Distorted Android

// Deform the whole shape of the Object by force V. Algorithm is as follows:

//

// Suppose we apply force (Vx,Vy) at point (Cx,Cy) (i.e. the center of the effect). Then, first of all,

// divide the rectangle into 4 smaller rectangles along the 1 horizontal + 1 vertical lines that pass

// through (Cx,Cy). Now suppose we have already understood the following case:

//

// A vertical (0,Vy) force applied to a rectangle (WxH) in size, at center which is the top-left corner

// of the rectangle.  (*)

//

// If we understand (*), then we understand everything, because in order to compute the movement of the

// whole rectangle we can apply (*) 8 times: for each one of the 4 sub-rectangles, apply (*) twice,

// once for the vertical component of the force vector, the second time for the horizontal one.

//

// Let's then compute (*):

// 1) the top-left point will move by exactly (0,Vy)

// 2) we arbitrarily decide that the top-right point will move by (|Vy|/(|Vy|+A*W))*Vy, where A is some

//    arbitrary constant (const float A below). The F(V,W) = (|Vy|/(|Vy|+A*W)) comes from the following:

//    a) we want F(V,0) = 1

//    b) we want lim V->inf (F) = 1

//    c) we actually want F() to only depend on W/V, which we have here.

// 3) then the top edge of the rectangle will move along the line Vy*G(x), where G(x) = (1 - (A*W/(|Vy|+A*W))*(x/W)^2)

// 4) Now we decide that the left edge of the rectangle will move along Vy*H(y), where H(y) = (1 - |y|/(|Vy|+C*|y|))

//    where C is again an arbitrary constant. Again, H(y) comes from the requirement that no matter how

//    strong we push the left edge of the rectangle up or down, it can never 'go over itself', but its

//    length will approach 0 if squeezed very hard.

// 5) The last point we need to compute is the left-right motion of the top-right corner (i.e. if we push

//    the top-left corner up very hard, we want to have the top-right corner not only move up, but also to

//    the left at least a little bit).

//    We arbitrarily decide that, in addition to moving up-down by Vy*F(V,W), the corner will also move

//    left-right by I(V,W) = B*W*F(V,W), where B is again an arbitrary constant.

// 6) combining 3), 4) and 5) together, we arrive at a movement of an arbitrary point (x,y) away from the

//    top-left corner:

//    X(x,y) = -B*x * (|Vy|/(|Vy|+A*W)) * (1-(y/H)^2)                               (**)

//    Y(x,y) = Vy * (1 - |y|/(|Vy|+C*|y|)) * (1 - (A*W/(|Vy|+A*W))*(x/W)^2)         (**)

//

// We notice that formulas (**) have been construed so that it is possible to continously mirror them

// left-right and up-down (i.e. apply not only to the 'bottom-right' rectangle of the 4 subrectangles

// but to all 4 of them!).

//

// Constants:

// a) A : valid values: (0,infinity). 'Bendiness' if the surface - the higher A is, the more the surface

//        bends. A<=0 destroys the system,

// b) B : valid values: <-1,1>. The amount side edges get 'sucked' inwards when we pull the middle of the

//        top edge up. B=0 --> not at all, B=1: a looot. B=-0.5: the edges will actually be pushed outwards

//        quite a bit. One can also set it to <-1 or >1, but it will look a bit ridiculous.

// c) C : valid values: <1,infinity). The derivative of the H(y) function at 0, i.e. the rate of 'squeeze'

//        surface gets along the force line. C=1: our point gets pulled very closely to points above it

//        even when we apply only small vertical force to it. The higher C is, the more 'uniform' movement

//        along the force line is.

//        0<=C<1 looks completely ridiculous and C<0 destroys the system.

  const vec2 one = vec2(1.0,1.0);

  const float B = 0.2;

  const float C = 5.0;

  quot = quot*quot;                          // ( (x/W)^2 , (y/H)^2 ) where x,y are distances from V to center

  float denomV = 1.0 / (aForce.y + Aw.x);

  float denomH = 1.0 / (aForce.x + Aw.y);

  vec2 vertCorr= one - aDist / ( aForce+C*aDist + (one-sign(aForce)) );

  float mvXvert = -B * dist.x * aForce.y * (1.0-quot.y) * denomV;    // impact the vertical   component of the force vector has on horizontal movement

  float mvYhorz = -B * dist.y * aForce.x * (1.0-quot.x) * denomH;    // impact the horizontal component of the force vector has on vertical   movement

  float mvYvert =  force.y * (1.0-quot.x*Aw.x*denomV) * vertCorr.y;  // impact the vertical   component of the force vector has on vertical   movement

  float mvXhorz = -force.x * (1.0-quot.y*Aw.y*denomH) * vertCorr.x;  // impact the horizontal component of the force vector has on horizontal movement