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Scream #02
29 января 2002 |
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Tutorials - coding: the effect of the implementation of "Mirror rotator" (article is intended for quite prepared demo coder).
| Coding
| Vivid / / brainwave
I would like to first make a digression. Some
of you have probably read zero release Kovrov e
Newspaper Kosme, let the group Placebo (ex-Eternity
Industry). The newspaper contained articles coder'a main groups,
Sairoos'a of the demoscene. Let me just say that I, as a coder,
in many respects solidarity with Cyrus. In many respects, but
not in all. Namely, I was incomprehensible to his wild reaction
to our DeMouy Tryptomine Dream. And if a personal dislike for
multicolor Cyrus, I can still understand (me, for example,
chunks do not really like), then his words of which explicitly
or implicitly followed the conclusion that almost all in
Tryptomine Dream done with animation, even calculate in
advance, could not vizvat in my soul storm indignation. Of
course, we are with him in person at CC'01 figured out all the
misunderstandings, but some readers Kosme after this article
may already formed a negative opinion about the group Brainwave
and demah. After CC, I tried to connect with Placebo via
e-mail'a requesting a rebuttal of negative words he addressed
to us, but had still not received response. So we have to do
their own refutation. ;) Taking this opportunity I can safely
say the entire Spectrum demoscene: "In all demah issued under
label Brainwave no animation in the conventional sense
the word! "That is no pre-loaded
sequence of frames in our demah was not there and, hopefully,
will not. Pre-calculated animation (ie animation, footage of
which calculated during dekryanchinga, and then just output) in
us demah also been applied. True, it was in the 4k Marazm
advance calculated chess heart, but it's been a long time, and
excuses for idiocy two-year statute of limitations I have not
going, besides it's an isolated case.
Now, the question of terminology. Clear separation between
animation and realtime not. More on CC'01 I had a dispute with
Flying ^ DR and Sair00s ^ PCB on this topic. Say, can we
consider 3d animation output facility beforehand a calculated
coordinates its vertices? And using the Look Up Tables (Bump
mapping, Sphere mapping, Tunnel ,...)? And the use of sine
tables when calculate 3d instead of an honest calculation of
sines formula Taylor? Everyone in this respect his opinion. So,
something I afield in the wrong direction. I'm, like, going to
write about the coding article. These and loans.
It is assumed that the article is designed to fairly
prepared a demo coder, which has a base set
knowledge.
Mirror rotator.
It first appeared on the Spectrum in Deme Refresh and GOA4k,
written Exploder ^ Extreme, then reincarnated in our Deme
Tryptomine Dream in Multicolor implementation. By the way,
Cyrus his accepted for prekalkuleyting (see, confused
multicolor, 25fps (Which he felt for 50) and podzagruzka in
front of him). Immediately the algorithm of its own
implementation.
I have a texture of size 128 * 128 pixels. And in druh
identical copies. In the center of each texture is so
called the View port, the size of the screen (in my case
64 * 48).
To get the effect you just use the normal
Rotate-Zoomer, using a pattern from the first buffer to output
Viewport into the second buffer. Further, the pattern of the
second buffer spreads on the screen. When drawing the next
frame is the role of texture of the source performs a second
buffer, and the role teksturypriemnika - the first.
This is a general algorithm. Now the details of my
implementation.
Rotozumer - pretty zhruschy effect, so use
classic 60 innerlupa clock is too
slow to resolve 64 * 48. Therefore been made
simplification (by the way, the Refresh and GOA was the same):
Using the tangent of the sine instead, limiting the angle of
rotation from-pi / 4 to + pi / 4. This gave the opportunity to
move on texture along the X axis with step 1, and the axis Y -
a step tg (alfa). Lack of - Zuming itself depends only on the
angle and its be flexible to change. Dignity - the calculation
of the color of one point it takes only 20 cycles:
ldi; toss the point and, simultaneously, shifts in X
nop; here in decrunching'a substituted Team
; Nop, inc h or dec h for the need to shift
, Y-axis in the texture
Further, direct that for which it was implemented:
multicolor himself. The effect is calculated in parallel with
the withdrawal multicolor. Advantage: rational use time
processor. Disadvantage: difficult to write, although it can be.
In order to create a multicolor 4 * 4, it is necessary (in my
implementation), so that even lines stored on a single screen
and odd - on the other. Thus it is necessary to switch from
screen to screen through 224 * 4 = 896 cycles (hereafter assumed
Timing under the Pentagon-128). On the calculation of one row
vysheupomnutym innerlupom takes 20 * 64 +? cycles, ie 1300
cycles. It turns out that to calculate a single line of 896
beats impossible. Hence we have two choices:
1. Calculate the start of the line, switch the screen
calculate the remainder of the line, to make the delay to 896 *
1792 cycles do not forget to switch the screen. In this case,
we lose just so about 500 cycles. I think, Full Screen 25 fps
Mirror rotator in this case is not done.
2. I chose this way, although it is more laborious. Must
switch screens through 896 cycles, without pausing between
calculations rows. This is a fairly trivial task, since
the nature of innerlupa (need recalculated team
standing after ldi, for each frame again) does not allow
razdekryanchit this code on all the available memory. In
addition, this remaining memory remains relatively small (32
kilobytes is texture, 8 kilobytes of the screen and the
variables of Basic, plus the code needed More and other
things). Only one way out: subverted with dynamic breakpoints.
Talk about this only briefly (for details, already rusty,
because more than a year. Who's supposed to, can see source).
In general, the main loop looks like this:
org # ed00; why # ed00, learn more
ld bc, # 7ffd
ld de, # 1018
ld h, # ed
exx
...
ld sp, AddTab
loop: calculate the address of the current row, etc.
rept 64
ldi: nop
endr
calculation addresses the underlying string
ret
exit:
One would think, why are ret? And here is why:
1. when necessary, performs the role of team djnz, only holds
for 10 cycles instead of 13;)
2. when necessary, removes the address of a small protsedurki
type:
exx
ld l, xx
ld (hl), # c9; command code ret
, Set a breakpoint on the location code #
ED
; Team ldi
exx
ret; go to top of the loop
Once this ret we turn to a procedure similar to the following
read:
exx
out (c), d; or out (c), d, depending on whether
; What screen should include
ld (hl), h; restore code # ed team ldi
; This is where that innerluprazmeschen on
; At # ed00;)
ld l, xx
ld (hl), # c9; put a new breakpoint
exx
ret; exit from the breakpoint
AdrTab table contains the addresses to go to these
protsedurki and addresses out of the breakpoints. The table is
compiled so that swapping screens do not occur during the upper
and lower border, saving precious cycles.
Once the picture is rendered in the buffer in the form
Munk'ov (Short Multicolor Chunk, invented by me for
denote elements of the image is one byte, and
non-color code), it is necessary to bring it (buffer) on the
screen in as attributes. This is a very simple operation, and
Pasha. Munk'i have the numbers to, say, # f8 on # ff. In the
address # f8f8 # ffff is the table of the form:
# F8f8: 00 01 02 03 04 05 06 07
# F9f8: 08 ... 0f
...
# Fff8: 38 39 3a 3b 3c 3d 3e 3f
To brighten the table must contain the numbers from # 40
to # 7f.
Conversion Munk'ov to attributes is satisfied innerlupom:
; Sp-munky buffer
; De-screen address (attr)
rept 32
pop hl
ldi
endr
26 cycles for a couple of lures.
The effect is ready. I hope that someone understood
something.
One frame multicolor Mandelbrot fractal zoom.
It can contemplate at least in our Deme Stellar Contour for
CC'01. Many mistook it for an animation, thinking that Spectrum
such work can not do. It turned out that at some wit
and dexterity, can be done using code.
First, briefly about the algorithm for drawing a fractal
Mandelbrot: We have a complex plane (or plane
complex numbers).
That over the complex plane (or plane of complex numbers)?
Those in the know, can skip the next couple of paragraphs.
Let it be known that the root of a negative number
you can still learn, except that the resulting number is not
real (Real) (1, 2, 5.6523) and imaginary (Image). Ie
For example:
sqrt (-9) = sqrt (-1 * 9) = sqrt (-1) * sqrt (9).
The square root of -1 is called the imaginary unit and
denoted by the letter i (in some literature, the letter j).
Hence, the root of -9 is:
sqrt (-1) * sqrt (9) = i * 3.
Complex is the number of Z = A + i * B, where A and B -
real numbers, i - imaginary unit. In this case, A -
real part (denoted by Re (Z)), B - the imaginary part
(Denoted by Im (Z)). The complex plane - it ploskot, Po
horizontal axis which defers the actual
component of a complex number, and the vertical axis -
imaginary. For example, a complex number of the form Z = 3 + 5
* i on the complex plane will be the point with coordinates (3,
5).
Since complex numbers are numbers, then for them
determined by the arithmetic (and not only the operation). We
are interested in primarily the operations of addition and
squaring:
Build:
C1 = A + i * B; the first number
C2 = X + i * Y; the second number
C3 = C1 + C2 = A + X + i * (B + Y); ie real numbers
are added separately, imaginary - separately.
Squaring:
(A + i * B) ^ 2 = A ^ 2 + 2 * A * i * B + i ^ 2 * B ^ 2 =
(taking into account the fact that i ^ 2 =- 1) = A ^ 2 - B ^ 2
+ i * 2 * A * B
Each complex number is characterized by a modular approach,
deystvitelnynm number equal to its distance from the beginning
coordinates:
R = | Z | = sqrt ((Re (Z)) ^ 2 + (Im (Z)) ^ 2)
So, with compl. ploskotyu understood, it remains to deal with
algorithm for drawing the Mandelbrot fractal. So, we have
plane of complex numbers, every point of which is painted in
certain color. Sovokoupnost these points as time and forms
Mandelbrot fractal. How to determine the color point of knowing
her coordinates? Here's how:
C = X + i * Y - a complex number, or, roughly speaking, our
point on the plane with coordinates (X, Y)
We have some complex number Z, which was originally set to 0 (or
0 + i * 0).
So, we calculate the loop following formula rekurentnuyu
Z (k) = (Z (k-1)) ^ 2 + C
up until the module Z (k) becomes a very large number
(About 10E100) or until the loop is not executed for some
number of iterations (about 100-10000). How many times
execute cycle, will depend on the color of our point.
Software can implement something like this:
Input:
X0, Y0 - coordinates of the point corresponding to the upper
left corner Screen cpl. plane.
SCALE - scale. (The smaller the greater the degree of
magnification). SCRX, SCRY - the size of the window, which will
be painted on the fractal.
double yy = Y0; / / Y coordinate of the upper corner of the
screen
/ / Cpl. plane
for (int Y = 0, / / loop through the rows
Y 0)''(Re2 + Im2 <1e100);
PutPixel (X, Y, color); / / draw point in the buffer
}
}
Everything would be fine, except that danna program, being
running on a Pentium-233, will draw in the window 128 * 64 8
colors of each frame somewhere along the half-second. What to
say about Speccy our poor thing: (. Yet all is not as bad as it
seems. The first thing that might come to mind, because it put
the steam pisyuk for 5 minutes, so we figured that a few
hundred frames size, say 64 * 32, and we then ask them to
Speccy somehow draw. And you can apply the delta-packing
(stored only difference between adjacent frames, the rest
remains unchanged). Data is stored as follows: first there is a
stream of bits, each set in one bit of which indicates that
that the corresponding byte of attributes (we're in a multicolor
do) you need to change, and thrown in zero indicates that
should leave it unchanged.
rl e; 8
jr nc, pausa0; 15/20
ld a, (hl); 22
ld (bc), a; 29
inc l, c; 33
jr next1; 45
pausa0: or (hl); 27
or (hl); 34
or (hl); 41
nop
next1: ....
Total 41 cycles per 1 byte. A string of 32 bytes takes about
1300 cycles. But, since we need to keep multicolor have
done at the end of the line delay to 1792 cycles (during this
time pentagon has time to display eight rows).
All is good, only I frame compression more than 8 times, not
receive, and other ways of packing for a multicolor
problematic. But the real picture will be compressed somewhere
4 times or 5, that the amount of frame-buffer 1964 * 32 will
make semolina about 250 bytes per frame. It turns out that for
some 5 seconds zuming we will take more than 60 kilobytes of
RAM. Given that the demo - is, above all, demonstrate the
possibilities of computer it turns out that only on the
spectral Galimov anime several seconds to turn. That is why I
strongly rejected this leymovogo ways to implement a fractal
zoom.
Realizing that assume a fractal in real-time on the Spectrum
- the idea Of course, the heroic, but no one party will not
wait 5 minutes, while our hero Speccy render another frame, it
was necessary act cleverly and with the help of PCs. Since the
soundtrack in Stellar Contour comes with a 3 rate, and under
zuming scheduled to take four pattern of 64 notes (768
Mounting), it was decided to implement effect as follows:
I'm using this prog to render to the HRC 27 phases
fractal zoom, each of which represents an increase
the same area of the fractal 2-fold greater than in
previous phase. Each frame was to render 128 * 64
(Output planned to make the window 60 * 32) in 8 colors, and
occupied, respectively, of 4096 bytes. The algorithm is as
follows: for Interrupt hanging procedure that gently (up to 28
frames) increases (right on the screen, without any additional
buffers) the current phase of fractal image dvuhkrantogo reduce
to normal size, while the other buffer
and burn the next phase. The idea is good, but 4k * 27 phases
- Is 108 kilobytes! Worse than that is the case with anime. The
solution came quickly - to keep in mind these 27 intermediate
phases in packed condition, and unpack them at the time zuming
the previous phase. Heh, clever idea. Here are just zuming
eats about 60,000 cycles, leaving about 11 free
thousand. 11 000 cycles * 28 = Mounting approximately 300,000
cycles, ie Roughly speaking, I should have time to unpack 4
kilobytes to 4 Inta! Crunching and hrum not good because of
insufficient speed unpacking. So I had to write your own
pakovschy and extractor, which would combine a decent degree of
compression and I unpack the required speed. Given the nature
of pakuemyh data (bytes from 0 to 63), it was decided to write
a wrapper, sharpened under the packing is of such data.
Algorithm for extracting (According to him, by the way, it
becomes clear packing algorithm):
* Codes # 00 to # 3f: just write the byte.
* Codes # 40 to # bf: for example, popallos number # ad, then
write # 0d +2 = 15 bytes with the code # 36 (inc = # A-4 = 6,
paper = 6)
* Codes # c0 on # cf: repeat the last byte of decompressed
(N-# be) again.
* Codes # d0 to # fe: toss n - # cd bytes of the following
the input stream are stored packed by 6 bits. Allows
saving of 2 bits in one byte nepakuyuschemsya
* Code # ff - a sign of the end of the block.
Packer, written by me on some frames to yield results
Even better than hrust 1.3 (natural comparison was made
without taking into account the lengths unpackers). By the way,
he squeezed every frame faster than a second. That's what
packer, sharpened under compression of a particular type of
data. In my case - an 8-color texture. Unpacking, of course,
fit into the bounding boxes with a small margin.
As a result, the output began to occupy about 28-29
kilobytes instead of 108. After compression Khrust already
packed Data managed to win some kilobytes.
Now calculate the total ratio:
During his tenure, is generated 28 * 27 = 756 frames size
30 * 32 = 960 bytes. Ie More than 700 kilobytes. Takes it all
farm of about 30 kilobytes. There is a compression somewhere in
the 24-fold.
Call this an animation effect or not? No brainer, that even in
name and contains the word Fractal Zoom, the calculation of the
fractal is not attending at all. But zuming realtaymovy. Well,
those intermediate 27 staff of 756 - want to count the
animation, you want - do not count.
Now a few words about zuming. Here, too, had to think (it
think, not s3.1415zdit from somewhere) algorithm sharper
larger bitmap. Feature of the first: he zumit image
stored in compressed form (2 munk'a in one byte) and
directly to the attributes (also sealed format). The problem
arises fast transcoding back and forth. I solved this problem
with using tables, which allow you to extract individual munk
from bytes from the source and move it to either the left or the
right half of the byte the receiver.
TBL2L TBL2R TBR2L TBR2R
L R L R L R L R
V V V V
L R L R
To improve the speed, I duplicated one of these tables, and
tables themselves placed in memory as follows
TBL2R equ xxxx
TBL2L equ TBL2R + # 100
TBR2R equ TBL2L + # 100
TBR2L equ TBR2R + # 100
TBL2R_ equ TBR2L + # 100
Innerlup for each phase of scaling had razdekryanchit
advance on the whole line. For example innerlup to increase to 1
just looks like this:
pop de; take 2 bytes of image
ld l, e
ld h, TBL2L/256
ld a, (hl); extract from the left half of the bytes in
the left
inc h; move to TBR2R
or (hl); combine with the right half of byte
ld (bc), a
inc c
ld l, d
ld h, TBL2L/256
ld a, (hl)
inc h; move to TBR2R
or (hl)
ld (bc), a
inc c
Naturally, at the end of each line must be provided
delay for the entire innerlup executed exactly 1792 cycles.
There. Reveal the secret of another effect.
Multicolor Doom.
Well, Doom - it loudly. Most likely, Wolf.
This effect - my pride. Even after CC'000 I had an idea
implement something in multicolor, at first glance
unrealizable in it. And so, at a cost of business more than a
month coding, I wrote to this effect. Brief technical
Features:
Resolution: 64 * 32
Number of colors: 8 multicolor
Frames per second: 16.7 (!). One frame is rendered in 3 Inta.
Map Size: 32 * 32
Texture Size: 16 * 32
Number of textures: 32
Additional features: there was an opportunity to put more on
Bottom Border to scroll type RAGE'ovskogo. However, due to lack
of Time had to scroll to score. Especially because not scroll
quite fit in with doom'om. Well, yes and God bless him.
I must say that this effect is completely realtaymovy. No
prekalkuleytinga Image not available. To prove
that I have in Peter compile this effect by adding to it
control of the keyboard and added to the resulting surrogate
As a bonus to Deme;). So that all non-believers may simply
steer on the map by pressing Q, A, O, P, L, Enter.
Applied the following "distorted":
1. Realtaymovaya ray tracing.
2. Realtaymovy scaling textures.
3. Inside innerlupa multicolor, the procedure of multiplication
bytes per word.
4. Innerlup contains a bunch of branches. While each branch
were counted manually.
5. All calculations are, of course, conducted in parallel with
the withdrawal multicolor.
Thus, the general idea of the effect.
I must say I have used is not quite correct algorithm.
In fact, it is done without ray tracing. First, it
somewhat faster, and, secondly, to avoid errors
calculations. However, the multicolor-free way to implement
trace in parallel with the withdrawal of multicolor impossible.
Thus, the essence of the trace:
We have a center of the chamber (indicated by a
symbol "o"), the camera direction (axis z).
Plane of the screen: (denoted by AB).
Plane of the screen is divided into 64 columns
(Each column width of 1 munk). We call
their clusters (I do not care how they
called, I'll call them
clusters). Carried out a ray from the center
chamber through each cluster to
collision with the wall (in the figure is a ray of oD) or until
exceeded the maximum length of the ray (I have it, as far as I
remember it 7 blocks of cards). The coordinate of intersection
determined which column in the texture should draw, and on
length of the projection beam to the axis direction is
determined by the height this column. It remains only to draw
it into the buffer.
Hehe, it's not so easy as we would like. If you approach
the matter bluntly, the rate will be very small. Firstly, in
I move around the map is not pixel by pixel, and immediately
block by block. Secondly, all the bias and the coefficients for
each angle (0 .. pi / 4) and each cluster is calculated in
advance (hence the pause somewhere in the 10 seconds at
dekryanchinge). Third, to find a point intersection of the
procedure byte multiplication on the floor, which had
razdekryanchit 256 times that it was done always for 204 cycles
(with the CALL and RET). In addition, it was necessary also
razdekryanchit procedure of scaling of textures and trace rays.
As a result, the size of the source is around 90 KBytes format
ZXAsm. Perhaps it is wrong. But write and 90 kilobytes of
source code to debug procedures similar to me pokazalo easier
than to write and debug dekryancher that himself would have
done the job. Okay, more importantly, what works and like, not
buggy.
Describe here all details is not desirable. Therefore, the
study source.
Free Directional Tunnel.
This can be seen in Baidu Deme Dogma by Eternity
Industry. Let's just say I was fascinated by the courage of
Cyrus that implemented this effect on the Spectrum. However, I
believe that this effect is still not for the Speccy, since its
implementation in chunk will be seen the error of computation,
so this article I shall confine ourselves algorithm that can
easy to implement on a more powerful machine is not
particularly izgolyayas with assembler.
This effect is realized on the principle of ray tracing
drawn from the camera focus to its intersection with the wall
of the tunnel.
Thus, the tunnel is the usual infinite cylinder
radius R0. To simplify the formulas we assume that the camera
can only move in a straight line is the axis of the
Cylinder:
=========== P ======================================
============ <
/ ^ X or Y
/
R0 /
O *> Z
U
>
================================================== ============
The texture is superimposed on the cylinder as follows:
U coordinate in the texture changes as well as Z, ie along
walls of the tunnel. V coordinate in the texture izmenyaets
uniformly circumference of the tunnel.
In this case, the camera can only move along the axis Z.
So, you need to find a point of intersection of the ray OP (x,
y, z) with wall of the tunnel.
Coordinate Zi intersection points from the condition:
R1 z z * R0
- = - => Zi = ----- R0 Zi R1
Here: R1 = sqrt (x ^ 2 + y ^ 2).
Knowing Zi can define U:
U = Zi * k + U0, here k - a rate from which
depends on how the texture is stretched along the axis Z. Can,
in Basically, take it to 1, U0 - basic coordinates in
texture, changing which can create the illusion of camera
movement along the axis of the tunnel.
Coordinate of V is determined from the condition that it is
linearly varies around the circumference of the tunnel. Ie
knowing the angle between vertical and the vector (x, y, 0) we
can calculate the coordinates of V:
arctan2 (x, y) * N
V = ---------------
2 * PI
Function arctan2 (x, y) returns the arctangent value
(X / y), if y <> 0, and 0 otherwise.
If the texture has dimensions Un x Vn, then N = Vn.
Thus, the formula for finding the coordinates in the texture
we have left to decide what to do with them. I hope that the
reader knows the formula of rotation around the axis point. If
not, just case of recall:
Around the axis x:
x '= x
y '=-sa * y + ca * z
z '= sa * z + ca * y
Around the axis y:
x '=-sa * x + ca * z
y '= y
z '= sa * z + ca * x
Around the axis z:
x '=-sa * x + ca * y
y '= sa * y + ca * x
z '= z
x ', y', z '- Tochni coordinates (x, y, z) after rotation.
sa - the sine of the angle of rotation around this axis
ca - cosine of the angle of rotation around this axis
The camera we have the following parameters:
SX - width in pixels
SY - height in pixels
SC - distance from the focus of the camera to the plane of the
screen. From this parameter depends on the angle of the camera.
It is equal to:
angle = arctan ((SX / 2) / SC) * 360/PI - angle camera on X.
Usually prinimat Scale equal to SX / 2. In this case, the
viewing angle is 90 degrees. With viewing angle of 120-130
degrees, and more becomes apparent prospect of an unnatural
image.
So, now we know the camera parameters and 3D rotation
formula. Now we just turn a mere 3 points the camera:
ULC (-sx / 2,-sy / 2, SC) - upper left corner of the screen
URC (sx / 2,-sy / 2, SC) - upper right corner of the screen
DLC (sx / 2, sy / 2, SC) - lower left corner of the screen
After turning obtain points:
ULC '(x0, y0, z0)
URC '(x1, y1, z1)
DLC '(x2, y2, z2)
Knowing them, we can find two vectors:
VX = (URC'-ULC ') / SX = ((x1-x0) / SX, (y1-y0) / SX, (z1-z0) /
SX) VY = (DLC'-ULC ') / SY = ((x2-x0) / SY, (y2-y0) / SY,
(z2-z0) / SY)
VX - a vector, which moves in the 3D coordinate of a point
rotated the plane of the screen when you shift to a single
pixel on Horizontal
VY - the same thing, but vertically.
Why do we have these vectors? And then, knowing them, we can
harvested from 3-m points easily find the coordinates of each
pixel rotated the plane of the screen, and it is nothing like
coordinate of the ray drawn from the focus of the camera at a
given pixel screen. Here's something for him and find the
coordinates by the formulas intersection with the wall of the
tunnel.
Of course, honestly cheat each pixel of the screen
the above formula - a very laborious exercise, even for
fairly powerful machines, not to mention the Speccy, so it is
usually is calculated by these formulas in the texture
coordinates for each of the 8th (or 16th) of every 8th (or
16th) line, ie in grid nodes, and then linearly interpolate
them within each square 8 * 8 (or 16 * 16). Thus it is possible
to achieve significant gain in speed with passable image
quality.
Similarly, by the way, you can create and the effect of
rotation camera inside the sphere, only the formulas for ray
tracing will somewhat different. I suggest the reader to take
them, as well as improved algorithms for ray tracing inside the
tunnel for that the camera could be not only on its axis, but
any point inside the tunnel.
For those interested in 3d graphics, I can recommend to read
Demo.Design 3d programming FAQ, which once could
find www.enlight.ru. There, he set out the basic minimum without
knowledge and understanding of which work properly with 3D
graphics quite problematic.
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