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//////////////////////////////////////////////////////////////////////////////////////////////
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// Copyright 2016 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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uniform vec3 u_objD; // half of object width x half of object height X half the depth;
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// point (0,0,0) is the center of the object
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uniform float u_Depth; // max absolute value of v.z ; beyond that the vertex would be culled by the near or far planes.
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// I read OpenGL ES has a built-in uniform variable gl_DepthRange.near = n,
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// .far = f, .diff = f-n so maybe u_Depth is redundant
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// Update: this struct is only available in fragment shaders
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uniform mat4 u_MVPMatrix; // the combined model/view/projection matrix.
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uniform mat4 u_MVMatrix; // the combined model/view matrix.
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attribute vec3 a_Position; // Per-vertex position.
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attribute vec3 a_Normal; // Per-vertex normal vector.
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attribute vec2 a_TexCoordinate; // Per-vertex texture coordinate.
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varying vec3 v_Position; //
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varying vec3 v_Normal; //
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varying vec2 v_TexCoordinate; //
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uniform int vNumEffects; // total number of vertex effects
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#if NUM_VERTEX>0
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uniform int vType[NUM_VERTEX]; // their types.
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uniform vec4 vUniforms[3*NUM_VERTEX];// i-th effect is 3 consecutive vec4's: [3*i], [3*i+1], [3*i+2].
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// The first vec4 is the Interpolated values,
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// next is half cache half Center, the third - the Region.
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#endif
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#if NUM_VERTEX>0
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//////////////////////////////////////////////////////////////////////////////////////////////
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// HELPER FUNCTIONS
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//////////////////////////////////////////////////////////////////////////////////////////////
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// The trick below is the if-less version of the
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//
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// t = dx<0.0 ? (u_objD.x-v.x) / (u_objD.x-ux) : (u_objD.x+v.x) / (u_objD.x+ux);
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// h = dy<0.0 ? (u_objD.y-v.y) / (u_objD.y-uy) : (u_objD.y+v.y) / (u_objD.y+uy);
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// d = min(t,h);
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//
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// float d = min(-ps.x/(sign(ps.x)*u_objD.x+p.x),-ps.y/(sign(ps.y)*u_objD.y+p.y))+1.0;
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//
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// We still have to avoid division by 0 when p.x = +- u_objD.x or p.y = +- u_objD.y (i.e on the edge of the Object)
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// We do that by first multiplying the above 'float d' with sign(denominator1*denominator2)^2.
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//
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//////////////////////////////////////////////////////////////////////////////////////////////
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// return degree of the point as defined by the bitmap rectangle
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float degree_bitmap(in vec2 S, in vec2 PS)
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{
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vec2 A = sign(PS)*u_objD.xy + S;
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vec2 signA = sign(A); //
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vec2 signA_SQ = signA*signA; // div = PS/A if A!=0, 0 otherwise.
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vec2 div = signA_SQ*PS/(A-(vec2(1,1)-signA_SQ));//
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return 1.0-max(div.x,div.y);
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}
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//////////////////////////////////////////////////////////////////////////////////////////////
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// Return degree of the point as defined by the Region. Currently only supports circular regions.
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//
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// Let us first introduce some notation.
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// Let 'PS' be the vector from point P (the current vertex) to point S (the center of the effect).
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// Let region.xy be the vector from point S to point O (the center point of the region circle)
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// Let region.z be the radius of the region circle.
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// (This all should work regardless if S is inside or outside of the circle).
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//
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// Then, the degree of a point with respect to a given (circular!) Region is defined by:
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//
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// If P is outside the circle, return 0.
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// Otherwise, let X be the point where the halfline SP meets the region circle - then return |PX|/||SX|,
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// aka the 'degree' of point P.
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//
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// We solve the triangle OPX.
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// We know the lengths |PO|, |OX| and the angle OPX, because cos(OPX) = cos(180-OPS) = -cos(OPS) = -PS*PO/(|PS|*|PO|)
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// then from the law of cosines PX^2 + PO^2 - 2*PX*PO*cos(OPX) = OX^2 so PX = -a + sqrt(a^2 + OX^2 - PO^2)
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// where a = PS*PO/|PS| but we are really looking for d = |PX|/(|PX|+|PS|) = 1/(1+ (|PS|/|PX|) ) and
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// |PX|/|PS| = -b + sqrt(b^2 + (OX^2-PO^2)/PS^2) where b=PS*PO/|PS|^2 which can be computed with only one sqrt.
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float degree_region(in vec4 region, in vec2 PS)
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{
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vec2 PO = PS + region.xy;
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float D = region.z*region.z-dot(PO,PO); // D = |OX|^2 - |PO|^2
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if( D<=0.0 ) return 0.0;
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float ps_sq = dot(PS,PS);
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float one_over_ps_sq = 1.0/(ps_sq-(sign(ps_sq)-1.0)); // return 1.0 if ps_sq = 0.0
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// Important: if we want to write
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// b = 1/a if a!=0, b=1 otherwise
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// we need to write that as
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// b = 1 / ( a-(sign(a)-1) )
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// [ and NOT 1 / ( a + 1 - sign(a) ) ]
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// because the latter, if 0<a<2^-24,
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// will suffer from round-off error and in this case
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// a + 1.0 = 1.0 !! so 1 / (a+1-sign(a)) = 1/0 !
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float DOT = dot(PS,PO)*one_over_ps_sq;
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return 1.0 / (1.0 + 1.0/(sqrt(DOT*DOT+D*one_over_ps_sq)-DOT));
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}
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//////////////////////////////////////////////////////////////////////////////////////////////
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// return min(degree_bitmap,degree_region). Just like degree_region, currently only supports circles.
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float degree(in vec4 region, in vec2 S, in vec2 PS)
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{
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vec2 PO = PS + region.xy;
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float D = region.z*region.z-dot(PO,PO); // D = |OX|^2 - |PO|^2
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if( D<=0.0 ) return 0.0;
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vec2 A = sign(PS)*u_objD.xy + S;
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vec2 signA = sign(A);
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vec2 signA_SQ = signA*signA;
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vec2 div = signA_SQ*PS/(A-(vec2(1,1)-signA_SQ));
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float E = 1.0-max(div.x,div.y);
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float ps_sq = dot(PS,PS);
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float one_over_ps_sq = 1.0/(ps_sq-(sign(ps_sq)-1.0)); // return 1.0 if ps_sq = 0.0
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float DOT = dot(PS,PO)*one_over_ps_sq;
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return min(1.0/(1.0 + 1.0/(sqrt(DOT*DOT+D*one_over_ps_sq)-DOT)),E);
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}
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//////////////////////////////////////////////////////////////////////////////////////////////
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// Clamp v.z to (-u_Depth,u_Depth) with the following function:
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// define h to be, say, 0.7; let H=u_Depth
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// if v.z < -hH then v.z = (-(1-h)^2 * H^2)/(v.z+(2h-1)H) -H (function satisfying f(-hH)=-hH, f'(-hH)=1, lim f(x) = -H)
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// else if v.z > hH then v.z = (-(1-h)^2 * H^2)/(v.z-(2h-1)H) +H (function satisfying f(+hH)=+hH, f'(+hH)=1, lim f(x) = +H)
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// else v.z = v.z
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void restrictZ(inout float v)
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{
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const float h = 0.7;
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float signV = 2.0*max(0.0,sign(v))-1.0;
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float c = ((1.0-h)*(h-1.0)*u_Depth*u_Depth)/(v-signV*(2.0*h-1.0)*u_Depth) +signV*u_Depth;
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float b = max(0.0,sign(abs(v)-h*u_Depth));
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v = b*c+(1.0-b)*v; // Avoid branching: if abs(v)>h*u_Depth, then v=c; otherwise v=v.
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}
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//////////////////////////////////////////////////////////////////////////////////////////////
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// DEFORM EFFECT
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//
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// Deform the whole shape of the Object by force V. Algorithm is as follows:
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//
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// Suppose we apply force (Vx,Vy) at point (Cx,Cy) (i.e. the center of the effect). Then, first of all,
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// divide the rectangle into 4 smaller rectangles along the 1 horizontal + 1 vertical lines that pass
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// through (Cx,Cy). Now suppose we have already understood the following case:
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//
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// A vertical (0,Vy) force applied to a rectangle (WxH) in size, at center which is the top-left corner
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// of the rectangle. (*)
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//
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// If we understand (*), then we understand everything, because in order to compute the movement of the
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// whole rectangle we can apply (*) 8 times: for each one of the 4 sub-rectangles, apply (*) twice,
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// once for the vertical component of the force vector, the second time for the horizontal one.
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//
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// Let's then compute (*):
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// 1) the top-left point will move by exactly (0,Vy)
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// 2) we arbitrarily decide that the top-right point will move by (|Vy|/(|Vy|+A*W))*Vy, where A is some
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// arbitrary constant (const float A below). The F(V,W) = (|Vy|/(|Vy|+A*W)) comes from the following:
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// a) we want F(V,0) = 1
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// b) we want lim V->inf (F) = 1
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// c) we actually want F() to only depend on W/V, which we have here.
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// 3) then the top edge of the rectangle will move along the line Vy*G(x), where G(x) = (1 - (A*W/(|Vy|+A*W))*(x/W)^2)
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// 4) Now we decide that the left edge of the rectangle will move along Vy*H(y), where H(y) = (1 - |y|/(|Vy|+C*|y|))
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// where C is again an arbitrary constant. Again, H(y) comes from the requirement that no matter how
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// strong we push the left edge of the rectangle up or down, it can never 'go over itself', but its
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// length will approach 0 if squeezed very hard.
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// 5) The last point we need to compute is the left-right motion of the top-right corner (i.e. if we push
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// the top-left corner up very hard, we want to have the top-right corner not only move up, but also to
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// the left at least a little bit).
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// We arbitrarily decide that, in addition to moving up-down by Vy*F(V,W), the corner will also move
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// left-right by I(V,W) = B*W*F(V,W), where B is again an arbitrary constant.
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// 6) combining 3), 4) and 5) together, we arrive at a movement of an arbitrary point (x,y) away from the
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// top-left corner:
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// X(x,y) = -B*x * (|Vy|/(|Vy|+A*W)) * (1-(y/H)^2) (**)
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// Y(x,y) = Vy * (1 - |y|/(|Vy|+C*|y|)) * (1 - (A*W/(|Vy|+A*W))*(x/W)^2) (**)
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//
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// We notice that formulas (**) have been construed so that it is possible to continously mirror them
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// left-right and up-down (i.e. apply not only to the 'bottom-right' rectangle of the 4 subrectangles
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// but to all 4 of them!).
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//
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// Constants:
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// a) A : valid values: (0,infinity). 'Bendiness' if the surface - the higher A is, the more the surface
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// bends. A<=0 destroys the system.
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// b) B : valid values: <-1,1>. The amount side edges get 'sucked' inwards when we pull the middle of the
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// top edge up. B=0 --> not at all, B=1: a looot. B=-0.5: the edges will actually be pushed outwards
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// quite a bit. One can also set it to <-1 or >1, but it will look a bit ridiculous.
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// c) C : valid values: <1,infinity). The derivative of the H(y) function at 0, i.e. the rate of 'squeeze'
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// surface gets along the force line. C=1: our point gets pulled very closely to points above it
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// even when we apply only small vertical force to it. The higher C is, the more 'uniform' movement
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// along the force line is.
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// 0<=C<1 looks completely ridiculous and C<0 destroys the system.
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void deform(in int effect, inout vec4 v, inout vec4 n)
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{
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const vec2 ONE = vec2(1.0,1.0);
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const float A = 0.5;
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const float B = 0.2;
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const float C = 5.0;
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vec2 center = vUniforms[effect+1].yz;
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vec2 ps = center-v.xy;
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vec2 aPS = abs(ps);
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vec2 maxps = u_objD.xy + abs(center);
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float d = degree_region(vUniforms[effect+2],ps);
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vec3 force = vUniforms[effect].xyz * d;
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vec2 aForce = abs(force.xy);
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float denom = dot(ps+(1.0-d)*force.xy,ps);
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float one_over_denom = 1.0/(denom-0.001*(sign(denom)-1.0));
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vec2 Aw = A*maxps;
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vec2 quot = ps / maxps;
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quot = quot*quot; // ( (x/W)^2 , (y/H)^2 ) where x,y are distances from V to center
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float denomV = 1.0 / (aForce.y + Aw.x);
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float denomH = 1.0 / (aForce.x + Aw.y);
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vec2 vertCorr= ONE - aPS / ( aForce+C*aPS + (ONE-sign(aForce)) ); // avoid division by 0 when force and PS both are 0
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float mvXvert = -B * ps.x * aForce.y * (1.0-quot.y) * denomV; // impact the vertical component of the force vector has on horizontal movement
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float mvYhorz = -B * ps.y * aForce.x * (1.0-quot.x) * denomH; // impact the horizontal component of the force vector has on vertical movement
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float mvYvert = force.y * (1.0-quot.x*Aw.x*denomV) * vertCorr.y; // impact the vertical component of the force vector has on vertical movement
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float mvXhorz = -force.x * (1.0-quot.y*Aw.y*denomH) * vertCorr.x; // impact the horizontal component of the force vector has on horizontal movement
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v.x -= (mvXvert+mvXhorz);
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v.y -= (mvYvert+mvYhorz);
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v.z += force.z*d*d*(3.0*d*d -8.0*d +6.0); // 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;//
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n.xy += n.z*b*ps;
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}
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//////////////////////////////////////////////////////////////////////////////////////////////
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// DISTORT EFFECT
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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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301
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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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void distort(in int effect, inout vec4 v, inout vec4 n)
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{
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312
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vec2 center = vUniforms[effect+1].yz;
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vec2 ps = center-v.xy;
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vec3 force = vUniforms[effect].xyz;
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float d = degree(vUniforms[effect+2],center,ps);
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float denom = dot(ps+(1.0-d)*force.xy,ps);
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float one_over_denom = 1.0/(denom-0.001*(sign(denom)-1.0)); // = 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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321
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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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325
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v.z += force.z*d*d*(3.0*d*d -8.0*d +6.0); // 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; //
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327
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328
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v.xy += d*force.xy;
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n.xy += n.z*b*ps;
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}
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332
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//////////////////////////////////////////////////////////////////////////////////////////////
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333
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// SINK EFFECT
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//
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335
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// Pull P=(v.x,v.y) towards center of the effect with P' = P + (1-h)*dist(S-P)
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336
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// when h>1 we are pushing points away from S: P' = P + (1/h-1)*dist(S-P)
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337
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338
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void sink(in int effect,inout vec4 v)
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339
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{
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340
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vec2 center = vUniforms[effect+1].yz;
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341
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vec2 ps = center-v.xy;
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342
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float h = vUniforms[effect].x;
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343
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float t = degree(vUniforms[effect+2],center,ps) * (1.0-h)/max(1.0,h);
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344
|
|
345
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v.xy += t*ps;
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346
|
}
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347
|
|
348
|
//////////////////////////////////////////////////////////////////////////////////////////////
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349
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// PINCH EFFECT
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350
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//
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351
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// Pull P=(v.x,v.y) towards the line that
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352
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// a) passes through the center of the effect
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353
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// b) forms angle defined in the 2nd interpolated value with the X-axis
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354
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// with P' = P + (1-h)*dist(line to P)
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355
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// when h>1 we are pushing points away from S: P' = P + (1/h-1)*dist(line to P)
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356
|
|
357
|
void pinch(in int effect,inout vec4 v)
|
358
|
{
|
359
|
vec2 center = vUniforms[effect+1].yz;
|
360
|
vec2 ps = center-v.xy;
|
361
|
float h = vUniforms[effect].x;
|
362
|
float t = degree(vUniforms[effect+2],center,ps) * (1.0-h)/max(1.0,h);
|
363
|
float angle = vUniforms[effect].y;
|
364
|
vec2 dir = vec2(sin(angle),-cos(angle));
|
365
|
|
366
|
v.xy += t*dot(ps,dir)*dir;
|
367
|
}
|
368
|
|
369
|
//////////////////////////////////////////////////////////////////////////////////////////////
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370
|
// SWIRL EFFECT
|
371
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//
|
372
|
// Let d be the degree of the current vertex V with respect to center of the effect S and Region vRegion.
|
373
|
// This effect rotates the current vertex V by vInterpolated.x radians clockwise around the circle dilated
|
374
|
// by (1-d) around the center of the effect S.
|
375
|
|
376
|
void swirl(in int effect, inout vec4 v)
|
377
|
{
|
378
|
vec2 center = vUniforms[effect+1].yz;
|
379
|
vec2 PS = center-v.xy;
|
380
|
vec4 SO = vUniforms[effect+2];
|
381
|
float d1_circle = degree_region(SO,PS);
|
382
|
float d1_bitmap = degree_bitmap(center,PS);
|
383
|
|
384
|
float alpha = vUniforms[effect].x;
|
385
|
float sinA = sin(alpha);
|
386
|
float cosA = cos(alpha);
|
387
|
|
388
|
vec2 PS2 = vec2( PS.x*cosA+PS.y*sinA,-PS.x*sinA+PS.y*cosA ); // vector PS rotated by A radians clockwise around center.
|
389
|
vec4 SG = (1.0-d1_circle)*SO; // coordinates of the dilated circle P is going to get rotated around
|
390
|
float d2 = max(0.0,degree(SG,center,PS2)); // make it a max(0,deg) because otherwise when center=left edge of the
|
391
|
// bitmap some points end up with d2<0 and they disappear off view.
|
392
|
v.xy += min(d1_circle,d1_bitmap)*(PS - PS2/(1.0-d2)); // if d2=1 (i.e P=center) we should have P unchanged. How to do it?
|
393
|
}
|
394
|
|
395
|
//////////////////////////////////////////////////////////////////////////////////////////////
|
396
|
// WAVE EFFECT
|
397
|
//
|
398
|
// Directional sinusoidal wave effect.
|
399
|
//
|
400
|
// This is an effect from a (hopefully!) generic family of effects of the form (vec3 V: |V|=1 , f(x,y) ) (*)
|
401
|
// i.e. effects defined by a unit vector and an arbitrary function. Those effects are defined to move each
|
402
|
// point (x,y,0) of the XY plane to the point (x,y,0) + V*f(x,y).
|
403
|
//
|
404
|
// In this case V is defined by angles A and B (sines and cosines of which are precomputed in
|
405
|
// EffectQueueVertex and passed in the uniforms).
|
406
|
// Let's move V to start at the origin O, let point C be the endpoint of V, and let C' be C's projection
|
407
|
// to the XY plane. Then A is defined to be the angle C0C' and angle B is the angle C'O(axisY).
|
408
|
//
|
409
|
// Also, in this case f(x,y) = amplitude*sin(x/length), with those 2 parameters passed in uniforms.
|
410
|
//
|
411
|
//////////////////////////////////////////////////////////////////////////////////////////////
|
412
|
// How to compute any generic effect of type (*)
|
413
|
//////////////////////////////////////////////////////////////////////////////////////////////
|
414
|
//
|
415
|
// By definition, the vertices move by f(x,y)*V.
|
416
|
//
|
417
|
// Normals are much more complicated.
|
418
|
// Let angle X be the angle (0,Vy,Vz)(0,Vy,0)(Vx,Vy,Vz).
|
419
|
// Let angle Y be the angle (Vx,0,Vz)(Vx,0,0)(Vx,Vy,Vz).
|
420
|
//
|
421
|
// Then it can be shown that the resulting surface, at point to which point (x0,y0,0) got moved to,
|
422
|
// has 2 tangent vectors given by
|
423
|
//
|
424
|
// SX = (1.0+cosX*fx , cosY*sinX*fx , |sinY|*sinX*fx); (**)
|
425
|
// SY = (cosX*sinY*fy , 1.0+cosY*fy , |sinX|*sinY*fy); (***)
|
426
|
//
|
427
|
// and then obviously the normal N is given by N= SX x SY .
|
428
|
//
|
429
|
// We still need to remember the note from the distort function about adding up normals:
|
430
|
// we first need to 'normalize' the normals to make their third components equal, and then we
|
431
|
// simply add up the first and the second component while leaving the third unchanged.
|
432
|
//
|
433
|
// How to see facts (**) and (***) ? Briefly:
|
434
|
// a) compute the 2D analogon and conclude that in this case the tangent SX is given by
|
435
|
// SX = ( cosA*f'(x) +1, sinA*f'(x) ) (where A is the angle vector V makes with X axis )
|
436
|
// b) cut the resulting surface with plane P which
|
437
|
// - includes vector V
|
438
|
// - crosses plane XY along line parallel to X axis
|
439
|
// c) apply the 2D analogon and notice that the tangent vector to the curve that is the common part of P
|
440
|
// and our surface (I am talking about the tangent vector which belongs to P) is given by
|
441
|
// (1+cosX*fx,0,sinX*fx) rotated by angle (90-|Y|) (where angles X,Y are defined above) along vector (1,0,0).
|
442
|
//
|
443
|
// Matrix of rotation:
|
444
|
//
|
445
|
// |sinY| cosY
|
446
|
// -cosY |sinY|
|
447
|
//
|
448
|
// d) compute the above and see that this is equal precisely to SX from (**).
|
449
|
// e) repeat points b,c,d in direction Y and come up with (***).
|
450
|
//
|
451
|
//////////////////////////////////////////////////////////////////////////////////////////////
|
452
|
// Note: we should avoid passing certain combinations of parameters to this function. One such known
|
453
|
// combination is ( A: small but positive, B: any, amplitude >= length ).
|
454
|
// In this case, certain 'unlucky' points have their normals almost horizontal (they got moved by (almost!)
|
455
|
// amplitude, and other point length (i.e. <=amplitude) away got moved by 0, so the slope in this point is
|
456
|
// very steep). Visual effect is: vast majority of surface pretty much unchanged, but random 'unlucky'
|
457
|
// points very dark)
|
458
|
//
|
459
|
// Generally speaking I'd keep to amplitude < length, as the opposite case has some other problems as well.
|
460
|
|
461
|
void wave(in int effect, inout vec4 v, inout vec4 n)
|
462
|
{
|
463
|
vec2 center = vUniforms[effect+1].yz;
|
464
|
float amplitude = vUniforms[effect ].x;
|
465
|
float length = vUniforms[effect ].y;
|
466
|
|
467
|
vec2 ps = center - v.xy;
|
468
|
float deg = amplitude*degree_region(vUniforms[effect+2],ps);
|
469
|
|
470
|
if( deg != 0.0 && length != 0.0 )
|
471
|
{
|
472
|
float phase = vUniforms[effect ].z;
|
473
|
float alpha = vUniforms[effect ].w;
|
474
|
float beta = vUniforms[effect+1].x;
|
475
|
|
476
|
float sinA = sin(alpha);
|
477
|
float cosA = cos(alpha);
|
478
|
float sinB = sin(beta);
|
479
|
float cosB = cos(beta);
|
480
|
|
481
|
float angle= 1.578*(ps.x*cosB-ps.y*sinB) / length + phase;
|
482
|
|
483
|
vec3 dir= vec3(sinB*cosA,cosB*cosA,sinA);
|
484
|
|
485
|
v.xyz += sin(angle)*deg*dir;
|
486
|
|
487
|
if( n.z != 0.0 )
|
488
|
{
|
489
|
float sqrtX = sqrt(dir.y*dir.y + dir.z*dir.z);
|
490
|
float sqrtY = sqrt(dir.x*dir.x + dir.z*dir.z);
|
491
|
|
492
|
float sinX = ( sqrtY==0.0 ? 0.0 : dir.z / sqrtY);
|
493
|
float cosX = ( sqrtY==0.0 ? 1.0 : dir.x / sqrtY);
|
494
|
float sinY = ( sqrtX==0.0 ? 0.0 : dir.z / sqrtX);
|
495
|
float cosY = ( sqrtX==0.0 ? 1.0 : dir.y / sqrtX);
|
496
|
|
497
|
float abs_z = dir.z <0.0 ? -(sinX*sinY) : (sinX*sinY);
|
498
|
|
499
|
float tmp = 1.578*cos(angle)*deg/length;
|
500
|
|
501
|
float fx =-cosB*tmp;
|
502
|
float fy = sinB*tmp;
|
503
|
|
504
|
vec3 sx = vec3 (1.0+cosX*fx,cosY*sinX*fx,abs_z*fx);
|
505
|
vec3 sy = vec3 (cosX*sinY*fy,1.0+cosY*fy,abs_z*fy);
|
506
|
|
507
|
vec3 normal = cross(sx,sy);
|
508
|
|
509
|
if( normal.z<=0.0 ) // Why this bizarre shit rather than the straightforward
|
510
|
{ //
|
511
|
normal.x= 0.0; // if( normal.z>0.0 )
|
512
|
normal.y= 0.0; // {
|
513
|
normal.z= 1.0; // n.x = (n.x*normal.z + n.z*normal.x);
|
514
|
} // n.y = (n.y*normal.z + n.z*normal.y);
|
515
|
// n.z = (n.z*normal.z);
|
516
|
// }
|
517
|
n.x = (n.x*normal.z + n.z*normal.x); //
|
518
|
n.y = (n.y*normal.z + n.z*normal.y); // ? Because if we do the above, my shitty Nexus4 crashes
|
519
|
n.z = (n.z*normal.z); // during shader compilation!
|
520
|
}
|
521
|
}
|
522
|
}
|
523
|
|
524
|
#endif
|
525
|
|
526
|
//////////////////////////////////////////////////////////////////////////////////////////////
|
527
|
|
528
|
void main()
|
529
|
{
|
530
|
vec4 v = vec4( 2.0*u_objD*a_Position,1.0 );
|
531
|
vec4 n = vec4(a_Normal,0.0);
|
532
|
|
533
|
#if NUM_VERTEX>0
|
534
|
for(int i=0; i<vNumEffects; i++)
|
535
|
{
|
536
|
if( vType[i]==DISTORT) distort(3*i,v,n);
|
537
|
else if( vType[i]==DEFORM ) deform (3*i,v,n);
|
538
|
else if( vType[i]==SINK ) sink (3*i,v);
|
539
|
else if( vType[i]==PINCH ) pinch (3*i,v);
|
540
|
else if( vType[i]==SWIRL ) swirl (3*i,v);
|
541
|
else if( vType[i]==WAVE ) wave (3*i,v,n);
|
542
|
}
|
543
|
|
544
|
restrictZ(v.z);
|
545
|
#endif
|
546
|
|
547
|
v_Position = v.xyz;
|
548
|
v_TexCoordinate = a_TexCoordinate;
|
549
|
v_Normal = normalize(vec3(u_MVMatrix*n));
|
550
|
gl_Position = u_MVPMatrix*v;
|
551
|
}
|