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ICON
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#version 330

layout (location = 0) in vec3 a_Position;
layout (location = 1) in vec3 a_Normal;
layout (location = 2) in vec2 a_TextureCoord;
layout (location = 3) in vec3 a_Tangent;
layout (location = 4) in vec3 a_Bitangent;
layout (location = 5) in vec3 a_PRT1;
layout (location = 6) in vec3 a_PRT2;
layout (location = 7) in vec3 a_PRT3;

out VertexData {
    vec3 Position;
    vec3 ModelNormal;
    vec3 CameraNormal;
    vec2 Texcoord;
    vec3 Tangent;
    vec3 Bitangent;
    vec3 PRT1;
    vec3 PRT2;
    vec3 PRT3;
} VertexOut;

uniform mat3 RotMat;
uniform mat4 NormMat;
uniform mat4 ModelMat;
uniform mat4 PerspMat;

#define pi 3.1415926535897932384626433832795

float s_c3 = 0.94617469575; // (3*sqrt(5))/(4*sqrt(pi))
float s_c4 = -0.31539156525;// (-sqrt(5))/(4*sqrt(pi))
float s_c5 = 0.54627421529; // (sqrt(15))/(4*sqrt(pi))

float s_c_scale = 1.0/0.91529123286551084;
float s_c_scale_inv = 0.91529123286551084;

float s_rc2 = 1.5853309190550713*s_c_scale;
float s_c4_div_c3 = s_c4/s_c3;
float s_c4_div_c3_x2 = (s_c4/s_c3)*2.0;

float s_scale_dst2 = s_c3 * s_c_scale_inv;
float s_scale_dst4 = s_c5 * s_c_scale_inv;

void OptRotateBand0(float x[1], mat3 R, out float dst[1])
{
    dst[0] = x[0];
}

// 9 multiplies
void OptRotateBand1(float x[3], mat3 R, out float dst[3])
{
    // derived from  SlowRotateBand1
    dst[0] = ( R[1][1])*x[0] + (-R[1][2])*x[1] + ( R[1][0])*x[2];
    dst[1] = (-R[2][1])*x[0] + ( R[2][2])*x[1] + (-R[2][0])*x[2];
    dst[2] = ( R[0][1])*x[0] + (-R[0][2])*x[1] + ( R[0][0])*x[2];
}

// 48 multiplies
void OptRotateBand2(float x[5], mat3 R, out float dst[5])
{
    // Sparse matrix multiply
    float sh0 =  x[3] + x[4] + x[4] - x[1];
    float sh1 =  x[0] + s_rc2*x[2] +  x[3] + x[4];
    float sh2 =  x[0];
    float sh3 = -x[3];
    float sh4 = -x[1];
    
    // Rotations.  R0 and R1 just use the raw matrix columns
    float r2x = R[0][0] + R[0][1];
    float r2y = R[1][0] + R[1][1];
    float r2z = R[2][0] + R[2][1];
    
    float r3x = R[0][0] + R[0][2];
    float r3y = R[1][0] + R[1][2];
    float r3z = R[2][0] + R[2][2];
    
    float r4x = R[0][1] + R[0][2];
    float r4y = R[1][1] + R[1][2];
    float r4z = R[2][1] + R[2][2];
    
    // dense matrix multiplication one column at a time
    
    // column 0
    float sh0_x = sh0 * R[0][0];
    float sh0_y = sh0 * R[1][0];
    float d0 = sh0_x * R[1][0];
    float d1 = sh0_y * R[2][0];
    float d2 = sh0 * (R[2][0] * R[2][0] + s_c4_div_c3);
    float d3 = sh0_x * R[2][0];
    float d4 = sh0_x * R[0][0] - sh0_y * R[1][0];
    
    // column 1
    float sh1_x = sh1 * R[0][2];
    float sh1_y = sh1 * R[1][2];
    d0 += sh1_x * R[1][2];
    d1 += sh1_y * R[2][2];
    d2 += sh1 * (R[2][2] * R[2][2] + s_c4_div_c3);
    d3 += sh1_x * R[2][2];
    d4 += sh1_x * R[0][2] - sh1_y * R[1][2];
    
    // column 2
    float sh2_x = sh2 * r2x;
    float sh2_y = sh2 * r2y;
    d0 += sh2_x * r2y;
    d1 += sh2_y * r2z;
    d2 += sh2 * (r2z * r2z + s_c4_div_c3_x2);
    d3 += sh2_x * r2z;
    d4 += sh2_x * r2x - sh2_y * r2y;
    
    // column 3
    float sh3_x = sh3 * r3x;
    float sh3_y = sh3 * r3y;
    d0 += sh3_x * r3y;
    d1 += sh3_y * r3z;
    d2 += sh3 * (r3z * r3z + s_c4_div_c3_x2);
    d3 += sh3_x * r3z;
    d4 += sh3_x * r3x - sh3_y * r3y;
    
    // column 4
    float sh4_x = sh4 * r4x;
    float sh4_y = sh4 * r4y;
    d0 += sh4_x * r4y;
    d1 += sh4_y * r4z;
    d2 += sh4 * (r4z * r4z + s_c4_div_c3_x2);
    d3 += sh4_x * r4z;
    d4 += sh4_x * r4x - sh4_y * r4y;
    
    // extra multipliers
    dst[0] = d0;
    dst[1] = -d1;
    dst[2] = d2 * s_scale_dst2;
    dst[3] = -d3;
    dst[4] = d4 * s_scale_dst4;
}

void main()
{ 
    // normalization
    mat3 R = mat3(ModelMat) * RotMat;
    VertexOut.ModelNormal = a_Normal;
    VertexOut.CameraNormal = (R * a_Normal);
    VertexOut.Position = a_Position;
    VertexOut.Texcoord = a_TextureCoord;
    VertexOut.Tangent = (R * a_Tangent);
    VertexOut.Bitangent = (R * a_Bitangent);
    float PRT0, PRT1[3], PRT2[5];
    PRT0 = a_PRT1[0];
    PRT1[0] = a_PRT1[1];
    PRT1[1] = a_PRT1[2];
    PRT1[2] = a_PRT2[0];
    PRT2[0] = a_PRT2[1];
    PRT2[1] = a_PRT2[2];
    PRT2[2] = a_PRT3[0];
    PRT2[3] = a_PRT3[1];
    PRT2[4] = a_PRT3[2];

    OptRotateBand1(PRT1, R, PRT1);
    OptRotateBand2(PRT2, R, PRT2);

    VertexOut.PRT1 = vec3(PRT0,PRT1[0],PRT1[1]);
    VertexOut.PRT2 = vec3(PRT1[2],PRT2[0],PRT2[1]);
    VertexOut.PRT3 = vec3(PRT2[2],PRT2[3],PRT2[4]);

    gl_Position = vec4(a_TextureCoord, 0.0, 1.0) - vec4(0.5, 0.5, 0, 0);
    gl_Position[0] *= 2.0;
    gl_Position[1] *= 2.0;
}