Distorted Android

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

// Copyright 2017 Leszek Koltunski                                                               //

//                                                                                               //

// the Free Software Foundation, either version 2 of the License, or                             //

// (at your option) any later version.                                                           //

//                                                                                               //

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                                 //

// GNU General Public License for more details.                                                  //

//                                                                                               //

// You should have received a copy of the GNU General Public License                             //

package org.distorted.library.effect;

import org.distorted.library.type.Data3D;

import org.distorted.library.type.Data4D;

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

 * Distort the Mesh by applying a 3D vector of force.

 */

  {

  private Data4D mRegion;

    {

    mRegion.get(uniforms,index+REGION_OFFSET,currentDuration,step);

// PUBLIC API

// the region circle (if P is inside the circle); (Vx,Vy,Vz) - force vector.

//

// horizontal part

// Point (Px,Py) gets moved by vector (Wx,Wy) where Wx/Wy = Vx/Vy i.e. Wx=aVx and Wy=aVy where

// 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)

//

// Let vector PS = (dx,dy), f(x) (0<=x<=|SX|) be the shape of the side of the bubble.

// H(Px,Py) = |PS|>|SX| ? 0 : f(|PX|)

// N(Px,Py) = |PS|>|SX| ? (0,0,1) : ( -(dx/|PS|)sin(beta), -(dy/|PS|)sin(beta), cos(beta) ) where tan(beta) is f'(|PX|)

// ( i.e. normalize( dx, dy, -|PS|/f'(|PX|) )

// 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

//    can be negative depending on the direction)

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

//

//

// Side of the bubble

//

// choose from one of the three bubble shapes: the cone, the thin bubble and the thick bubble

// Case 1:

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

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

// Case 2:

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

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

// 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!

// so finally -|PS|/f'(|PX|) = -ps_sq/ (12Vz*d*(1-d)^3)

// 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 ).

// so if we have two surfaces defined by f1(x,y) and f2(x,y) with their normals expressed as (f1x,f1y,1) and (f2x,f2y,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.

//

// 2019-01-09 fixes for stuff discovered with the Earth testing app

// Now, the above stuff works only if the normal vector is close to (0,0,1). To make it work for any situation,

// rotate the normal, force and ps vectors along the axis (n.y,-n.x,0) and angle A between the normal and (0,0,1)

// then modify the rotated normal (so (0,0,1)) and rotate the modified normal back.

//

// if we have a vector (vx,vy,vz) that w want to rotate with a rotation that turns the normal into (0,0,1), then

// a) axis of rotation = (n.x,n.y,n.z) x (0,0,1) = (n.y,-n.x,0)

// b) angle of rotation A: cosA = (n.x,n.y,n.z)*(0,0,1) = n.z     (and sinA = + sqrt(1-n.z^2))

//

// so normalized axisNor = (n.x/ sinA, -n.y/sinA, 0) and now from Rodrigues rotation formula

// Vrot = v*cosA + (axisNor x v)*sinA + axisNor*(axis*v)*(1-cosA)

//

// which makes Vrot = (a+n.y*c , b-n.y*c , v*n) where

// a = vx*nz-vz*nx , b = vy*nz-vz*ny , c = (vx*ny-vy*nx)/(1+nz)    (unless n=(0,0,-1))

/**

    {

    addEffect(EffectName.DISTORT,

      + "vec4 region= vUniforms[effect+2];                             \n"

      + "if( d>0.0 )                                                   \n"

      + "  {                                                           \n"

      + "  v += d*force;                                               \n"

      + "  float tr = 1.0 / (tp - (1.0 - sign(tp)));                   \n"

      + "  float bp = ps.y*n.z - ps.z*n.y;                             \n"   //

      + "  float cp =(ps.x*n.y - ps.y*n.x)*tr;                         \n"   //

      + "  vec3 psRot = vec3( ap+n.y*cp , bp-n.x*cp , dot(ps,n) );     \n"   //

      + "  float corr= sign(len)-1.0;                                  \n"   // make N (0,0,1) if ps=(0,0,0)

      + "  vec3 N = vec3( -dot(force,n)*psRot.xy, region.w*len-corr ); \n"   // modified rotated normal

      + "  float an = N.x*n.z + N.z*n.x;                               \n"   // now create the normal vector

      + "  float bn = N.y*n.z + N.z*n.y;                               \n"   // back from our modified normal

      + "  float cn =(N.x*n.y - N.y*n.x)*tr;                           \n"   // rotated back

      + "  n = vec3( an+n.y*cn , bn-n.x*cn , -N.x*n.x-N.y*n.y+N.z*n.z);\n"   // notice 4 signs change!

      + "  }                                                           \n"

    }

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

/**

 * @param vector vector of force the Center of the Effect is currently being dragged with.

 * @param center 3-dimensional Data that, at any given time, returns the Center of the Effect.

 * @param region Region that masks the Effect.

 */

  public VertexEffectDistort(Data3D vector, Data3D center, Data4D region)

    {

    super(EffectName.DISTORT);

    mVector = vector;

    mCenter = center;

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

/**

 * @param vector vector of force the Center of the Effect is currently being dragged with.

 * @param center 3-dimensional Data that, at any given time, returns the Center of the Effect.

 */

  public VertexEffectDistort(Data3D vector, Data3D center)

    {

    super(EffectName.DISTORT);

    mVector = vector;

    mCenter = center;