Angle Collisions

[OldMoses]

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