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+---- Thread: Angle Collisions (/showthread.php?tid=972)
RE: Angle Collisions - james2464 - 11-03-2022
This is my first attempt at higher speed collisions.
Side collisions only for now. I haven't thought through the endpoints yet - not sure how that'll work.
For the side collisions, the math used for this allowed for an opportunity that I didn't realize until now. Until now, I was checking for a collision only. So when the ball was actually touching the line. That meant that high speeds would result in missed collisions, if the frame by frame movement was larger than the diameter of the ball. It seems simple now, but I had to set up a comparison of the current frame and the previous one and determine if the ball had completely crossed the line, instead of just intersecting it. And with the same position correction I had already set up, it was just a matter of applying this correction.
One thing that's interesting with the vector math. The dot product calculation identifies one side of the line as positive and the other negative. I think OldMoses mentioned that earlier. But it turned out that this was important with the lookahead, because it directly helps to know if the ball went across the line (from positive to negative or vice versa).
This program starts with a 29 speed and 2 ball radius.
Code: (Select All)
'vector reflection and line detection demo
'side collision lookahead added Nov 2 2022
'james2464
'CONTROLS:
'Arrow keys: Left and right: change size of ball
' Up and Down: change speed
'Space Bar : Random Restart
'Escape key: Quit
Dim Shared scx, scy As Integer
scx = 800: scy = 600
Screen _NewImage(scx, scy, 32)
Const PI = 3.141592654#
Randomize Timer
Dim Shared x, y, h, xv, yv, ndpx, ndpy, rx, ry, rt, i2w, i2ws
Dim Shared cpa, cpb, a, b, a2, b2, sbx, sby, newxv, newyv, oldxv, oldyv
Dim Shared lastcollision, collisiontype, correctionwasmade
Dim Shared ndpprevious, ndpxprevious, ndpyprevious, psbx, psby, pastwall, pastline1
Dim Shared bg&
bg& = _NewImage(scx + 1, scy + 1, 32)
Dim Shared c(30) As Long
colour1
Type fixedwall
x1 As Integer
x2 As Integer
y1 As Integer
y2 As Integer
b As Integer
bx1 As Integer
bx2 As Integer
by1 As Integer
by2 As Integer
xx As Single
yy As Single
wlen As Single
nx As Single
ny As Single
sc As Single
sc1 As Single
sc2 As Single
End Type
Dim Shared w(50) As fixedwall
Dim Shared walltotal, ballrad
ballrad = 2 'ball radius
walltotal = 8
For t = 1 To walltotal
w(t).b = ballrad + 2
Next t
wallsetup
_PutImage (1, 1)-(scx - 1, scy - 1), 0, bg&, (1, 1)-(scx - 1, scy - 1) 'take snapshot of screen
'start
xv01 = 15
yv01 = 25
sbx01 = 350
sby01 = 300
xv = xv01 'starting ball x velocity
yv = yv01 'starting ball y velocity
sbx = sbx01 'starting x position
sby = sby01 'starting y position
flag = 0
Do
_Limit 20
Cls
_PutImage (0, 0)-(scx, scy), bg&, 0 'draw background
'rcirc = Rnd * 20 + 3 'display to show program is active
'Circle (700, 100), rcirc, c(6)
'Paint (400, 300), c(30), c(1)
'=====================================================
'_MouseHide
sbx = sbx + xv
sby = sby + yv
If sbx > (scx - ballrad) Then
xv = xv * -1
t = sbx - (scx - ballrad)
sbx = (scx - ballrad) - t
End If
If sby > (scy - ballrad) Then
yv = yv * -1
t = sby - (scy - ballrad)
sby = (sby - ballrad) - t
End If
If sbx < ballrad Then
xv = xv * -1
t = ballrad - sbx
sbx = ballrad + t
End If
If sby < ballrad Then
yv = yv * -1
t = ballrad - sby
sby = ballrad + t
End If
'=====================================================
correctionwasmade = 0: collisiontype = 0
rt = 0
rt = nearestwall 'determine the nearest wall
Line (w(rt).x1, w(rt).y1)-(w(rt).x2, w(rt).y2), c(4) 'highlight the nearest wall (green)
nearestwallcheck 'check the nearest wall for collision
If cpb > 0 Then
If rt = lastcollision Then
'Locate 1, 1
'Print i2ws; i2w
'Line (cpb, cpa)-(cpb + x, cpa - y), c(2) 'collision to point I
'Line (cpb, cpa)-(sbx, sby), c(2) 'collision to point I
'Line (cpb, cpa)-(cpb - oldxv * ballrad * 4, cpa - oldyv * ballrad * 4), c(1) 'collision to point I
'Line (cpb + x, cpa - y)-(cpb + rx, cpa + ry), c(4) 'line A
'Line (cpb, cpa)-(cpb + newxv * ballrad * 4, cpa + newyv * ballrad * 4), c(1) 'collision to point R
'Line (cpb, cpa)-(cpb + ndpx * 50, cpa - ndpy * 50), c(5) 'line N
Circle (cpb, cpa), 1, c(4) 'circle the collision point
End If
Else
rt = 0
cpa = 0: cpb = 0: x = 0: y = 0
rx = 0: ry = 0: ndpx = 0: ndpy = 0
End If
'=====================================================
Circle (sbx, sby), (ballrad - 1), c(2) 'screen location of ball
'Paint (sbx, sby), c(17), c(2)
'_Delay .5 'use to step through animation to see each frame separately
If _KeyDown(18432) Then ' IF up arrow key was pressed
yv = yv * 1.1
xv = xv * 1.1
End If
If _KeyDown(20480) Then ' IF down arrow key was pressed
yv = yv * .9
xv = xv * .9
End If
If _KeyDown(19200) Then ' IF left arrow key was pressed
ballrad = ballrad * .9
If ballrad < 2 Then ballrad = 2
End If
If _KeyDown(19712) Then ' IF right arrow key was pressed
ballrad = ballrad * 1.1
If ballrad > 40 Then ballrad = 40
End If
For t = 1 To walltotal
w(t).b = ballrad + 2
Next t
If _KeyDown(32) Then ' IF space bar was pressed
Cls
_Delay .5
wallsetup
_PutImage (1, 1)-(scx - 1, scy - 1), 0, bg&, (1, 1)-(scx - 1, scy - 1) 'take snapshot of screen
xv = xv01 'starting ball x velocity
yv = yv01 'starting ball y velocity
sbx = sbx01 'starting x position
sby = sby01 'starting y position
rt = 0
cpa = 0: cpb = 0: x = 0: y = 0
rx = 0: ry = 0: ndpx = 0: ndpy = 0
End If
If _KeyDown(27) Then ' IF escape key was pressed
End
End If
displayspd = _Hypot(xv, yv)
Locate 1, 1
Print "LEFT and RIGHT keys : Ball radius:"; Int(ballrad)
Print "UP and DOWN keys : Speed:"; displayspd
Print "SPACE BAR : Random Restart"
Print "ESC : Quit"
_Display
If mouseclick2 = 1 Then flag = 1
Loop Until flag = 1
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
'==============================================================================
Function nearestwall
nearestwall = 0
scoretobeat = 1000
closest = 0
Locate 1, 1
For ct = 1 To walltotal 'get each wall endpoints and mid point distances from ball
tdx1 = Abs(sbx - w(ct).x1)
tdy1 = Abs(sby - w(ct).y1)
score1 = _Hypot(tdx1, tdy1) 'distance from ball center to line endpoint 1
tdx2 = Abs(sbx - w(ct).x2)
tdy2 = Abs(sby - w(ct).y2)
score2 = _Hypot(tdx2, tdy2) 'distance from ball center to line endpoint 2
If score2 < score1 Then
lowscore = score2: low$ = "E2"
Else
lowscore = score1: low$ = "E1"
End If
tdxx = Abs(sbx - w(ct).xx)
tdyy = Abs(sby - w(ct).yy)
score3 = _Hypot(tdxx, tdyy) 'distance from ball center to line mid point
If score3 < lowscore Then
lowscore = score3: low$ = "M"
End If
x = sbx - w(ct).xx: y = 0 - sby + w(ct).yy
dx = -x * w(ct).ny * -1: dy = y * w(ct).nx
ndp = dx + dy
score4 = Abs(ndp) 'distance ball center to side of wall (using vector dot product) aka "POINT N"
'find if score4 is valid (ball is within the line, if outside then endpoints are used)
ndpx = w(ct).ny * (ndp): ndpy = w(ct).nx * (ndp) 'screen position of point N
score4distx = Abs(sbx - (w(ct).xx + ndpx))
score4disty = Abs(sby - (w(ct).yy - ndpy))
score4disth = _Hypot(score4distx, score4disty)
If score4disth <= w(ct).wlen Then 'if within the line segment then score4 counts
If score4 < ballrad * 5 Then
'display line N
'Line (w(ct).xx, w(ct).yy)-(w(ct).xx + ndpx, w(ct).yy - ndpy), c(ct)
'Circle (w(ct).xx + ndpx, w(ct).yy - ndpy), 2, c(ct)
End If
If score4 < lowscore Then
lowscore = score4: low$ = "N"
End If
End If
w(ct).sc = lowscore
If lowscore < scoretobeat Then
scoretobeat = lowscore
closest = ct
End If
'Print ct; w(ct).sc; "scores"; score1; score2; score3; score4; low$
Next ct
nearestwall = closest
End Function
Sub nearestwallcheck
'start by getting position info
x = sbx - w(rt).xx: y = 0 - sby + w(rt).yy 'location relative to wall mid point
h = (_Hypot(-x, y))
dx = -x * w(rt).ny * -1: dy = y * w(rt).nx: ndp = dx + dy
'dot product V.N - used to find distance of N
ndpx = w(rt).ny * ndp
ndpy = w(rt).nx * ndp
'calculate new vector (point R)
th1 = _Atan2(-y, x) 'radian value of ball (point I)
th2 = _Atan2(-ndpy, ndpx) 'radian value of line N (orthagonal to wall)
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 collision point
'angled wall endpoints
a = w(rt).ny * w(rt).wlen: b = w(rt).nx * w(rt).wlen: a2 = a * -1: b2 = b * -1
'find length of line A
segx = Abs(x - rx): segy = Abs((w(rt).yy - y) - (w(rt).yy + ry)): sega = _Hypot(segx, segy)
'find distance from point I to wall endpoints
i2w1x = Abs(x - b): i2w1y = Abs(a + y): i2w2x = Abs(x + b): i2w2y = Abs(y - a)
i2wh1 = _Hypot(i2w1x, i2w1y): i2wh2 = _Hypot(i2w2x, i2w2y)
If i2wh1 < i2wh2 Then 'determine which end the ball is closer to
i2ws = 1: i2w = i2wh1
Else
i2ws = 2: i2w = i2wh2
End If
If sega < (w(rt).wlen * 2) Then
ndpcurrent = ndp
ndpxcurrent = ndpx
ndpycurrent = ndpy
'Locate 1, 1
'Print "current position"
'Print sbx; sby; ndpcurrent; ndpxcurrent; ndpycurrent
'Print "previous"
'Print psbx; psby; ndpprevious; ndpxprevious; ndpyprevious
If ndpcurrent > 0 Then
If ndpprevious < 0 Then
pastwall = 1
Else
pastwall = 0
End If
Else
If ndpprevious > 0 Then
pastwall = 1
Else
pastwall = 0
End If
End If
'Sleep
If pastwall = 1 Then
'perform a major position correction
'=================================
pastline1 = ballrad + Abs(ndp)
ballspd = _Hypot(xv, yv)
cor2 = pastline1 / ballspd
corx = xv * cor2: cory = yv * cor2
csbx = sbx - corx: csby = sby - cory
'=================================
sbx = csbx
sby = csby
If ndp > 0 Then
ndp = -ballrad
Else
ndp = ballrad
End If
End If
'Print pastline1
'Sleep
If Abs(ndp) <= ballrad Then
'side collision
If pastwall = 0 Then
positioncorrection 'perform correction
End If
collisionpointa = w(rt).ny * (sega / 2)
collisionpointb = w(rt).nx * (sega / 2)
If i2ws = 1 Then
cpa = w(rt).yy + collisionpointa: cpb = w(rt).xx + collisionpointb
End If
If i2ws = 2 Then
cpa = w(rt).yy - collisionpointa: cpb = w(rt).xx - collisionpointb
End If
sidecollisionvector 'find new vector
'add position correction back into new vector
'get new vector normals
tx = xv: ty = yv: th = _Hypot(tx, ty)
tx2 = tx / th: ty2 = ty / th
corx = tx2 * pastline1
cory = ty2 * pastline1
sbx = sbx + corx
sby = sby + cory
End If
Else
If i2w <= ballrad Then '***** collision with endpoint of the line *****
If i2ws = 1 Then
cpa = w(rt).yy - a2: cpb = w(rt).xx + b
endpointcollision1
End If
If i2ws = 2 Then
cpa = w(rt).yy - a: cpb = w(rt).xx + b2
endpointcollision2
End If
End If
End If
ndpprevious = ndp
ndpxprevious = ndpx
ndpyprevious = ndpy
psbx = sbx
psby = sby
End Sub
Sub positioncorrection '(for side collisions)
x = sbx - w(rt).xx: y = 0 - sby + w(rt).yy 'location relative to wall mid point
h = (_Hypot(-x, y))
dx = -x * w(rt).ny * -1: dy = y * w(rt).nx: ndp = dx + dy
pastline1 = ballrad - Abs(ndp)
If pastline1 > 0 Then
'=================================
ballspd = _Hypot(xv, yv)
cor2 = pastline1 / ballspd
corx = xv * cor2: cory = yv * cor2
csbx = sbx - corx: csby = sby - cory
'=================================
sbx = csbx
sby = csby
End If
End Sub
Sub sidecollisionvector
tx = xv: ty = yv: th = _Hypot(tx, ty)
tx2 = tx / th: ty2 = ty / th
spd = _Hypot(tx, ty) 'speed of existing motion vector
th1 = _Atan2(tx, -ty) 'radian value of motion vector
th2 = _Atan2(-ndpy, ndpx) 'radian value of line N
thd = th1 - th2 'find difference
th3 = th2 - thd 'subtract difference from line N
newxv = Sin(th3): newyv = Cos(th3)
'position correction
corx = newxv * pastline1: cory = newyv * pastline1
oldxv = tx2: oldyv = ty2
xv = newxv * spd: yv = newyv * spd * -1
newh = _Hypot(xv, yv)
newxv = xv / newh: newyv = yv / newh
lastcollision = rt
End Sub
Sub endpointcollision1
tx = x - b: ty = y + a2: th = _Hypot(tx, ty) 'tx, ty are distances from ball to end of line
If th < ballrad Then
past1 = ballrad - th
'position correction
txv = xv: tyv = yv: tspd = _Hypot(xv, yv)
cor2 = past1 / tspd
corx = xv * cor2: cory = yv * cor2
'Locate 1, 1
'Print "End1"; ballrad; th; past1; tspd; cor2; xv; corx; yv; cory
'Print sbx; sby
'_Display
'Sleep
'apply correction
csbx = sbx - corx: csby = sby - cory
tx = tx - corx: ty = ty - cory: th = _Hypot(tx, ty)
sbx = csbx: sby = csby
'Print "corrected"; sbx; sby
'_Display
'Sleep
End If
'continue to calculate new vector
tx2 = tx / th: ty2 = ty / th 'tx2, ty2 are normalized
txv = Abs(xv): tyv = Abs(yv): spd = _Hypot(txv, tyv)
oldxv = xv: oldyv = yv
oldh = _Hypot(xv, yv)
oldxv = oldxv / oldh: oldyv = oldyv / oldh
xv = tx2 * spd: yv = ty2 * spd * -1
newh = _Hypot(xv, yv)
newxv = xv / newh: newyv = yv / newh
lastcollision = rt
End Sub
Sub endpointcollision2
tx = x - b2: ty = y - a: th = _Hypot(tx, ty)
If th < ballrad Then
past2 = ballrad - th
'position correction
txv = xv: tyv = yv: tspd = _Hypot(xv, yv)
cor2 = past2 / tspd
corx = xv * cor2: cory = yv * cor2
'Locate 1, 1
'Print "End2"; ballrad; th; past2; tspd; cor2; xv; corx; yv; cory
'Print sbx; sby
'_Display
'Sleep
'apply correction
csbx = sbx - corx: csby = sby - cory
tx = tx - corx: ty = ty - cory: th = _Hypot(tx, ty)
sbx = csbx: sby = csby
'Print "corrected"; sbx; sby
'_Display
'Sleep
End If
'continue to calculate new vector
tx2 = tx / th: ty2 = ty / th
txv = Abs(xv): tyv = Abs(yv): spd = _Hypot(txv, tyv)
oldxv = xv: oldyv = yv
oldh = _Hypot(xv, yv)
oldxv = oldxv / oldh: oldyv = oldyv / oldh
xv = tx2 * spd: yv = ty2 * spd * -1
newh = _Hypot(xv, yv)
newxv = xv / newh: newyv = yv / newh
lastcollision = rt
End Sub
Sub wallsetup
'w(1).x1 = 500: w(1).x2 = 300: w(1).y2 = 1: w(1).y1 = scy
w(1).x1 = 400: w(1).x2 = w(1).x1 + Rnd * 100 + 50: w(1).y1 = 200: w(1).y2 = 250
w(2).x1 = w(1).x2: w(2).x2 = w(2).x1 + Rnd * 100: w(2).y1 = 250: w(2).y2 = 350
w(3).x1 = w(2).x2: w(3).x2 = w(3).x1 + Rnd * 100: w(3).y1 = 350: w(3).y2 = 450
w(4).x1 = w(3).x2: w(4).x2 = w(4).x1 - Rnd * 100 - 50: w(4).y1 = 450: w(4).y2 = 470
w(5).x1 = w(4).x2: w(5).x2 = w(5).x1 - Rnd * 100 - 100: w(5).y1 = 470: w(5).y2 = 450
w(6).x1 = w(5).x2: w(6).x2 = w(6).x1 - Rnd * 100 - 100: w(6).y1 = 450: w(6).y2 = 350
w(7).x1 = w(6).x2: w(7).x2 = w(7).x1 - Rnd * 100 - 50: w(7).y1 = 350: w(7).y2 = 250
w(8).x1 = w(7).x2: w(8).x2 = w(1).x1: w(8).y1 = 250: w(8).y2 = 200
'inner walls
'w(9).x1 = 400: w(9).x2 = w(9).x1 + Rnd * 50 + 10: w(9).y1 = 320: w(9).y2 = 350
'w(10).x1 = 400: w(10).x2 = w(10).x1 - Rnd * 50 - 10: w(10).y1 = 320: w(10).y2 = 350
'w(11).x1 = w(10).x2: w(11).x2 = w(9).x2: w(11).y1 = w(10).y2: w(11).y2 = w(9).y2
For wct = 1 To walltotal
w(wct).bx1 = w(wct).x1: w(wct).bx2 = w(wct).x2
w(wct).by1 = w(wct).y1: w(wct).by2 = w(wct).y2
'orient outer box
If w(wct).bx1 > w(wct).bx2 Then
t = w(wct).bx1
w(wct).bx1 = w(wct).bx2
w(wct).bx2 = t
End If
If w(wct).by1 > w(wct).by2 Then
t = w(wct).by1
w(wct).by1 = w(wct).by2
w(wct).by2 = t
End If
w(wct).bx1 = w(wct).bx1 - w(wct).b: w(wct).bx2 = w(wct).bx2 + w(wct).b
w(wct).by1 = w(wct).by1 - w(wct).b: w(wct).by2 = w(wct).by2 + w(wct).b
Line (w(wct).x1, w(wct).y1)-(w(wct).x2, w(wct).y2), c(1)
'Line (w(wct).bx1, w(wct).by1)-(w(wct).bx2, w(wct).by2), c(2), B
w(wct).xx = (w(wct).x2 - w(wct).x1) / 2 + w(wct).x1
w(wct).yy = (w(wct).y2 - w(wct).y1) / 2 + w(wct).y1
'Circle (w(wct).xx, w(wct).yy), 5, c(4)
tx = w(wct).x2 - w(wct).xx: ty = w(wct).y2 - w(wct).yy
w(wct).wlen = _Hypot(tx, ty)
w(wct).nx = tx / w(wct).wlen 'normalized wall angle
w(wct).ny = ty / w(wct).wlen 'normalized wall angle
Next wct
End Sub
Sub colour1
c(0) = _RGB(0, 100, 0)
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)
c(6) = _RGB(255, 0, 255)
c(7) = _RGB(30, 30, 255)
c(8) = _RGB(150, 150, 250)
c(9) = _RGB(250, 150, 150)
c(10) = _RGB(150, 250, 150)
c(11) = _RGB(255, 255, 255)
c(12) = _RGB(255, 255, 0)
c(13) = _RGB(255, 0, 0)
c(14) = _RGB(0, 255, 0)
c(15) = _RGB(0, 255, 255)
c(16) = _RGB(255, 0, 255)
c(17) = _RGB(30, 30, 255)
c(18) = _RGB(150, 150, 250)
c(19) = _RGB(250, 150, 150)
c(20) = _RGB(150, 250, 150)
c(21) = _RGB(255, 255, 255)
c(22) = _RGB(255, 255, 0)
c(23) = _RGB(255, 0, 0)
c(24) = _RGB(0, 255, 0)
c(25) = _RGB(0, 255, 255)
c(26) = _RGB(255, 0, 255)
c(27) = _RGB(30, 30, 255)
c(28) = _RGB(150, 150, 250)
c(29) = _RGB(250, 150, 150)
c(30) = _RGBA(0, 0, 0, 5)
End SubRE: Angle Collisions - OldMoses - 11-04-2022
I like how that dynamically resizes the impactor and changes speed.
Dot product returning a negative was how I got mine to readily let a ball back in if one escaped. Given that all the orthogonals in mine were pointed inward, it was as simple as skipping the bounce code if the dot product result was negative. If it was negative it meant that the ball had to be outside already. However, before I implemented that test, the ball would reflect off the out side just the same as the inside, meaning that the bounce calculation is insensitive to the sign of the result. That was an eye opener for me. A very useful tool indeed. It also figures heavily in my pool program, doing the two moving ball deflections.