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Equation for ball deflection

  1. Nov 16, 2013 #1
    Hi First Post so go easy.

    I am teaching a programming course for kids between 10-14.

    We are using scratch which is a sprite animator.

    We are trying to make a breakout game (you know the one where you break block with a ball)

    We have a ball sprite that we can easily bounce around the screen as there is a build in function called "If on edge,bounce".

    The issue we are having is when the ball collides with another sprite (a block or the paddle).

    We would like to know if there is an equation that would work for all collisions so that,

    The angle of the ball after the collision is equal and opposite to the angle of the ball before the collision.

    e.g. If the ball is moving from left to right and up the screen and collides with block at a 25 degree angle, it continues left to right but leaves the block at a 25 degree angle but is now moving in a downward direction.

    Here is what we know ,

    The direction of the sprite in degrees. This is measured between (-179 and 180)

    0 degrees is North (up)
    90 degrees is East (right)
    180 degrees is South (down)
    -90 degrees is West (left)

    We can turn a sprite either left or right by a number of degrees

    So in my 25 degree example above the spirtes direction would be 25 degrees (NE) before the collision and 115 degrees (SE) after the collision,

    If the sprite were to be travelling right to left :

    Its direction would be -25 degrees (NW) before the collision and -115 degrees (SW) after the collision

    Can one of you Physics Geniuses come up with an equation that would work for all collisions?

    i.e. on all 4 sides of the block from all possible directions ?

    Thanks in advance,

    Drumbrae Coder Dojo Pupils
  2. jcsd
  3. Nov 17, 2013 #2


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    Can you define the sides of the blocks as "edges" and reuse the function you already have?
  4. Nov 17, 2013 #3


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    If the velocity of the ball has horizontal and vertical components then I think you only need to change the sign of one of them depending on the orientation of the face it hits. eg if it hits a vertical edge then change the sign of the horizontal component. Likewise if it hits a horizontal edge change the sign of the vertical component...

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  5. Nov 18, 2013 #4
    It would have to depend on what you have defined as 180 and 0 degrees. The only thing you need to know is that angle of incidence is equal to the angle of reflection. The angle the ball comes in on will equal the angle that the ball will deflect. In your program your class definition (I do not know syntax for scratch) you could simple take the supplement or you could just take the opposite.
  6. Nov 19, 2013 #5


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    The easiest thing to do is just reflect the horizontal or vertical velocity, depending on which side of the block or paddle was hit. If you want to give the player a little more control, you can change the angle by hitting the corner of a block or paddle. To handle this case, you need the radius of curvature of the corner plus the radius of the ball. In the simple case, only the ball is curved.

    Something like the following should work for a corner collision..

    R = radius of ball
    (x0, y0) = position of ball center
    (x1, y1) = position of corner
    most programming languages have a function called atan2 which gives the angle based on a vertical and horizontal displacement.
    angle = atan2(y1-y0, x1-x0)
    (vxi, vyi) = initial velocity of ball
    (vxf, vyf) = final velocity of ball
    vxf = -vxi*cos(2*angle) + vyi*sin(2*angle)
    vyf = vxi*sin(2*angle) + vyi*cos(2*angle)

    You might need to fiddle with the signs if I messed them up.
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