = ax+by+cz+d=0 abc=plane normal.
If the above is >0 then xyz is on the normal side of the plane, i.e. In-front or visible.
We know the cam is at origo+some z-dist hence we only get:
cz+d=0
Z is constant, i.e. The added z-dist to the object to get it in front of the cam. D is also static and only depends on the object, for a cube with size 1 D will be 1. So shuffle:
Z=-d/c
The -d/c is constant per face in the object, hence:
Z=k
Now z is the z-component of the normal. For a cube it's simply one of z-values of your vectors in the rotmatrix.
So to backface cull a side of the cube u have ALL already calced except for a cmp.
Simply look up the correct z-value in the rot matrix and cmp by the precalced K per face. if it's hard to get then picture each row in the rot-matrix defining the world axises of the rotated space. In normal unrotated space the x-axis is the normal to the sides od the cube. The y-axis to the top and bottom... Same in rotated space but the the x-axis isn't simply 1,0,0 but some x,y,z and u only need the z-value since the cam is in origo. |
| |
Oswald
Registered: Apr 2002
Posts: 5094 |
I have to think on this one, sounds like a method graham described earlier. does it work with perspective projection? |
| |
JackAsser
Registered: Jun 2002
Posts: 2014 |
Quote: I have to think on this one, sounds like a method graham described earlier. does it work with perspective projection?
It's the exact same method but Graham uses another way of thinking but yields the same result. I'll draw u a pic tonight. Yes, it works with perspective (it's built into the -z/d part, -z is really your distance to the screen which determins field of view) |
| |
Oswald
Registered: Apr 2002
Posts: 5094 |
According to your answers I do everything to the book, I think my perspective projection might be the problem (zooming more than available bits), thanks, and waiting for the pic, its really hard to get it by words :) |
| |
chatGPZ
Registered: Dec 2001
Posts: 11386 |
Quote:you really can't trust the least significant bit. So adding two untrusted bits will give you a really untrustworthy bit.
i'll print that on a t-shirt :) |
| |
JackAsser
Registered: Jun 2002
Posts: 2014 |
Quote: Quote:you really can't trust the least significant bit. So adding two untrusted bits will give you a really untrustworthy bit.
i'll print that on a t-shirt :)
:) one up!
Anyway, after rounding you are of at worst by 0.5 i.e. Half a bit. Each add will propagate the error so after n additions u'll be of by n/2. |
| |
Bitbreaker
Registered: Oct 2002
Posts: 508 |
As for negation of a 16 bit number see the example in http://www.codebase64.org/doku.php?id=base:advanced_optimizing#..
in general it is a good thing to think about swapping add/sbc at times also in term of saving clc/sec. Means, you can always add one too much and then again subtract one too much if carry has the wrong state and such and order your addition/subtraction that way that you merely never need to explicitely set the carry. |
| |
chatGPZ
Registered: Dec 2001
Posts: 11386 |
or just comment out all CLC and SEC and make a smash design demo =) |
... 13 posts hidden. Click here to view all posts....
|
| Previous - 1 | 2 | 3 - Next |
