Distorted Android

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

// Copyright 2017 Leszek Koltunski                                                               //

//                                                                                               //

// This file is part of Distorted.                                                               //

//                                                                                               //

// Distorted is free software: you can redistribute it and/or modify                             //

// it under the terms of the GNU General Public License as published by                          //

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

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

//                                                                                               //

// Distorted is distributed in the hope that it will be useful,                                  //

// but WITHOUT ANY WARRANTY; without even the implied warranty of                                //

// 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                             //

// along with Distorted.  If not, see <http://www.gnu.org/licenses/>.                            //

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

package org.distorted.library.effect;

import org.distorted.library.type.Data3D;

import org.distorted.library.type.Data4D;

import org.distorted.library.type.Static4D;

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

public class VertexEffectDistort extends VertexEffect

  {

  private Data3D mVector, mCenter;

  private Data4D mRegion;

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

/**

 * Distort a (possibly changing in time) part of the Object by a (possibly changing in time) vector of force.

 *

 * @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;

    mRegion = (region==null ? new Static4D(0,0,Float.MAX_VALUE, Float.MAX_VALUE) : region);

    }

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

/**

 * Distort the whole Object by a (possibly changing in time) vector of force.

 *

 * @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;

    mRegion = new Static4D(0,0,Float.MAX_VALUE, Float.MAX_VALUE);

    }

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

  public boolean compute(float[] uniforms, int index, long currentDuration, long step )

    {

    mCenter.get(uniforms,index+5,currentDuration,step);

    mRegion.get(uniforms,index+8,currentDuration,step);

    boolean ret = mVector.get(uniforms,index,currentDuration,step);

    uniforms[index+1] =-uniforms[index+1];

    uniforms[index+9] =-uniforms[index+9];

    return ret;

    }

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

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

// a=Py/Sy (N --> when (Px,Py) is above (Sx,Sy)) or a=Px/Sx (W) or a=(w-Px)/(w-Sx) (E) or a=(h-Py)/(h-Sy) (S)

// 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|)

// N(v.x,v.y) = |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|))

//

// 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.

// Solution:

// 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!

//

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

// a =  (|SX| - |Vpar|)/|SX| = 1 - |Vpar|/((sqrt(ps_sq)/(1-d)) = 1 - (1-d)*|Vpar|/sqrt(ps_sq) = 1-(1-d)*(Vx*dx-Vy*dy)/ps_sq

//

// Side of the bubble

//

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

// Case 1:

// 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))

//

// Case 2:

// 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!

// then -|PS|/f'(|PX|) = (-|PS|*|SX)) / (12uz*d*(d-1)^2) but |PS|*|SX| = ps_sq/(1-d) (see above!)

// so finally -|PS|/f'(|PX|) = -ps_sq/ (12uz*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.

//

// 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)

  public static void enable()

    {

    addEffect(EffectName.DISTORT,

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

      + "vec2 ps = center-v.xy; \n"

      + "vec3 force = vUniforms[effect].xyz; \n"

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

      + "float denom = dot(ps+(1.0-d)*force.xy,ps); \n"

      + "float one_over_denom = 1.0/(denom-0.001*(sign(denom)-1.0)); \n"          // = denom==0 ? 1000:1/denom;

       //v.z += force.z*d;                                                        // cone

       //b = -(force.z*(1.0-d))*one_over_denom;                                   //

       //v.z += force.z*d*d*(3.0-2.0*d);                                          // thin bubble

       //b = -(6.0*force.z*d*(1.0-d)*(1.0-d))*one_over_denom;                     //

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

      + "float b = -(12.0*force.z*d*(1.0-d)*(1.0-d)*(1.0-d))*one_over_denom; \n"  //

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

      + "n.xy += n.z*b*ps;"

      );

    }

  }