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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Copyright 2017 Leszek Koltunski //
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// //
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// This file is part of Distorted. //
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// //
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// Distorted is free software: you can redistribute it and/or modify //
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// it under the terms of the GNU General Public License as published by //
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// the Free Software Foundation, either version 2 of the License, or //
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// (at your option) any later version. //
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// //
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// Distorted is distributed in the hope that it will be useful, //
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// but WITHOUT ANY WARRANTY; without even the implied warranty of //
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
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// GNU General Public License for more details. //
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// //
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// You should have received a copy of the GNU General Public License //
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// along with Distorted. If not, see <http://www.gnu.org/licenses/>. //
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///////////////////////////////////////////////////////////////////////////////////////////////////
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package org.distorted.library.effect;
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import org.distorted.library.type.Data3D;
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import org.distorted.library.type.Data4D;
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import org.distorted.library.type.Static4D;
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Distort the Mesh by applying a 3D vector of force.
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*/
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public class VertexEffectDistort extends VertexEffect
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{
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private Data3D mVector, mCenter;
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private Data4D mRegion;
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Only for use by the library itself.
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*
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* @y.exclude
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*/
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public boolean compute(float[] uniforms, int index, long currentDuration, long step )
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{
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mCenter.get(uniforms,index+5,currentDuration,step);
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mRegion.get(uniforms,index+8,currentDuration,step);
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boolean ret = mVector.get(uniforms,index,currentDuration,step);
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uniforms[index+1] =-uniforms[index+1];
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uniforms[index+9] =-uniforms[index+9];
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return ret;
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// PUBLIC API
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Point (Px,Py) gets moved by vector (Wx,Wy,Wz) where Wx/Wy = Vx/Vy i.e. Wx=aVx and Wy=aVy where
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// 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)
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// 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) ]
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// Computations above are valid for screen (0,0)x(w,h) but here we have (-w/2,-h/2)x(w/2,h/2)
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//
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// the vertical part
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// 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.
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// H(v.x,v.y) = |PS|>|SX| ? 0 : f(|PX|)
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// 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|)
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// ( i.e. normalize( dx, dy, -|PS|/f'(|PX|))
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//
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// 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.
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// Solution:
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// 1. Decompose the V into two subcomponents, one parallel to SX and another perpendicular.
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// 2. Convince yourself (draw!) that the perpendicular component has no effect on normals.
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// 3. The parallel component changes the length of |SX| by the factor of a=(|SX|-|Vpar|)/|SX| (where the length
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// can be negative depending on the direction)
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// 4. that in turn leaves the x and y parts of the normal unchanged and multiplies the z component by a!
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//
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// |Vpar| = (u_dVx[i]*dx - u_dVy[i]*dy) / sqrt(ps_sq) = (Vx*dx-Vy*dy)/ sqrt(ps_sq) (-Vy because y is inverted)
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// 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
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//
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// Side of the bubble
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//
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// choose from one of the three bubble shapes: the cone, the thin bubble and the thick bubble
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// Case 1:
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// f(t) = t, i.e. f(x) = uz * x/|SX| (a cone)
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// -|PS|/f'(|PX|) = -|PS|*|SX|/uz but since ps_sq=|PS|^2 and d=|PX|/|SX| then |PS|*|SX| = ps_sq/(1-d)
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// so finally -|PS|/f'(|PX|) = -ps_sq/(uz*(1-d))
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//
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// Case 2:
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// f(t) = 3t^2 - 2t^3 --> f(0)=0, f'(0)=0, f'(1)=0, f(1)=1 (the bell curve)
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// here we have t = x/|SX| which makes f'(|PX|) = 6*uz*|PS|*|PX|/|SX|^3.
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// so -|PS|/f'(|PX|) = (-|SX|^3)/(6uz|PX|) = (-|SX|^2) / (6*uz*d) but
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// d = |PX|/|SX| and ps_sq = |PS|^2 so |SX|^2 = ps_sq/(1-d)^2
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// so finally -|PS|/f'(|PX|) = -ps_sq/ (6uz*d*(1-d)^2)
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//
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// Case 3:
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// 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,
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// f(0.5)=0.7 and f'(t)= t(t-1)^2 >=0 for t>=0 so this produces a fuller, thicker bubble!
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// then -|PS|/f'(|PX|) = (-|PS|*|SX)) / (12uz*d*(d-1)^2) but |PS|*|SX| = ps_sq/(1-d) (see above!)
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// so finally -|PS|/f'(|PX|) = -ps_sq/ (12uz*d*(1-d)^3)
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//
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// Now, new requirement: we have to be able to add up normal vectors, i.e. distort already distorted surfaces.
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// 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 ).
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// 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)
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// 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
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// can simply add up the first and second components.
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//
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// Thus we actually want to compute N(v.x,v.y) = a*(-(dx/|PS|)*f'(|PX|), -(dy/|PS|)*f'(|PX|), 1) and keep adding
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// the first two components. (a is the horizontal part)
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Have to call this before the shaders get compiled (i.e before Distorted.onCreate()) for the Effect to work.
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*/
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public static void enable()
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{
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addEffect(EffectName.DISTORT,
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"vec2 center = vUniforms[effect+1].yz; \n"
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+ "vec2 ps = center-v.xy; \n"
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+ "vec3 force = vUniforms[effect].xyz; \n"
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+ "float d = degree(vUniforms[effect+2],center,ps); \n"
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+ "float denom = dot(ps+(1.0-d)*force.xy,ps); \n"
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+ "float one_over_denom = 1.0/(denom-0.001*(sign(denom)-1.0)); \n" // = denom==0 ? 1000:1/denom;
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//v.z += force.z*d; // cone
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//b = -(force.z*(1.0-d))*one_over_denom; //
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//v.z += force.z*d*d*(3.0-2.0*d); // thin bubble
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//b = -(6.0*force.z*d*(1.0-d)*(1.0-d))*one_over_denom; //
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+ "v.z += force.z*d*d*(3.0*d*d -8.0*d +6.0); \n" // thick bubble
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+ "float b = -(12.0*force.z*d*(1.0-d)*(1.0-d)*(1.0-d))*one_over_denom; \n" //
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+ "v.xy += d*force.xy; \n"
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+ "n.xy += n.z*b*ps;"
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);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Distort a (possibly changing in time) part of the Mesh by a (possibly changing in time) vector of force.
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*
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* @param vector vector of force the Center of the Effect is currently being dragged with.
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* @param center 3-dimensional Data that, at any given time, returns the Center of the Effect.
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* @param region Region that masks the Effect.
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*/
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public VertexEffectDistort(Data3D vector, Data3D center, Data4D region)
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{
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super(EffectName.DISTORT);
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mVector = vector;
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mCenter = center;
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mRegion = (region==null ? new Static4D(0,0,Float.MAX_VALUE, Float.MAX_VALUE) : region);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Distort the whole Mesh by a (possibly changing in time) vector of force.
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*
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* @param vector vector of force the Center of the Effect is currently being dragged with.
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* @param center 3-dimensional Data that, at any given time, returns the Center of the Effect.
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*/
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public VertexEffectDistort(Data3D vector, Data3D center)
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{
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super(EffectName.DISTORT);
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mVector = vector;
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mCenter = center;
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mRegion = new Static4D(0,0,Float.MAX_VALUE, Float.MAX_VALUE);
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}
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}
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