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(10-18-2022, 03:27 PM)bplus Wrote: (10-18-2022, 03:57 AM)james2464 Wrote: Changed from arrow keys to mouse wheel for rotating the wall
Code: (Select All) 'vector reflection demo
'james2464
Screen _NewImage(800, 600, 32)
Const PI = 3.141592654#
Dim Shared x, y, h, dx, dy, nx, ny, na As Single
Dim c(10) As Long
c(0) = _RGB(30, 30, 30)
c(1) = _RGB(255, 255, 255)
c(2) = _RGB(255, 255, 0)
c(3) = _RGB(255, 0, 0)
'0,0 origin
xx = 400
yy = 300
Line (0, yy)-(800, yy), c(0)
Line (xx, 0)-(xx, 600), c(0)
x = 70: y = 90 'ball position
na = 60 'reflecting surface angle
flag = 0
Do
_Limit 10
Cls
'chip starting pos - using mouse
mouseclick1 = 0
Do While _MouseInput
na = na + _MouseWheel
Loop
mx% = _MouseX
my% = _MouseY
If mx% < xx - 400 Then mx% = xx - 400
If mx% > xx + 400 Then mx% = xx + 400
If my% < yy - 300 Then my% = yy - 300
If my% > yy + 300 Then my% = yy + 300
lc% = _MouseButton(1)
If lc% = -1 Then mouseclick1 = 1
x = 0 - xx + mx%
y = yy - my%
'origin lines
Line (0, yy)-(800, yy), c(0)
Line (xx, 0)-(xx, 600), c(0)
h = _Hypot(-x, y)
nx = Sin(na * (PI / 180)) 'normalize wall angle
ny = Cos(na * (PI / 180)) 'normalize wall angle
dx = -x * nx * -1: dy = y * ny: ndp = dx + dy
'dot product V.N - used to find distance of N
'The distance of N is from the point of origin to the middle of line A
'line A is a line from point I to point R (parallel to the angled wall)
ard = Sqr(h ^ 2 - ndp ^ 2) 'distance from mid point of line A to point R
w2x = ny * ard: w2y = nx * ard
u2x = nx * ndp: u2y = ny * ndp
rx = w2x + u2x: ry = w2y - u2y 'point R
Circle (xx + rx, yy + ry), 10, c(3) 'point R
Line (xx, yy)-(xx + rx, yy + ry), c(3) 'line from origin to point R
'angled wall
A = (Sin(na * (PI / 180))) * 200
B = (Cos(na * (PI / 180))) * 200
Line (xx, yy)-(xx + B, yy + A), c(1)
Line (xx, yy)-(xx - B, yy - A), c(1)
Circle (xx + x, yy - y), 10, c(2) 'point I
Line (xx, yy)-(xx + x, yy - y), c(2)
Locate 1, 1
Print "Vector Reflection"
Print "Use mouse wheel to rotate wall"
Locate 35, 1
Print "Wall angle:"; na
Locate 1, 70
Print "I ="; x; ","; y;
Locate 35, 70
Print "R ="; Int(rx); ","; Int(-ry)
_Display
Loop Until flag = 1
Nice app, I would have done it this way https://qb64phoenix.com/forum/showthread...74#pid8074
Yes indeed, that is excellent - thank you!
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(10-16-2022, 12:17 AM)james2464 Wrote: This video explains the reflection of a vector, but I don't know what 'n' is. At 10:27 he says "don't forget if n is unit length you know that n.n is 1 and you can cross that out". But there are still more n's in the formula and I can't figure out what they are supposed to represent. He just said n=1 !! Or n.n = 1 anyway. I just wish there were numbers involved instead of just letters. That would be a huge help.
https://youtu.be/naaeH1qbjdQ
I took a shot at doing a test bed program that uses the video procedure.
This is what I came up with, that is mostly vector based.
Code: (Select All) TYPE V2
x AS SINGLE
y AS SINGLE
END TYPE
DIM AS V2 wall, ball, reflec, orth, tempv
wall.x = -1: wall.y = 2
orth.x = -wall.y: orth.y = wall.x
SCREEN _NEWIMAGE(600, 600, 32) ' setup screen & display grid
WINDOW (-300, 300)-(300, -300)
DO UNTIL x% > 300
IF x% = 0 THEN c~& = &HFF00FF00 ELSE c~& = &H7F7F7F7F
LINE (-300, x%)-(300, x%), c~&
LINE (-300, -x%)-(300, -x%), c~&
LINE (x%, 300)-(x%, -300), c~&
LINE (-x%, 300)-(-x%, -300), c~&
x% = x% + 50
LOOP
back& = _COPYIMAGE(0)
DO
WHILE _MOUSEINPUT: WEND ' get inputs
ball.x = PMAP(_MOUSEX, 2): ball.y = PMAP(_MOUSEY, 3)
IF _KEYDOWN(18432) THEN ' up arrow
d! = _ATAN2(wall.y, wall.x)
d! = d! + (_PI / 180)
wall.x = COS(d!): wall.y = SIN(d!)
orth.x = -wall.y: orth.y = wall.x
END IF
IF _KEYDOWN(20480) THEN ' down arrow
d! = _ATAN2(wall.y, wall.x)
d! = d! - (_PI / 180)
wall.x = COS(d!): wall.y = SIN(d!)
orth.x = -wall.y: orth.y = wall.x
END IF
CLS
_PUTIMAGE , back&
R2_Norm wall, wall, 200 ' draw wall legs 200 long
R2_Norm orth, orth, 50 ' draw orthogonals 50 long
LINE (wall.x, wall.y)-(-wall.x, -wall.y)
LINE (orth.x, orth.y)-(-orth.x, -orth.y), &HFF0000FF
CIRCLE (ball.x, ball.y), 30 ' draw incoming ball & vector
LINE (ball.x, ball.y)-(0, 0)
R2_Norm orth, orth, 1 ' reset orthogonal to unit length
R2_Norm tempv, orth, DotP(ball, orth) * 2 ' get ball projection to orthogonal * 2
reflec.x = tempv.x - ball.x ' compute reflection vector
reflec.y = tempv.y - ball.y
LINE (0, 0)-(reflec.x, reflec.y), &HFFFF0000 ' move reflection to impact point
CIRCLE (reflec.x, reflec.y), 30, &HFFFF0000 ' show reflected ball
_LIMIT 100
_DISPLAY
LOOP UNTIL _KEYDOWN(27)
_FREEIMAGE back&
END
FUNCTION DotP (a AS V2, b AS V2)
DotP = a.x * b.x + a.y * b.y
END FUNCTION 'DotP
SUB R2_Norm (re AS V2, v AS V2, scalar AS INTEGER)
x! = v.x: y! = v.y
m! = _HYPOT(x!, y!)
IF m! = 0 THEN
re.x = 0: re.y = 0
ELSE
re.x = (x! / m!) * scalar
re.y = (y! / m!) * scalar
END IF
END SUB 'R2_Norm
DO: LOOP: DO: LOOP
sha_na_na_na_na_na_na_na_na_na:
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Thumbs up! Works without a hitch, nice job!
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10-18-2022, 08:44 PM
(This post was last modified: 10-18-2022, 08:44 PM by Pete.)
Mark, did you ever get your balls ball unstuck? Your ball in the cave routine worked great, but like you stated, it eventually gets stuck, too. I think I ran it 5 or 10 minutes before that happened, and it got stuck in the same place as the pic you posted.
Pete
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10-18-2022, 10:10 PM
(This post was last modified: 10-18-2022, 10:17 PM by bplus.)
(10-18-2022, 08:44 PM)Pete Wrote: Mark, did you ever get your balls ball unstuck? Your ball in the cave routine worked great, but like you stated, it eventually gets stuck, too. I think I ran it 5 or 10 minutes before that happened, and it got stuck in the same place as the pic you posted.
Pete
I have been thinking of a hack for that, eg if x,y in same place for too long to just kick it off the normal angle for the line segment. Maybe if I do a pinball machine app...
BTW this morning I was revisiting my Pool app which does use a ton of vector stuff: https://qb64phoenix.com/forum/showthread...748#pid748
Old Moses got the perfect link for doing serious calculations, the rack breaks pretty darn well.
I know Pete just wants to talk about bplus balls, do you remember my first post in my little corner?
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Put my SAM routine to work for ya!
Code: (Select All) z = TIMER
DO
x = foo: y = foo2
IF oldx = x AND oldy = y THEN
IF z < TIMER THEN z = z - 86400 ' midnight adj.
IF z - TIMER > .2 THEN
' MOVE VARMINT!
z = TIMER
END IF
oldx = x: oldy = y
END IF
LOOP
Pete
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(10-18-2022, 08:20 PM)OldMoses Wrote: (10-16-2022, 12:17 AM)james2464 Wrote: This video explains the reflection of a vector, but I don't know what 'n' is. At 10:27 he says "don't forget if n is unit length you know that n.n is 1 and you can cross that out". But there are still more n's in the formula and I can't figure out what they are supposed to represent. He just said n=1 !! Or n.n = 1 anyway. I just wish there were numbers involved instead of just letters. That would be a huge help.
https://youtu.be/naaeH1qbjdQ
I took a shot at doing a test bed program that uses the video procedure.
This is what I came up with, that is mostly vector based.
Code: (Select All) TYPE V2
x AS SINGLE
y AS SINGLE
END TYPE
DIM AS V2 wall, ball, reflec, orth, tempv
wall.x = -1: wall.y = 2
orth.x = -wall.y: orth.y = wall.x
SCREEN _NEWIMAGE(600, 600, 32) ' setup screen & display grid
WINDOW (-300, 300)-(300, -300)
DO UNTIL x% > 300
IF x% = 0 THEN c~& = &HFF00FF00 ELSE c~& = &H7F7F7F7F
LINE (-300, x%)-(300, x%), c~&
LINE (-300, -x%)-(300, -x%), c~&
LINE (x%, 300)-(x%, -300), c~&
LINE (-x%, 300)-(-x%, -300), c~&
x% = x% + 50
LOOP
back& = _COPYIMAGE(0)
DO
WHILE _MOUSEINPUT: WEND ' get inputs
ball.x = PMAP(_MOUSEX, 2): ball.y = PMAP(_MOUSEY, 3)
IF _KEYDOWN(18432) THEN ' up arrow
d! = _ATAN2(wall.y, wall.x)
d! = d! + (_PI / 180)
wall.x = COS(d!): wall.y = SIN(d!)
orth.x = -wall.y: orth.y = wall.x
END IF
IF _KEYDOWN(20480) THEN ' down arrow
d! = _ATAN2(wall.y, wall.x)
d! = d! - (_PI / 180)
wall.x = COS(d!): wall.y = SIN(d!)
orth.x = -wall.y: orth.y = wall.x
END IF
CLS
_PUTIMAGE , back&
R2_Norm wall, wall, 200 ' draw wall legs 200 long
R2_Norm orth, orth, 50 ' draw orthogonals 50 long
LINE (wall.x, wall.y)-(-wall.x, -wall.y)
LINE (orth.x, orth.y)-(-orth.x, -orth.y), &HFF0000FF
CIRCLE (ball.x, ball.y), 30 ' draw incoming ball & vector
LINE (ball.x, ball.y)-(0, 0)
R2_Norm orth, orth, 1 ' reset orthogonal to unit length
R2_Norm tempv, orth, DotP(ball, orth) * 2 ' get ball projection to orthogonal * 2
reflec.x = tempv.x - ball.x ' compute reflection vector
reflec.y = tempv.y - ball.y
LINE (0, 0)-(reflec.x, reflec.y), &HFFFF0000 ' move reflection to impact point
CIRCLE (reflec.x, reflec.y), 30, &HFFFF0000 ' show reflected ball
_LIMIT 100
_DISPLAY
LOOP UNTIL _KEYDOWN(27)
_FREEIMAGE back&
END
FUNCTION DotP (a AS V2, b AS V2)
DotP = a.x * b.x + a.y * b.y
END FUNCTION 'DotP
SUB R2_Norm (re AS V2, v AS V2, scalar AS INTEGER)
x! = v.x: y! = v.y
m! = _HYPOT(x!, y!)
IF m! = 0 THEN
re.x = 0: re.y = 0
ELSE
re.x = (x! / m!) * scalar
re.y = (y! / m!) * scalar
END IF
END SUB 'R2_Norm
Works great! Thanks for giving this a go. I'm still trying to figure it out but I think I'll get there. Right now I'm trying to get the full 360 degree rotation but I did get the reflection to work at least. Cheers!
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(10-18-2022, 10:47 PM)james2464 Wrote: [quote pid="8096" dateline="1666124430"]
Works great! Thanks for giving this a go. I'm still trying to figure it out but I think I'll get there. Right now I'm trying to get the full 360 degree rotation but I did get the reflection to work at least. Cheers!
[/quote]
It was giving me a screwy result until I realized that the orthogonal vector had to be a unit length before applying the dot product calculation. After that the diagonal of the parallelogram was the proper length for obtaining the reflecting vector.
I was pleasantly surprised that dot product handles either side of the reflecting wall perfectly and...
it doesn't matter which orthogonal is constructed...
both...
orth.x = -wall.y: orth.y = wall.x
and...
orth.x = wall.y: orth.y = -wall.x
work exactly the same. I originally thought there would be a difference. I might be starting to get the hang of this stuff.
DO: LOOP: DO: LOOP
sha_na_na_na_na_na_na_na_na_na:
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I finally got it. Had to make use of _ATAN2 and that made a huge difference. I didn't know what it meant but it's a great command for this. Without using degrees it captures the radian value of any x,y position and you can add and subtract these radian values to get a reflection. That makes this simple. I threw out most of my code once I got this concept going.
Code: (Select All) 'vector reflection demo
'james2464
Screen _NewImage(800, 600, 32)
Const PI = 3.141592654#
Dim c(10) As Long
c(0) = _RGB(30, 30, 30)
c(1) = _RGB(255, 255, 255)
c(2) = _RGB(255, 255, 0)
c(3) = _RGB(255, 0, 0)
c(4) = _RGB(0, 255, 0)
c(5) = _RGB(0, 255, 255)
'0,0 origin
xx = 400
yy = 300
na = 45 'wall starting angle (mouse wheel controlled)
flag = 0
Do
_Limit 50
Cls
'=====================================================
mouseclick1 = 0
Do While _MouseInput
na = na + _MouseWheel * 5
Loop
mx% = _MouseX
my% = _MouseY
If mx% < xx - 400 Then mx% = xx - 400
If mx% > xx + 400 Then mx% = xx + 400
If my% < yy - 300 Then my% = yy - 300
If my% > yy + 300 Then my% = yy + 300
lc% = _MouseButton(1)
If lc% = -1 Then mouseclick1 = 1
x = 0 - xx + mx%
y = yy - my%
'=====================================================
h = _Hypot(-x, y)
'=====================================================
'origin lines
Line (0, yy)-(800, yy), c(0)
Line (xx, 0)-(xx, 600), c(0)
'=====================================================
'angled wall
a = (Sin(na * .017453292)) * 200
b = (Cos(na * .017453292)) * 200
Line (xx, yy)-(xx + b, yy + a), c(1)
Line (xx, yy)-(xx - b, yy - a), c(1)
'=====================================================
Circle (xx + x, yy - y), 10, c(2) 'point I
Line (xx, yy)-(xx + x, yy - y), c(2) 'line from origin to point I
'=====================================================
nx = Cos(na * (PI / 180)) 'normalize wall angle
ny = Sin(na * (PI / 180)) 'normalize wall angle
dx = -x * ny * -1: dy = y * nx: ndp = dx + dy
'dot product V.N - used to find distance of N
'The distance of N is from the point of origin to the middle of line A
'line A is a line from point I to point R (parallel to the angled wall)
ndpx = Sin(na * (PI / 180)) * ndp
ndpy = Cos(na * (PI / 180)) * ndp
'=====================================================
'calculate point R
th1 = _Atan2(-y, x) 'radian value of ball (point I)
th2 = _Atan2(-ndpy, ndpx) 'radian value of line N
thd = th1 - th2 'find difference
th3 = th2 - thd 'subtract difference from line N
rx = Cos(th3) * h: ry = Sin(th3) * h 'point R position - th3 * length of point I to origin
Circle (xx + rx, yy + ry), 10, c(3) 'point R
Line (xx, yy)-(xx + rx, yy + ry), c(3) 'origin to point R
_Display
Loop Until flag = 1
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Congrats James,
Looks like you've worked it out for yourself.
And dang if I haven't found another AAU (Aliens among us).
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