What are the maths behind 'Raiden 2' purple laser?

Question

The path of the laser is affected by user input and enemies present on the screen. Here is a video, at 5:00 minutes the laser in question is shown : Raiden II (PS) - 1 Loop Clear - Part 2

UPDATE

Here is a test using Inkscape, ship is at bottom, the first 4 enemies are targeted by the plasma. There seems to be a sort of pattern. I moved the ship first, then the handle from it to form a 45° angle, then while trying to fit the curve I found a pattern of parallel handles and continued so until I reached the last enemy.

Update, 5/26/2012 : I started an XNA project using beziers, there is still some work needed, will update the question next week. Stay tuned !

Update : 5/30/2012 : It really seems that they are using Bézier curves, I think I will be able to replicate/imitate a plasma of such grade. There are two new topics I discovered since last time : Arc length, Runge's phenomenon, first one should help in having a linear movement possible over a Bézier curve, second should help in optimizing the number of vertices. Next time I will put a video so you can see the progress 8-)

Answer 1

I just created something that may help you. It was in response to help somebody on the GLBasic forums.

Here is the forum link with my suggestion: Random Textured Rolling Hills

This is written in GLBasic, but I tried to keep it easy to read, so it should be easily converted to any language.

To use it for your needs, you would need to generate your spline data / points. Replace the 'hill' points in my example with your spline points. You would only need to add an animation / flickering effect somehow. Maybe a random texture shift.

The real 'magic' happens in my 'AddPoint' function:

FUNCTION AddPoint: h AS THillPoint
    DIMPUSH self.points[], h

    // Is this the very first data point?
    IF LEN(self.points[]) = 1
        self.points[0].pu.Set(0, self.points[0].pm.y - self.texture_ht_up)
        self.points[0].pd.Set(0, self.points[0].pm.y + self.texture_ht_dn)
        RETURN
    ENDIF

    ALIAS h0 AS self.points[-2]  // Reference to the 2nd last point
    ALIAS h1 AS self.points[-1]  // Reference to the last point
    LOCAL angle#
    LOCAL v1 AS TVector
    LOCAL v0 AS TVector

    // Calculate 'p2' of HillPoint - form rectangle with previous point
    angle = ATAN(h1.pm.y - h0.pm.y, h1.pm.x - h0.pm.x)  -90// Angle of the two points

    v1.x = COS(angle) * self.texture_ht_up + h1.pm.x
    v1.y = SIN(angle) * self.texture_ht_up + h1.pm.y
    v0.x = COS(angle) * self.texture_ht_up + h0.pm.x
    v0.y = SIN(angle) * self.texture_ht_up + h0.pm.y
    h0.pu = h0.pu.AverageWith(v0)
    h1.pu.Copy(v1)

    v1.x = COS(angle) * -self.texture_ht_dn + h1.pm.x
    v1.y = SIN(angle) * -self.texture_ht_dn + h1.pm.y
    v0.x = COS(angle) * -self.texture_ht_dn + h0.pm.x
    v0.y = SIN(angle) * -self.texture_ht_dn + h0.pm.y
    h0.pd = h0.pd.AverageWith(v0)
    h1.pd.Copy(v1)
ENDFUNCTION

This is where I calculate the final quads / polygons that plots the sprite along the line.

Here's the final results:

And with the polygons' wireframe turned on: