Distorted Android

//        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);

  v.x -= (mvXvert+mvXhorz);

  v.y -= (mvYvert+mvYhorz);

  v.z += force.z*d*d*(3.0*d*d -8.0*d +6.0);                          // thick bubble

  }

//////////////////////////////////////////////////////////////////////////////////////////////

// DISTORT EFFECT

//

// It remains to be computed which of the N,W,E or S case we have: answer: a = min[ Px/Sx , Py/Sy , (w-Px)/(w-Sx) , (h-Py)/(h-Sy) ]

// Computations above are valid for screen (0,0)x(w,h) but here we have (-w/2,-h/2)x(w/2,h/2)

// the vertical part

// Let |(v.x,v.y),(ux,uy)| = |PS|, ux-v.x=dx,uy-v.y=dy, f(x) (0<=x<=|SX|) be the shape of the side of the bubble.

// H(v.x,v.y) = |PS|>|SX| ? 0 : f(|PX|)

//

// Now we also have to take into account the effect horizontal move by V=(u_dVx[i],u_dVy[i]) will have on the normal vector.

// 1. Decompose the V into two subcomponents, one parallel to SX and another perpendicular.

// 2. Convince yourself (draw!) that the perpendicular component has no effect on normals.

// 3. The parallel component changes the length of |SX| by the factor of a=(|SX|-|Vpar|)/|SX| (where the length

// 4. that in turn leaves the x and y parts of the normal unchanged and multiplies the z component by a!

//

// |Vpar| = (u_dVx[i]*dx - u_dVy[i]*dy) / sqrt(ps_sq) = (Vx*dx-Vy*dy)/ sqrt(ps_sq)  (-Vy because y is inverted)

//

// Side of the bubble

// f(t) = t, i.e. f(x) = uz * x/|SX|   (a cone)

// -|PS|/f'(|PX|) = -|PS|*|SX|/uz but since ps_sq=|PS|^2 and d=|PX|/|SX| then |PS|*|SX| = ps_sq/(1-d)

// so finally -|PS|/f'(|PX|) = -ps_sq/(uz*(1-d))

// f(t) = 3t^2 - 2t^3 --> f(0)=0, f'(0)=0, f'(1)=0, f(1)=1 (the bell curve)

// here we have t = x/|SX| which makes f'(|PX|) = 6*uz*|PS|*|PX|/|SX|^3.

// so -|PS|/f'(|PX|) = (-|SX|^3)/(6uz|PX|) =  (-|SX|^2) / (6*uz*d) but

// d = |PX|/|SX| and ps_sq = |PS|^2 so |SX|^2 = ps_sq/(1-d)^2

// so finally -|PS|/f'(|PX|) = -ps_sq/ (6uz*d*(1-d)^2)

// Case 3:

// f(t) = 3t^4-8t^3+6t^2 would be better as this satisfies f(0)=0, f'(0)=0, f'(1)=0, f(1)=1,

// f(0.5)=0.7 and f'(t)= t(t-1)^2 >=0 for t>=0 so this produces a fuller, thicker bubble!

//

// Now, new requirement: we have to be able to add up normal vectors, i.e. distort already distorted surfaces.

// If a surface is given by z = f(x,y), then the normal vector at (x0,y0) is given by (-df/dx (x0,y0), -df/dy (x0,y0), 1 ).

// then the normal to g = f1+f2 is simply given by (f1x+f2x,f1y+f2y,1), i.e. if the third components are equal, then we

// can simply add up the first and second components.

//

// Thus we actually want to compute N(v.x,v.y) = a*(-(dx/|PS|)*f'(|PX|), -(dy/|PS|)*f'(|PX|), 1) and keep adding

// the first two components. (a is the horizontal part)

  {

  vec2 center = vUniforms[effect+1].yz;

  vec2 ps = center-v.xy;

  vec3 force = vUniforms[effect].xyz;

  float d = degree(vUniforms[effect+2],center,ps);

  v.xy += d*force.xy;

  }

//////////////////////////////////////////////////////////////////////////////////////////////

// SINK EFFECT

//

// Pull P=(v.x,v.y) towards center of the effect with P' = P + (1-h)*dist(S-P)

// when h>1 we are pushing points away from S: P' = P + (1/h-1)*dist(S-P)

void sink(in int effect,inout vec3 v)

  {

  vec2 center = vUniforms[effect+1].yz;

  vec2 ps = center-v.xy;

  float h = vUniforms[effect].x;

  float t = degree(vUniforms[effect+2],center,ps) * (1.0-h)/max(1.0,h);

  }

//////////////////////////////////////////////////////////////////////////////////////////////

// SWIRL EFFECT

//

// Let d be the degree of the current vertex V with respect to center of the effect S and Region vRegion.

// by (1-d) around the center of the effect S.

void swirl(in int effect, inout vec3 v)

//

// Generally speaking I'd keep to amplitude < length, as the opposite case has some other problems as well.

  {

  vec2 center     = vUniforms[effect+1].yz;

  float amplitude = vUniforms[effect  ].x;

    vec3 dir= vec3(sinB*cosA,cosB*cosA,sinA);

    v += sin(angle)*deg*dir;

    }

  }

#endif

//////////////////////////////////////////////////////////////////////////////////////////////

  vec3 v = 2.0*u_objD*a_Position;

  vec3 n = a_Normal;

#if NUM_VERTEX>0

  int j=0;

  for(int i=0; i<vNumEffects; i++)

    {

    j+=3;

    }

  restrictZ(v.z);

#endif