| 70 |
70 |
|
| 71 |
71 |
vec2 signA = sign(A); //
|
| 72 |
72 |
vec2 signA_SQ = signA*signA; // div = PS/A if A!=0, 0 otherwise.
|
| 73 |
|
vec2 div = signA_SQ*PS/(A+signA_SQ-vec2(1,1)); //
|
|
73 |
vec2 div = signA_SQ*PS/(A-(vec2(1,1)-signA_SQ));//
|
| 74 |
74 |
|
| 75 |
75 |
return 1.0-max(div.x,div.y);
|
| 76 |
76 |
}
|
| ... | ... | |
| 101 |
101 |
if( D<=0.0 ) return 0.0;
|
| 102 |
102 |
|
| 103 |
103 |
float ps_sq = dot(PS,PS);
|
| 104 |
|
float one_over_ps_sq = 1.0/(ps_sq+1.0-sign(ps_sq)); // return 1.0 if ps_sq = 0.0
|
|
104 |
float one_over_ps_sq = 1.0/(ps_sq-(sign(ps_sq)-1.0)); // return 1.0 if ps_sq = 0.0
|
|
105 |
// Important: if we want to write
|
|
106 |
// b = 1/a if a!=0, b=1 otherwise
|
|
107 |
// we need to write that as
|
|
108 |
// b = 1 / ( a-(sign(a)-1) )
|
|
109 |
// [ and NOT 1 / ( a + 1 - sign(a) ) ]
|
|
110 |
// because the latter, if 0<a<2^-24,
|
|
111 |
// will suffer from round-off error and in this case
|
|
112 |
// a + 1.0 = 1.0 !! so 1 / (a+1-sign(a)) = 1/0 !
|
| 105 |
113 |
float DOT = dot(PS,PO)*one_over_ps_sq;
|
| 106 |
114 |
|
| 107 |
115 |
return 1.0 / (1.0 + 1.0/(sqrt(DOT*DOT+D*one_over_ps_sq)-DOT));
|
| ... | ... | |
| 120 |
128 |
vec2 A = sign(PS)*u_objD.xy + S;
|
| 121 |
129 |
vec2 signA = sign(A);
|
| 122 |
130 |
vec2 signA_SQ = signA*signA;
|
| 123 |
|
vec2 div = signA_SQ*PS/(A+signA_SQ-vec2(1,1));
|
|
131 |
vec2 div = signA_SQ*PS/(A-(vec2(1,1)-signA_SQ));
|
| 124 |
132 |
float E = 1.0-max(div.x,div.y);
|
| 125 |
133 |
|
| 126 |
134 |
float ps_sq = dot(PS,PS);
|
| 127 |
|
float one_over_ps_sq = 1.0/(ps_sq+1.0-sign(ps_sq)); // return 1.0 if ps_sq = 0.0
|
|
135 |
float one_over_ps_sq = 1.0/(ps_sq-(sign(ps_sq)-1.0)); // return 1.0 if ps_sq = 0.0
|
| 128 |
136 |
float DOT = dot(PS,PO)*one_over_ps_sq;
|
| 129 |
137 |
|
| 130 |
138 |
return min(1.0/(1.0 + 1.0/(sqrt(DOT*DOT+D*one_over_ps_sq)-DOT)),E);
|
| ... | ... | |
| 281 |
289 |
vec2 w = vec2(vUniforms[effect].x, -vUniforms[effect].y);
|
| 282 |
290 |
float uz = vUniforms[effect].z; // height of the bubble
|
| 283 |
291 |
float denominator = dot(ps+(1.0-d)*w,ps);
|
| 284 |
|
float one_over_denom = 1.0/(denominator+0.001*(1.0-sign(denominator))); // = denominator==0 ? 1000:1/denominator;
|
|
292 |
float one_over_denom = 1.0/(denominator-0.001*(sign(denominator)-1.0)); // = denominator==0 ? 1000:1/denominator;
|
| 285 |
293 |
|
| 286 |
294 |
//v.z += uz*d; // cone
|
| 287 |
295 |
//b = -(uz*(1.0-d))*one_over_denom; //
|
| ... | ... | |
| 326 |
334 |
vec3 SO = vUniforms[effect+1];
|
| 327 |
335 |
float d1_circle = degree_region(SO,PS);
|
| 328 |
336 |
float d1_bitmap = degree_bitmap(S,PS);
|
| 329 |
|
float sinA = vUniforms[effect].y; // sin(A) precomputed in EffectListVertex.postprocess
|
| 330 |
|
float cosA = vUniforms[effect].z; // cos(A) precomputed in EffectListVertex.postprocess
|
| 331 |
|
vec2 PS2 = vec2( PS.x*cosA+PS.y*sinA,-PS.x*sinA+PS.y*cosA ); // vector PS rotated by A radians clockwise around S.
|
|
337 |
float sinA = vUniforms[effect].y; // sin(A) precomputed in EffectListVertex.postprocess
|
|
338 |
float cosA = vUniforms[effect].z; // cos(A) precomputed in EffectListVertex.postprocess
|
|
339 |
vec2 PS2 = vec2( PS.x*cosA+PS.y*sinA,-PS.x*sinA+PS.y*cosA ); // vector PS rotated by A radians clockwise around S.
|
| 332 |
340 |
vec3 SG = (1.0-d1_circle)*SO; // coordinates of the dilated circle P is going to get rotated around
|
| 333 |
|
float d2 = max(0.0,degree(SG,S,PS2)); // make it a max(0,deg) because when S=left edge of the bitmap, otherwise
|
| 334 |
|
// some points end up with d2<0 and they disappear off view.
|
|
341 |
float d2 = max(0.0,degree(SG,S,PS2)); // make it a max(0,deg) because otherwise when S=left edge of the
|
|
342 |
// bitmap some points end up with d2<0 and they disappear off view.
|
| 335 |
343 |
v.xy += min(d1_circle,d1_bitmap)*(PS - PS2/(1.0-d2)); // if d2=1 (i.e P=S) we should have P unchanged. How to do it?
|
| 336 |
344 |
}
|
| 337 |
345 |
|
Correct an important bug in the vertex shader.
b = 1/a if a!=0, 1 otherwise was incorrectly computed as b = 1.0 / (a+1.0-sign(a)). This, when 0<a<2^-24, suffers from 'round-off error': then a+1.0 = 1.0 (sic!) thus b = 1/0 !.
Correct way: b = 1.0 / ( a - (sign(a)-1.0) )