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Revision 353f7580

Added by Leszek Koltunski over 5 years ago

Make Distort truly 3D.

View differences:

src/main/java/org/distorted/library/effect/VertexEffectDistort.java
48 48 
///////////////////////////////////////////////////////////////////////////////////////////////////
49 49 
// PUBLIC API
50 50 
///////////////////////////////////////////////////////////////////////////////////////////////////
51 
// Point (Px,Py) gets moved by vector (Wx,Wy,Wz) where Wx/Wy = Vx/Vy i.e. Wx=aVx and Wy=aVy where
51 
// Def: P-current vertex being distorted, S - center of the effect, X- point where half-line SP meets
52 
// the region circle (if P is inside the circle); (Vx,Vy,Vz) - force vector.
53 
//
54 
// horizontal part
55 
// Point (Px,Py) gets moved by vector (Wx,Wy) where Wx/Wy = Vx/Vy i.e. Wx=aVx and Wy=aVy where
52 56 
// 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)
53 57 
// 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) ]
54 58 
// Computations above are valid for screen (0,0)x(w,h) but here we have (-w/2,-h/2)x(w/2,h/2)
55 59 
//
56 
// the vertical part
57 
// 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.
58 
// H(v.x,v.y) = |PS|>|SX| ? 0 : f(|PX|)
59 
// 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|)
60 
// ( i.e. normalize( dx, dy, -|PS|/f'(|PX|))
60 
// vertical part
61 
// Let vector PS = (dx,dy), f(x) (0<=x<=|SX|) be the shape of the side of the bubble.
62 
// H(Px,Py) = |PS|>|SX| ? 0 : f(|PX|)
63 
// N(Px,Py) = |PS|>|SX| ? (0,0,1) : ( -(dx/|PS|)sin(beta), -(dy/|PS|)sin(beta), cos(beta) ) where tan(beta) is f'(|PX|)
64 
// ( i.e. normalize( dx, dy, -|PS|/f'(|PX|) )
61 65 
//
62 
// 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.
66 
// Now we also have to take into account the effect horizontal move by V=(Vx,Vy) will have on the normal vector.
63 67 
// Solution:
64 68 
// 1. Decompose the V into two subcomponents, one parallel to SX and another perpendicular.
65 69 
// 2. Convince yourself (draw!) that the perpendicular component has no effect on normals.
......
67 71 
//    can be negative depending on the direction)
68 72 
// 4. that in turn leaves the x and y parts of the normal unchanged and multiplies the z component by a!
69 73 
//
70 
// |Vpar| = (u_dVx[i]*dx - u_dVy[i]*dy) / sqrt(ps_sq) = (Vx*dx-Vy*dy)/ sqrt(ps_sq)  (-Vy because y is inverted)
74 
// |Vpar| = (Vx*dx-Vy*dy) / sqrt(ps_sq)  (-Vy because y is inverted)
71 75 
// 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
72 76 
//
73 77 
// Side of the bubble
74 78 
//
75 79 
// choose from one of the three bubble shapes: the cone, the thin bubble and the thick bubble
76 80 
// Case 1:
77 
// 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)
79 
// so finally -|PS|/f'(|PX|) = -ps_sq/(uz*(1-d))
81 
// f(t) = t, i.e. f(x) = Vz * x/|SX|   (a cone)
82 
// -|PS|/f'(|PX|) = -|PS|*|SX|/Vz but since ps_sq=|PS|^2 and d=|PX|/|SX| then |PS|*|SX| = ps_sq/(1-d)
83 
// so finally -|PS|/f'(|PX|) = -ps_sq/(Vz*(1-d))
80 84 
//
81 85 
// Case 2:
82 86 
// f(t) = 3t^2 - 2t^3 --> f(0)=0, f'(0)=0, f'(1)=0, f(1)=1 (the bell curve)
83 
// here we have t = x/|SX| which makes f'(|PX|) = 6*uz*|PS|*|PX|/|SX|^3.
84 
// so -|PS|/f'(|PX|) = (-|SX|^3)/(6uz|PX|) =  (-|SX|^2) / (6*uz*d) but
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// here we have t = x/|SX| which makes f'(|PX|) = 6*Vz*|PS|*|PX|/|SX|^3.
88 
// so -|PS|/f'(|PX|) = (-|SX|^3)/(6Vz|PX|) =  (-|SX|^2) / (6*Vz*d) but
85 89 
// d = |PX|/|SX| and ps_sq = |PS|^2 so |SX|^2 = ps_sq/(1-d)^2
86 
// so finally -|PS|/f'(|PX|) = -ps_sq/ (6uz*d*(1-d)^2)
90 
// so finally -|PS|/f'(|PX|) = -ps_sq/ (6Vz*d*(1-d)^2)
87 91 
//
88 92 
// Case 3:
89 93 
// 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,
90 94 
// f(0.5)=0.7 and f'(t)= t(t-1)^2 >=0 for t>=0 so this produces a fuller, thicker bubble!
91 
// 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)
95 
// then -|PS|/f'(|PX|) = (-|PS|*|SX)) / (12Vz*d*(d-1)^2) but |PS|*|SX| = ps_sq/(1-d) (see above!)
96 
// so finally -|PS|/f'(|PX|) = -ps_sq/ (12Vz*d*(1-d)^3)
93 97 
//
94 98 
// Now, new requirement: we have to be able to add up normal vectors, i.e. distort already distorted surfaces.
95 99 
// 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 ).
......
97 101 
// 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
98 102 
// can simply add up the first and second components.
99 103 
//
100 
// Thus we actually want to compute N(v.x,v.y) = a*(-(dx/|PS|)*f'(|PX|), -(dy/|PS|)*f'(|PX|), 1) and keep adding
104 
// Thus we actually want to compute N(Px,Py) = a*(-(dx/|PS|)*f'(|PX|), -(dy/|PS|)*f'(|PX|), 1) and keep adding
101 105 
// the first two components. (a is the horizontal part)
106 
//
107 
// 2019-01-09 fixes for stuff discovered with the Earth testing app
108 
// Now, the above stuff works only if the normal vector is close to (0,0,1). To make it work for any situation,
109 
// 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)
110 
// then modify the rotated normal (so (0,0,1)) and rotate the modified normal back.
111 
//
112 
// 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
113 
// a) axis of rotation = (n.x,n.y,n.z) x (0,0,1) = (n.y,-n.x,0)
114 
// b) angle of rotation A: cosA = (n.x,n.y,n.z)*(0,0,1) = n.z     (and sinA = + sqrt(1-n.z^2))
115 
//
116 
// so normalized axisNor = (n.x/ sinA, -n.y/sinA, 0) and now from Rodrigues rotation formula
117 
// Vrot = v*cosA + (axisNor x v)*sinA + axisNor*(axis*v)*(1-cosA)
118 
//
119 
// which makes Vrot = (a+n.y*c , b-n.y*c , v*n) where
120 
// a = vx*nz-vz*nx , b = vy*nz-vz*ny , c = (vx*ny-vy*nx)/(1+nz)    (unless n=(0,0,-1))
102 121 
///////////////////////////////////////////////////////////////////////////////////////////////////
103 122 
/**
104 123 
 * Have to call this before the shaders get compiled (i.e before Distorted.onCreate()) for the Effect to work.
......
107 126 
    {
108 127 
    addEffect(EffectName.DISTORT,
109 128 

  		




  110
  
  
    
        "vec3 center = vUniforms[effect+1].yzw; \n"


  		




  111
  
  
    
      + "vec3 ps = center-v; \n"


  		




  112
  
  
    
      + "vec3 force = vUniforms[effect].xyz; \n"


  		




  113
  
  
    
      + "float d = degree(vUniforms[effect+2],center,ps); \n"


  		




  114
  
  
    
      + "float denom = dot(ps+(1.0-d)*force,ps); \n"


  		




  115
  
  
    
      + "float one_over_denom = 1.0/(denom-0.001*(sign(denom)-1.0)); \n"          // = denom==0 ? 1000:1/denom;


  		




  
  129
  
    
        "vec3 center = vUniforms[effect+1].yzw;                        \n"


  		




  
  130
  
    
      + "vec3 ps = center-v;                                           \n"


  		




  
  131
  
    
      + "vec3 force = vUniforms[effect].xyz;                           \n"


  		




  
  132
  
    
      + "vec4 region= vUniforms[effect+2];                             \n"


  		




  
  133
  
    
      + "float d = degree(region,center,ps);                           \n"


  		




  
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  135
  
    
      + "if( d>0.0 )                                                   \n"


  		




  
  136
  
    
      + "  {                                                           \n"


  		




  
  137
  
    
      + "  v += d*force;                                               \n"


  		




  116
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  117
  
  
    
       //v.z += force.z*d;                                                        // cone


  		




  118
  
  
    
       //b = -(force.z*(1.0-d))*one_over_denom;                                   //


  		




  
  139
  
    
      + "  float tp = 1.0+n.z;                                         \n"


  		




  
  140
  
    
      + "  float tr = 1.0 / (tp - (1.0 - sign(tp)));                   \n"


  		




  119
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  120
  
  
    
       //v.z += force.z*d*d*(3.0-2.0*d);                                          // thin bubble


  		




  121
  
  
    
       //b = -(6.0*force.z*d*(1.0-d)*(1.0-d))*one_over_denom;                     //


  		




  
  142
  
    
      + "  float ap = ps.x*n.z - ps.z*n.x;                             \n"   // likewise rotate the ps vector


  		




  
  143
  
    
      + "  float bp = ps.y*n.z - ps.z*n.y;                             \n"   //


  		




  
  144
  
    
      + "  float cp =(ps.x*n.y - ps.y*n.x)*tr;                         \n"   //


  		




  
  145
  
    
      + "  vec3 psRot = vec3( ap+n.y*cp , bp-n.x*cp , dot(ps,n) );     \n"   //


  		




  122
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  123
  
  
    
      + "v.z += force.z*d*d*(3.0*d*d -8.0*d +6.0); \n"                            // thick bubble


  		




  124
  
  
    
      + "float b = -(12.0*force.z*d*(1.0-d)*(1.0-d)*(1.0-d))*one_over_denom; \n"  //


  		




  
  147
  
    
      + "  psRot = normalize(psRot);                                   \n"


  		




  
  148
  
    
      + "  vec3 N = vec3( -dot(force,n)*psRot.xy, region.w );          \n"   // modified rotated normal


  		




  
  149
  
    
                                                                             // dot(force,n) is rotated force.z


  		




  
  150
  
    
      + "  float an = N.x*n.z + N.z*n.x;                               \n"   // now create the normal vector


  		




  
  151
  
    
      + "  float bn = N.y*n.z + N.z*n.y;                               \n"   // back from our modified normal


  		




  
  152
  
    
      + "  float cn =(N.x*n.y - N.y*n.x)*tr;                           \n"   // rotated back


  		




  
  153
  
    
      + "  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!


  		




  125
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  126
  
  
    
      + "v.xy += d*force.xy; \n"


  		




  127
  
  
    
      + "n.xy += n.z*b*ps.xy;"


  		




  
  155
  
    
      + "  n = normalize(n);                                           \n"


  		




  
  156
  
    
      + "  }                                                           \n"


  		




  128
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      );


  		




  129
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    }


  		




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