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Angle Collisions
#91
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

'==============================================================================
'==============================================================================
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'==============================================================================
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'==============================================================================





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 Sub
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#92
I like how that dynamically resizes the impactor and changes speed.  Cool

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.
DO: LOOP: DO: LOOP
sha_na_na_na_na_na_na_na_na_na:
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