Echo #01 31 октября 1996

Программирование

Assembler - The image of three-dimensional objects. Fast output point AT X, Y. The procedure of multiplication.

    ---------------------
     Three-dimensional image

          objects.

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   Everyone saw the Slovak demo
ECHOLOGY. Is not it cool?
(We are talking about its 3D PART).


   Now I try to tell
how to do it.

 1) you need to write a quick conclusion
point, because he has a bigger impact on the final performance
the program;

 2) then write a quick conclusion
entire length (or rather the vector)
speed of this procedure
in second place in importance;

 3) Do what you want ...
(With jokes I napryazhenka!)


    I will cite a few figures to
which we should strive to write the output point and a segment:


   Point - about 100/110T

   Point in the interval 200T

I have got these results,
but it does not mean that
can be done faster ...


  Now we must do in order to coordinate the sequence was 
connected segments (those you'll get a stable position object 
on the screen, such sustained, that even the sequence of 
commands di: halt does not erase a screen fruits of your labor).



  In the end, you still
tired of footing the monitor ... ugh! ... screen, and ought to 
his povertet (or twist). 


  Ah! I forgot to remind that
in 3DGRAPH (well, this is where the three axes:
X, Y and Z), each point is given by
three coordinates.


  And now I will smite you all,
stating that the derivation for
screen 3D-points should be used
only two coordinates: X and Y (not
Is it true you hit?).


  Okay, back to the question of
turns (and bloat) figures.


  Let me give a few formulas that I use (and probably
someone else):


   a) rotation by an angle (a) around
axis X: X '= X;

         Y '= COS (a) * Y-SIN (a) * Z;

         Z '= SIN (a) * Y + COS (a) * Z;


   b) rotation by an angle (a) around
axis Y: X '= SIN (a) * Z + COS (a) * X;

         Y '= Y;

         Z '= COS (a) * Z-SIN (a) * X;


   c) rotation by (a) around
axis Z: X '= COS (a) * X-SIN (a) * Y;

         Y '= SIN (a) * X + COS (a) * Y;

         Z '= Z;


   I hope that you will not be before output figures count
its position, and pre-create the table (if the object is drawn
segments, the table is better
do not store the coordinates of the vertices, and
vector, so it will be faster ...).


   How to store a number or vector
in the table?


   Personally, I use this method: the number of modulo unlikely 
to be more than # 7F, then the seventh bit will be a milestone: 
1 number is negative, 0 positive. 


   For a vector we need to know
displacements and their directions. Ie
vector will hold in memory 2
bytes (first byte offset and the direction of axis X, the 
second - on Y). 


    On the question of errors.


   When I wrote a three-dimensional
effect, it just did not get a heart attack, seeing my lovely
cube in 2 seconds of rotation has turned in the wrong Allen 
(also a good effect!) It turned out that the whole point of 
error, which was in the calculations. 


   I can give you a few tips:

 1) All calculations are performed in
calculator ROM (or, in his);

 2) the intermediate results
Keep a 5-byte format;

 3) rounding of be carried out only
for those numbers that are entered
in the table, but their real
value left for subsequent calculations;


   I speed up the table for a cube of 200 of its provisions, 
using ROM, about 40 seconds. 


   I roughly know what to do
that figure is not only rotate
but increased and decreased
during the rotation, but he has not yet
do (laziness).

 P.S. If This is all

       ably filtered, then

       from it can be pulled

       some useful information
       mation.

 P. P. S. Almost everything I RASSC
       Hall of 3D-graphics you shall see
       babe in our DISTURBANCE

       Demo, which will soon long
       zhno out (or maybe not

       exit).


       DISTORTER (Demkovich Ivan)

       ADIA SOFT, Brest, 08.27.1996


            224017, Brest

            Moscow, 267/3-47

            Call (0162) 411655

+------------------------------+


   Comment VfNG / NHG:


   That's ADIA poprikalyvatsya.
Article as a whole is interesting,
something really pull
possible. I will cite, in addition
several useful things:

1) rapid withdrawal point AT X, Y:


   LD H, D; 4

   LD E, (HL); 7

   INC H; 4

   LD A, (HL); 7

   LD L, B; 4

   INC H; 4

   OR (HL); 7

   LD C, A; 4

   INC H; 4

   LD B, (HL); 7

   LD A, (BC); 7

   OR E; 4

   LD (BC), A; 7


   Only 70 cycles.


   What-where to be on vhodene say that was interesting.
Nobody said that it is this
procedure must be used when
output. This is so for a workout.

2) Classroom protsedurka multiplication
(Much like a sticking
ECHOLOGY):


   H-number 1;

   E-number 2;

   L, D = 0;


   ADD HL, HL

   JR NC, L1

   ADD HL, DE
L1 ADD HL, HL

   JR NC, L2

   ADD HL, DE
L2 ADD HL, HL

   JR NC, L3

   ADD HL, DE
L3 ADD HL, HL

   JR NC, L4

   ADD HL, DE
L4 ADD HL, HL

   JR NC, L5

   ADD HL, DE
L5 ADD HL, HL

   JR NC, L6

   ADD HL, DE
L6 ADD HL, HL

   JR NC, L7

   ADD HL, DE
L7 ADD HL, HL

   JR NC, L8

   ADD HL, DE
L8

   Output - the HL result.


   Here, wisely applied the decomposition of numbers into 
binary factors. I strongly advise to look into This protsedurke!


3) The numbers in the interval [0, 1) recommend multiplying by 
256 and in a format to store. If you necessary, for example, to 
multiply the sine number on any crap, then

protsedurkoy previous one is done as: H-sine * 256 (if it
is equal to 1 and you still going to
him something to multiply, then ...),
E-this same crap at the output: in
H integer, L the fractional part of the result.

4) The angles are much nicer to consider
not in degrees or radians, and
1 / 256 full twist.

5) Use of calculator
ROM-barbarism. For intermediate research is still here and 
there, but no more. Work with your own, cleverly written 
procedures gives the acceleration factor of 10-20 compared with 
Rom. Error Actually, not so scary.

Quite enough accuracy to 1 / 256.

6) With zoom in / out, too, is simple: multiply the X and Y
??? / Z (again, think of yourself!).


   All I'm here ponapisyval,
In no case can not be used directly in the oak. Here
you some ideas, hints: think.
We can not say, of course,
that it is my highest achievement
(Like any normal person
their secrets so just will not tell). Incidentally, my 
conclusion is chertilochke 22-110 (Mean 40) beats ... And in 
general in the scriber point output should go faster than just 
from goosey.



         Can do better?

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