Garland of pearls

[bplus]

There is much more to it than interesting!
I asked the question on a Hungarian physics forum on facebook. If there is a meaningful answer, I will inform you! It needs to be addressed!

Hello !
It will be a little longer now. I want an answer to a question I haven't been able to sleep in days :)
Anyone who follows the group may know that I am involved in programming. It used to be machine control, more recently the math behind games. (Interestingly, behind the game programming are the most outdated applications of mathematics)
My recent creations:

I have only considered it important to note this now because I have been dealing with them feverishly lately. The basic development environment, in which I program, can only draw 1 triangle on the screen. That's why I wrote the graphic "engine", the camera movement, the physical background of the movements myself. This developer is so unpopular that I don't think QB64 is known in Hungary. I like to be active in a foreign forum because there are about a handful of people (a handful on a global scale) who struggle with this outdated developer and appreciate it.
Here a forum member wrote a simulation of a pendulum motion. This should be imagined as a fixed point + rigid connector + some weight + rigid connector + some weight .... What happens if we push? He returned the thing quite realistically on the screen. It’s some crazy math, a lot of computation, and limited because it works with 2 “weights,” and with 3, but 4 or more has so much computation that it crumbles all over and can’t be shown in real time.
I had an idea then. What if we created points in space / plane without giving it fixed coordinates. All you need to know about that point is that it is located relative to another point. There should be nothing else for that point other than to strive to maintain its relation to the other point specified.
Do this: "current situation" = "current situation" + ("where you should be" - "current situation") x "all"
This is important here. If "all" is 0, no change is made. If 1, an immediate change occurs. If all are between 0 and 1, it gives a proportionality to the dynamics / flexibility / speed of change.
Now I want to express the point somehow. Imagine a "space." It contains objects. Objects are defined by point clouds. In point clouds, we make connections between points. To an adjacent, or object center, or just a smooth random point, we connect the 1 given point within the point cloud that we just want to define, "smart." We determine for him how far away he should be from that other point ... We will try to make as many such "connections" as possible at all points in that point and that object so that he is as smart as possible and will know "where he is. ".
If this is the case, start the "simulation"! Suppose thousands of points are defined as above. Each point begins to move at such a speed / direction that the connections assigned to it can be fulfilled. All right, we're waiting ... after a while, all movement will stop. "system balanced". The shapes are nicely outlined in front of us.
Now move only 1 out of position !!! that is, ONE point !!!!!!!! This will affect the points you are connected to ... and also the points you are connected to ... and those .... so everyone is running that 1 pulse. A mechanism is starting. Impulses give and take ...
The video shows how I programmed this principle differently. Chain, an image, and a cobweb. In each case, I gave relationships to the points as above. The thing works. And here comes the point. Smart people have already written the mathematical model for every event in Newtonian physics. Rigid-body, wave curves, collision of bodies, pendulum motion, centrifugal force .... what else to say ???????????????
This idea, which I did, completely bypasses the knowledge and use of these. The screen is fully functional. You don't need any physical knowledge or complications. We need a point and the strengths of its connections and connections (or how long we tie it to another point) (perhaps a metaphor for mass?)
Using the principle, we can in principle simulate all Newtonian physics by completely circumventing their use. Example..something .... if we create a brick wall based on the above principle, we can shoot a brick out of it so that the wall collapses in reality..etc ... that's just 1 of the many options.
Here's my question. Unfortunately, I did not study mathematics or physics at higher levels. I'm sure this thing isn't some kind of invention. This can only be new to me. This may be a known, existing theory that is also taught in good places. I would like to ask those who were so lucky to learn things like what it is? what is it used for where can i find writing about this
Thank you!

(just a small philosophical remark: if we hit the wall! the above principle would show the tiny vibration of every part of the wall. what if the above principle simulates the connection between molecules? since reality "renders" so fast that we can't even measure it with instruments, we're just amazed at the end result, because it happens so fast that we can't see, so we don't understand)
To download programs running under video (running under windows) with source code:
https://drive.google.com/file/d/1hkIqbFx_JGzhYpGdQjZ1h0lZYFtiw3Ce/view?usp=sharing

Ha! I don't think a spring connects every particle with every other but makes an interesting computer experiment.

Code: QB64: [Select]

1. _Title "Mouse down, drag ball, release...  Boing" 'B+ 2019-01-08 from
2. 'boing.bas for SmallBASIC 2015-07-25 MGA/B+
3. 'coloring mods
4.  
5. Const xmax = 1200
6. Const ymax = 700
7. Screen _NewImage(xmax, ymax, 32)
8. _ScreenMove 80, 20
9.  
10. Dim s(1 To 4, 1 To 2)
11. s(1, 1) = 0: s(1, 2) = 50
12. s(2, 1) = 0: s(2, 2) = ymax - 50
13. s(3, 1) = xmax + 30: s(3, 2) = 50
14. s(4, 1) = xmax + 30: s(4, 2) = ymax - 50
15. oldtx = 0: oldtyty = 0: da = .03
16. boingx = 0: boingy = 0
17. While 1
18.     While _MouseInput: Wend
19.     mb = _MouseButton(1)
20.     If mb Then
21.         tx = _MouseX + 20
22.         ty = _MouseY
23.     Else
24.         tx = xmax / 2
25.         ty = ymax / 2
26.         If tx <> oldtx Or ty <> oldty Then
27.             boingx = 3 * (tx - oldtx) / 4
28.             boingy = 3 * (ty - oldty) / 4
29.         Else
30.             boingx = -3 * boingx / 4
31.             boingy = -3 * boingy / 4
32.         End If
33.         tx = tx + boingx
34.         ty = ty + boingy
35.     End If
36.     a = 0
37.     oldtx = tx
38.     oldty = ty
39.     Cls
40.     For corner = 1 To 4
41.         s1x = s(corner, 1)
42.         s1y = s(corner, 2)
43.         dx = (tx - s1x) / 2000
44.         dy = (ty - s1y) / 2000
45.         x = tx - 20
46.         y = ty
47.         For i = 1 To 2000
48.             sx = 20 * Cos(a) + x
49.             sy = 20 * Sin(a) + y
50.             Line (sx, sy + 5)-(sx + 4, sy + 5), _RGB32(118, 118, 118), BF
51.             Line (sx, sy + 4)-(sx + 4, sy + 4), _RGB32(148, 148, 148), BF
52.             Line (sx, sy + 3)-(sx + 4, sy + 3), _RGB32(238, 238, 238), BF
53.             Line (sx, sy + 2)-(sx + 4, sy + 3), _RGB32(208, 208, 208), BF
54.             Line (sx, sy + 1)-(sx + 4, sy + 1), _RGB32(168, 168, 168), BF
55.             Line (sx, sy)-(sx + 4, sy), _RGB32(108, 108, 108), BF
56.             Line (sx, sy - 1)-(sx + 4, sy - 1), _RGB32(68, 68, 68), BF
57.             x = x - dx: y = y - dy
58.             a = a + da
59.         Next
60.     Next
61.     For r = 50 To 1 Step -1
62.         g = (50 - r) * 5 + 5
63.         Color _RGB32(g, g, g)
64.         fcirc tx - 20, ty, r
65.     Next
66.     _Display
67.     _Limit 15
68. Wend
69.  
70. 'Steve McNeil's  copied from his forum   note: Radius is too common a name
71. Sub fcirc (CX As Long, CY As Long, R As Long)
72.     Dim subRadius As Long, RadiusError As Long
73.     Dim X As Long, Y As Long
74.  
75.     subRadius = Abs(R)
76.     RadiusError = -subRadius
77.     X = subRadius
78.     Y = 0
79.  
80.     If subRadius = 0 Then PSet (CX, CY): Exit Sub
81.  
82.     ' Draw the middle span here so we don't draw it twice in the main loop,
83.     ' which would be a problem with blending turned on.
84.     Line (CX - X, CY)-(CX + X, CY), , BF
85.  
86.     While X > Y
87.         RadiusError = RadiusError + Y * 2 + 1
88.         If RadiusError >= 0 Then
89.             If X <> Y + 1 Then
90.                 Line (CX - Y, CY - X)-(CX + Y, CY - X), , BF
91.                 Line (CX - Y, CY + X)-(CX + Y, CY + X), , BF
92.             End If
93.             X = X - 1
94.             RadiusError = RadiusError - X * 2
95.         End If
96.         Y = Y + 1
97.         Line (CX - X, CY - Y)-(CX + X, CY - Y), , BF
98.         Line (CX - X, CY + Y)-(CX + X, CY + Y), , BF
99.     Wend
100. End Sub
101.  
102.  

@MasterGy try and get some sleep.

[jack]

To download programs running under video (running under windows) with source code:
https://drive.google.com/file/d/1hkIqbFx_JGzhYpGdQjZ1h0lZYFtiw3Ce/view?usp=sharing

I get an error from google not allowing me to download, is there another way you can share your creations?
btw, the programs you presented in this thread are fantastic! :)

[MasterGy]

I'm very interested in this thing. Unfortunately I had little time, the season started. The above programs work in 2d. I started simulating the behavior of points in 3d. The goal would be collisions. I would like to see what I have described above. For now, you can see that it works nicely in 3D as well. Stretched mesh, gravity, WASD + mouse like in games. Use the space bar to move 1 point out of place. All other points will then respond and the system will attempt to return to the idle state.

Code: QB64: [Select]

1. mouse_sens = .5
2. tightness = 2
3. gravity = .005
4. lass = .94
5. power = -0.3
6.  
7.  
8.  
9. RANDOMIZE TIMER
10. CONST pip180 = 3.141592 / 180
11. DIM SHARED monx, mony: monx = 800: mony = monx / _DESKTOPWIDTH * _DESKTOPHEIGHT: mon = _NEWIMAGE(monx, mony, 32): SCREEN mon: _FULLSCREEN: _MOUSEHIDE
12.  
13. DIM SHARED points_c_arr, conn_c_arr
14. points_c_arr = 2000
15. conn_c_arr = 2000
16.  
17. DIM SHARED points(points_c_arr, 19), conn(conn_c_arr, 9), cam(19), me(19), conn_c, points_c
18.  
19.  
20. make_grid 1, -10, -10, 10, 10, -10, 0, -10, 10, 0, 10, 10, 0, 1.2
21.  
22.  
23.  
24.  
25.  
26. 'make_sphere 2, 0, 10, 0, 5, 8 'ident,X,Y,Z,RAD,POINTS
27. DO: _LIMIT 30
28.  
29.     'control
30.     mousex = 0: mousey = 0: mw = 0: WHILE _MOUSEINPUT: mousex = mousex + _MOUSEMOVEMENTX: mousey = mousey + _MOUSEMOVEMENTY: mw = mw + _MOUSEWHEEL: WEND
31.     k_left = _KEYDOWN(19200) OR _KEYDOWN(ASC("a")): k_right = _KEYDOWN(19712) OR _KEYDOWN(ASC("d"))
32.     k_up = _KEYDOWN(18432) OR _KEYDOWN(ASC("w")): k_down = _KEYDOWN(20480) OR _KEYDOWN(ASC("s"))
33.     me(2) = me(2) + mw: me(3) = me(3) - mousex * mouse_sens: me(4) = me(4) + mousey * mouse_sens: IF ABS(me(4)) > 80 THEN me(4) = 80 * SGN(me(4))
34.     go = -.5 * ABS(k_left OR k_right OR k_up OR k_down): go_ang = -90 * (k_left - k_right) + (me(3)) - 90
35.     ang1 = go_ang * pip180: ang2 = (90 - me(4)) * pip180: IF k_down THEN go = -go
36.     me(0) = me(0) + SIN(ang2) * COS(ang1) * go: me(1) = me(1) + SIN(ang2) * SIN(ang1) * go: me(2) = me(2) + COS(ang2) * go
37.     FOR t = 0 TO 9: cam(t) = me(t): NEXT t: cam(13) = cam(3) * pip180: cam(14) = cam(4) * pip180
38.  
39.  
40.  
41.     'calculate moving
42.  
43.     FOR a = 0 TO points_c_arr - 1: FOR t = 0 TO 2: points(a, 11 + t) = points(a, t): NEXT t: IF (points(a, 14) = 0 OR points(a, 6) = 0) THEN _CONTINUE
44.  
45.         'connections vector
46.         vec(0) = 0: vec(1) = 0: vec(2) = 0: vec_c = 0
47.         FOR t = 0 TO conn_c - 1: IF conn(t, 3) = 0 THEN _CONTINUE
48.             x = -1: FOR t2 = 0 TO 1: IF conn(t, t2) = a THEN x = conn(t, t2 XOR 1)
49.             NEXT t2
50.             IF x <> -1 THEN
51.                 FOR av = 0 TO 2: disv = points(a, av) - points(x, av): vec(av) = vec(av) + ((ABS(disv) - conn(t, 4 + av))) * SGN(disv) * power
52.                 NEXT av: vec_c = vec_c + 1
53.             END IF
54.         NEXT t
55.  
56.         FOR av = 0 TO 2: points(a, 3 + av) = (points(a, 3 + av) + vec(av) / vec_c) * lass: NEXT av: points(a, 4) = points(a, 4) - gravity
57.         FOR av = 0 TO 2: points(a, 11 + av) = points(a, av) + points(a, 3 + av): NEXT av
58.     NEXT a
59.  
60.     FOR a = 0 TO points_c_arr - 1: FOR t = 0 TO 2: points(a, t) = points(a, 11 + t): NEXT t, a
61.  
62.     inkey2$ = INKEY$
63.     IF inkey2$ = " " THEN
64.         DO: a = INT(points_c_arr * RND(1)): LOOP UNTIL points(a, 14) AND points(a, 6)
65.         rand = 30: FOR t = 0 TO 2: points(a, t) = points(a, t) + rand * RND(1) - rand / 2: NEXT t
66.     END IF
67.  
68.     'calculating points
69.     FOR ap = 0 TO points_c_arr - 1: IF points(ap, 6) = 0 THEN _CONTINUE
70.         points(ap, 8) = points(ap, 0): points(ap, 9) = points(ap, 1): points(ap, 10) = points(ap, 2)
71.     rotate_display points(ap, 8), points(ap, 9), points(ap, 10): NEXT ap
72.  
73.     'draw connections
74.     FOR ac = 0 TO conn_c_arr - 1: IF conn(ac, 3) = 0 THEN _CONTINUE
75.         FOR t1 = 0 TO 1: FOR t2 = 0 TO 2: coo(t1, t2) = points(conn(ac, t1), 8 + t2): NEXT t2, t1
76.         line_3d coo(0, 0), coo(0, 1), coo(0, 2), coo(1, 0), coo(1, 1), coo(1, 2)
77.     NEXT ac
78.  
79.     'fix points draw signal
80.     FOR ap = 0 TO points_c_arr - 1: IF points(ap, 6) = 0 OR points(ap, 14) OR points(ap, 10) > -1 THEN _CONTINUE
81.         FOR t2 = 0 TO 2: coo(0, t2) = points(ap, 8 + t2): NEXT t2
82.         point3d_to_pset coo(0, 0), coo(0, 1), coo(0, 2): CIRCLE (coo(0, 0), coo(0, 1)), 12000 / coo(0, 2)
83.     NEXT ap
84.  
85.     COLOR _RGB32(200, 200, 200): LOCATE mony / 16 - 2: PRINT "WASD+mouse      SPACE - impulse to a random point ";
86.     _DISPLAY
87.     CLS
88. LOOP
89.  
90.  
91. SUB line_3d (x0, y0, z0, x1, y1, z1)
92.     IF z0 < -1 AND z1 < -1 THEN point3d_to_pset x0, y0, z0: point3d_to_pset x1, y1, z1: LINE (x0, y0)-(x1, y1)
93. END SUB
94.  
95. SUB point3d_to_pset (x, y, z): multi = 400: zlimit = -2: x = monx / 2 + (x + zlimit) / -z * multi: y = mony / 2 + (y + zlimit) / z * multi
96.     grey = 255 - ABS(z) * .1: IF grey < 10 THEN grey = 10
97.     COLOR _RGB32(grey, grey, grey)
98. END SUB
99.  
100. SUB make_grid (acc, x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3, res): p_start = points_c
101.     resA = INT((dis(x0 - x1, y0 - y1, z0 - z1) + dis(x2 - x3, y2 - y3, z2 - z3)) / 2 / res)
102.     resB = INT((dis(x0 - x2, y0 - y2, z0 - z2) + dis(x1 - x3, y1 - y3, z1 - z3)) / 2 / res)
103.     FOR a = 0 TO resA - 1: n = 1 / resA * a
104.         tx1 = scale(x0, x1, n): ty1 = scale(y0, y1, n): tz1 = scale(z0, z1, n): tx2 = scale(x2, x3, n): ty2 = scale(y2, y3, n): tz2 = scale(z2, z3, n)
105.         FOR b = 0 TO resB - 1: n = 1 / resB * b: l = p_start + b * resA + a
106.             points(l, 0) = scale(tx1, tx2, n): points(l, 2) = scale(ty1, ty2, n): points(l, 1) = scale(tz1, tz2, n)
107.             points(l, 6) = 1: points(l, 7) = acc: points(l, 14) = 1: IF (a = 0 OR a = resA - 1) AND (b = 0 OR b = resB - 1) THEN points(l, 14) = 0
108.     NEXT b, a
109.     FOR ty = 0 TO resB - 1: FOR tx = 0 TO resA - 2: p1 = tx + ty * resA: conn_add p1, p1 + 1, tightness: NEXT tx, ty
110.     FOR tx = 0 TO resA - 1: FOR ty = 0 TO resB - 2: p1 = tx + ty * resA: conn_add p1, p1 + resA, tightness: NEXT ty, tx
111.     points_c = points_c + resA * resB
112. END SUB
113.  
114. FUNCTION dis (a, b, c): dis = SQR(a * a + b * b + c * c): END FUNCTION
115. FUNCTION scale (a, b, n): scale = a + (b - a) * n: END FUNCTION
116. SUB conn_add (p1, p2, tightness): IF p1 = p2 THEN EXIT SUB
117.     FOR t = 0 TO conn_c_arr - 1: IF (conn(t, 0) = p1 AND conn(t, 1) = p2) OR (conn(t, 0) = p2 AND conn(t, 1) = p1) THEN EXIT SUB
118.     NEXT t: REDIM disx(2): conn(conn_c, 0) = p1: conn(conn_c, 1) = p2
119.     FOR t = 0 TO 2: conn(conn_c, 4 + t) = (ABS(points(p1, t) - points(p2, t))) * tightness: NEXT t
120.     conn(conn_c, 2) = dis(conn(conn_c, 4), conn(conn_c, 5), conn(conn_c, 6)): conn(conn_c, 3) = 1: conn_c = conn_c + 1
121. END SUB
122. SUB rotate_2d (x, y, ang): x1 = x * COS(ang) - y * SIN(ang): y1 = x * SIN(ang) + y * COS(ang): x = x1: y = y1: END SUB
123. SUB rotate_display (x, y, z)
124.     x = (x - cam(0)) * 100: y = (y - cam(2)) * 100: z = -(z - cam(1)) * 100: rotate_2d x, z, cam(13): rotate_2d y, z, cam(14)
125. END SUB
126. FUNCTION degree (a, b): degreex = ATN(a / (b + .00001)) / pip180: degreex = degreex - 180 * ABS(0 > b): degreex = degreex - 360 * (degreex < 0): degree = degreex: END FUNCTION
127.  
128.  
129.  
130.  
131.  
132. 'POINTS array
133. '0,1,2 : X,Y,Z
134. '3,4,5 : X,Y,Z vector
135. '6:active 7:identifier
136. '8,9,10 :X,Y,Z calculated to maptriangle
137. '11,12,13 :X,Y,Z moving temporary calculating
138. '14: 0:FIX 1:MOVING
139.  
140.  
141. 'CONN array
142. '0:point#1
143. '1:point#2
144. '2:distance
145. '3:active
146. '4:disX
147. '5:disY
148. '6:disZ
149.  
150.  
151.  
152.  
153.  
154.  

[MasterGy]

I added another curiosity. (but I haven't covered the point yet)
I recently had a question with _MAPTRIANGLE that calculates 2d points. I wanted to know so I could move with a mouse in 3d. This has now been achieved with a simple solution.
Stretched mesh in 3d. Walkable with WASD + mouse like in 3D games. If you press the Q key, you can grab the point with the mouse and move it. You can nail it with the SPACE key.

Code: QB64: [Select]

1. mouse_sens = .5
2. tightness = 1
3. gravity = .005
4. lass = .94
5. power = -0.3
6. adj = .8 'moving speed 3d point mouse
7.  
8.  
9. RANDOMIZE TIMER
10. CONST pip180 = 3.141592 / 180
11. DIM SHARED monx, mony: monx = 800: mony = monx / _DESKTOPWIDTH * _DESKTOPHEIGHT: mon = _NEWIMAGE(monx, mony, 32): SCREEN mon: _FULLSCREEN: _MOUSEHIDE
12.  
13. DIM SHARED points_c_arr, conn_c_arr
14. points_c_arr = 2000
15. conn_c_arr = 2000
16.  
17. DIM SHARED points(points_c_arr, 19), conn(conn_c_arr, 9), cam(19), me(19), conn_c, points_c
18.  
19.  
20. make_grid 1, -10, -10, 10, 10, -10, 0, -10, 10, 0, 10, 10, 0, 1.5
21.  
22.  
23.  
24.  
25.  
26. DO: _LIMIT 30
27.  
28.     'control
29.     mousex = 0: mousey = 0: mw = 0: WHILE _MOUSEINPUT: mousex = mousex + _MOUSEMOVEMENTX: mousey = mousey + _MOUSEMOVEMENTY: mw = mw + _MOUSEWHEEL: WEND
30.     k_left = _KEYDOWN(19200) OR _KEYDOWN(ASC("a")): k_right = _KEYDOWN(19712) OR _KEYDOWN(ASC("d")): inkey2$ = INKEY$: IF inkey2$ = CHR$(27) THEN END
31.     k_up = _KEYDOWN(18432) OR _KEYDOWN(ASC("w")): k_down = _KEYDOWN(20480) OR _KEYDOWN(ASC("s")): key_take = _KEYDOWN(ASC("q"))
32.     me(2) = me(2) + mw: IF key_take THEN _MOUSESHOW ELSE _MOUSEHIDE
33.     IF key_take = 0 THEN me(3) = me(3) - mousex * mouse_sens: me(4) = me(4) + mousey * mouse_sens: IF ABS(me(4)) > 80 THEN me(4) = 80 * SGN(me(4))
34.     go = -.5 * ABS(k_left OR k_right OR k_up OR k_down): go_ang = -90 * (k_left - k_right) + (me(3)) - 90
35.     ang1 = go_ang * pip180: ang2 = (90 - me(4)) * pip180: IF k_down THEN go = -go
36.     me(0) = me(0) + SIN(ang2) * COS(ang1) * go: me(1) = me(1) + SIN(ang2) * SIN(ang1) * go: me(2) = me(2) + COS(ang2) * go
37.     FOR t = 0 TO 9: cam(t) = me(t): NEXT t: cam(13) = cam(3) * pip180: cam(14) = cam(4) * pip180
38.  
39.  
40.  
41.     'calculate moving
42.     FOR a = 0 TO points_c_arr - 1: FOR t = 0 TO 2: points(a, 11 + t) = points(a, t): NEXT t
43.         IF (points(a, 14) = 0 OR points(a, 6) = 0) OR a = take_moving THEN _CONTINUE
44.  
45.         'connections vector
46.         vec(0) = 0: vec(1) = 0: vec(2) = 0: vec_c = 0
47.         FOR t = 0 TO conn_c - 1: IF conn(t, 3) = 0 THEN _CONTINUE
48.             x = -1: FOR t2 = 0 TO 1: IF conn(t, t2) = a THEN x = conn(t, t2 XOR 1)
49.             NEXT t2
50.             IF x <> -1 THEN
51.                 FOR av = 0 TO 2: disv = points(a, av) - points(x, av): vec(av) = vec(av) + ((ABS(disv) - conn(t, 4 + av))) * SGN(disv) * power
52.                 NEXT av: vec_c = vec_c + 1
53.             END IF
54.         NEXT t
55.  
56.         FOR av = 0 TO 2: points(a, 3 + av) = (points(a, 3 + av) + vec(av) / vec_c) * lass: NEXT av: points(a, 4) = points(a, 4) - gravity
57.         FOR av = 0 TO 2: points(a, 11 + av) = points(a, av) + points(a, 3 + av): NEXT av
58.     NEXT a
59.  
60.     FOR a = 0 TO points_c_arr - 1: FOR t = 0 TO 2: points(a, t) = points(a, 11 + t): NEXT t, a
61.  
62.  
63.  
64.     'calculating points
65.     FOR ap = 0 TO points_c_arr - 1: IF points(ap, 6) = 0 THEN _CONTINUE
66.         points(ap, 8) = points(ap, 0): points(ap, 9) = points(ap, 1): points(ap, 10) = points(ap, 2)
67.         rotate_display points(ap, 8), points(ap, 9), points(ap, 10)
68.         FOR t = 0 TO 2: points(ap, 15 + t) = points(ap, 8 + t): NEXT t: point3d_to_pset points(ap, 15), points(ap, 16), points(ap, 17)
69.     NEXT ap
70.  
71.     'draw connections
72.     FOR ac = 0 TO conn_c_arr - 1: IF conn(ac, 3) = 0 THEN _CONTINUE
73.         FOR t1 = 0 TO 1: FOR t2 = 0 TO 2: coo(t1, t2) = points(conn(ac, t1), 15 + t2): NEXT t2, t1
74.         IF points(conn(ac, 0), 10) < -1 AND points(conn(ac, 1), 10) < -1 THEN
75.             LINE (coo(0, 0), coo(0, 1))-(coo(1, 0), coo(1, 1)), _RGB32(coo(0, 2), coo(0, 2), coo(0, 2))
76.         END IF
77.     NEXT ac
78.  
79.     'fix points draw signal
80.     FOR ap = 0 TO points_c_arr - 1: IF points(ap, 6) = 0 OR points(ap, 14) OR points(ap, 10) > -1 THEN _CONTINUE
81.         CIRCLE (points(ap, 15), points(ap, 16)), 12000 / points(ap, 10), _RGB32(points(ap, 17), points(ap, 17), points(ap, 17))
82.     NEXT ap
83.  
84.     'take point with mouse
85.     IF key_take AND take_moving = -1 THEN
86.         take_sens = monx * 0.01: mindis = 999999: take = -1
87.         FOR ap = 0 TO points_c_arr - 1: IF points(ap, 6) = 0 OR points(ap, 10) > -1 THEN _CONTINUE
88.             disx = ABS(_MOUSEX - points(ap, 15)): IF disx > take_sens THEN _CONTINUE
89.             disy = ABS(_MOUSEY - points(ap, 16)): IF disy > take_sens THEN _CONTINUE
90.             disv = dis(disx, disy, 0): IF disv > take_sens OR disv > mindis THEN _CONTINUE
91.         take = ap: mindis = disv: NEXT ap: IF take <> -1 THEN CIRCLE (points(take, 15), points(take, 16)), 5000 / points(take, 10), _RGB32(255, 0, 0)
92.     END IF
93.     IF _MOUSEBUTTON(1) = 0 OR key_take = 0 THEN take_moving = -1
94.     IF key_take AND _MOUSEBUTTON(1) AND take_moving = -1 AND take <> -1 THEN take_moving = take: dis_take = dis(points(take, 8), points(take, 9), points(take, 10))
95.     IF take <> -1 AND inkey2$ = " " THEN points(take, 14) = points(take, 14) XOR 1
96.  
97.     'move with mouse 3d point
98.     IF take_moving <> -1 THEN
99.         IF dis(_MOUSEX - points(take_moving, 15), _MOUSEY - points(take_moving, 16), 0) > 20 THEN
100.             mindis = 99999: FOR ang1 = 0 TO 360 * pip180 STEP 10 * pip180: FOR ang2 = 0 TO 180 * pip180 STEP 10 * pip180
101.                     px = points(take_moving, 0) + adj * SIN(ang2) * COS(ang1): py = points(take_moving, 1) + adj * SIN(ang2) * SIN(ang1)
102.                     pz = points(take_moving, 2) + adj * COS(ang2): vx = px: vy = py: vz = pz
103.                     rotate_display vx, vy, vz: IF ABS(dis(vx, vy, vz) - dis_take) > 300 THEN _CONTINUE
104.                     point3d_to_pset vx, vy, vz: disx = dis(_MOUSEX - vx, _MOUSEY - vy, 0)
105.                     IF disx < mindis THEN mindis = disx: cx = px: cy = py: cz = pz
106.             NEXT ang2, ang1: points(take_moving, 0) = cx: points(take_moving, 1) = cy: points(take_moving, 2) = cz
107.         END IF
108.     END IF
109.  
110.     mess$ = "moving WASD+mouse      Q-key fixing and moving point"
111.     IF key_take THEN mess$ = "SPACE-fix/float point  MOUSEBUTTON - hold point"
112.     IF take_moving <> -1 THEN mess$ = "moving the point with mouse"
113.     COLOR _RGB32(200, 200, 200): LOCATE mony / 16 - 2: PRINT mess$;
114.     _DISPLAY
115.     CLS
116. LOOP
117.  
118.  
119. SUB point3d_to_pset (x, y, z): zlimit = -2: x = monx * .5 + (x + zlimit) / -z * 400: y = mony * .5 + (y + zlimit) / z * 400
120.     z = 255 - ABS(z) * .1: IF z < 10 THEN grey = 10
121. END SUB
122.  
123. SUB make_grid (acc, x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3, res): p_start = points_c
124.     resA = INT((dis(x0 - x1, y0 - y1, z0 - z1) + dis(x2 - x3, y2 - y3, z2 - z3)) / 2 / res)
125.     resB = INT((dis(x0 - x2, y0 - y2, z0 - z2) + dis(x1 - x3, y1 - y3, z1 - z3)) / 2 / res)
126.     FOR a = 0 TO resA - 1: n = 1 / resA * a
127.         tx1 = scale(x0, x1, n): ty1 = scale(y0, y1, n): tz1 = scale(z0, z1, n): tx2 = scale(x2, x3, n): ty2 = scale(y2, y3, n): tz2 = scale(z2, z3, n)
128.         FOR b = 0 TO resB - 1: n = 1 / resB * b: l = p_start + b * resA + a
129.             points(l, 0) = scale(tx1, tx2, n): points(l, 2) = scale(ty1, ty2, n): points(l, 1) = scale(tz1, tz2, n)
130.             points(l, 6) = 1: points(l, 7) = acc: points(l, 14) = 1: IF (a = 0 OR a = resA - 1) AND (b = 0 OR b = resB - 1) THEN points(l, 14) = 0
131.     NEXT b, a
132.     FOR ty = 0 TO resB - 1: FOR tx = 0 TO resA - 2: p1 = tx + ty * resA: conn_add p1, p1 + 1, tightness: NEXT tx, ty
133.     FOR tx = 0 TO resA - 1: FOR ty = 0 TO resB - 2: p1 = tx + ty * resA: conn_add p1, p1 + resA, tightness: NEXT ty, tx
134.     points_c = points_c + resA * resB
135. END SUB
136.  
137. FUNCTION dis (a, b, c): dis = SQR(a * a + b * b + c * c): END FUNCTION
138. FUNCTION scale (a, b, n): scale = a + (b - a) * n: END FUNCTION
139. SUB conn_add (p1, p2, tightness): IF p1 = p2 THEN EXIT SUB
140.     FOR t = 0 TO conn_c_arr - 1: IF (conn(t, 0) = p1 AND conn(t, 1) = p2) OR (conn(t, 0) = p2 AND conn(t, 1) = p1) THEN EXIT SUB
141.     NEXT t: REDIM disx(2): conn(conn_c, 0) = p1: conn(conn_c, 1) = p2
142.     FOR t = 0 TO 2: conn(conn_c, 4 + t) = (ABS(points(p1, t) - points(p2, t))) * tightness: NEXT t
143.     conn(conn_c, 2) = dis(conn(conn_c, 4), conn(conn_c, 5), conn(conn_c, 6)): conn(conn_c, 3) = 1: conn_c = conn_c + 1
144. END SUB
145. SUB rotate_2d (x, y, ang): x1 = x * COS(ang) - y * SIN(ang): y1 = x * SIN(ang) + y * COS(ang): x = x1: y = y1: END SUB
146. SUB rotate_display (x, y, z)
147.     x = (x - cam(0)) * 100: y = (y - cam(2)) * 100: z = -(z - cam(1)) * 100: rotate_2d x, z, cam(13): rotate_2d y, z, cam(14)
148. END SUB
149. FUNCTION degree (a, b): degreex = ATN(a / (b + .00001)) / pip180: degreex = degreex - 180 * ABS(0 > b): degreex = degreex - 360 * (degreex < 0): degree = degreex: END FUNCTION
150.  
151.  
152.  
153.  
154.  
155. 'POINTS array
156. '0,1,2 : XYZ
157. '3,4,5 : XYZ vector
158. '6:active 7:identifier
159. '8,9,10 :XYZ calculated to maptriangle
160. '11,12,13 :XYZ moving temporary calculating
161. '14: 0:FIX 1:MOVING
162. '15,16,17 2D-X,Y, greyscale
163.  
164.  
165. 'CONN array
166. '0:point#1
167. '1:point#2
168. '2:distance
169. '3:active
170. '4:disX
171. '5:disY
172. '6:disZ
173.  
174.  
175.  
176.  
177.  
178.