// these are shaping functions taken from various places of https://flong.com

// Polynominal shaping

float blinn_wyvill_cos_approx(float x) {
  float x2 = x*x;
  float x4 = x2*x2;
  float x6 = x4*x2;

  float fa = ( 4.0/9.0);
  float fb = (17.0/9.0);
  float fc = (22.0/9.0);

  return fa*x6 - fb*x4 + fc*x2;
}

// TODO: factor out clamping
float double_cubic_seat(float x, vec2 ab) {
  float epsilon = 0.00001;
  float min_param_a = 0.0 + epsilon;
  float max_param_a = 1.0 - epsilon;
  float min_param_b = 0.0;
  float max_param_b = 1.0;
  float a = clamp(ab.x, min_param_a, max_param_a);
  float b = clamp(ab.y, min_param_b, max_param_b);

  if (x <= a){
    return b - b*pow(1.-x/a, 3.0);
  }
  return b + (1.-b)*pow((x-a)/(1.-a), 3.0);
}

float double_cubic_seat_linear_blend(float x, vec2 ab) {
  float epsilon = 0.00001;
  float min_param_a = 0.0 + epsilon;
  float max_param_a = 1.0 - epsilon;
  float min_param_b = 0.0;
  float max_param_b = 1.0;
  float a = clamp(ab.x, min_param_a, max_param_a);
  float b = clamp(ab.y, min_param_b, max_param_b);
  b = 1.0 - b;

  if (x<=a){
    return b*x + (1.-b)*a*(1.-pow(1.-x/a, 3.));
  }
  return b*x + (1.-b)*(a + (1.-a)*pow((x-a)/(1.-a), 3.));
}

float double_odd_polynomial_seat(float x, float a, float b, float n) {
  float epsilon = 0.00001;
  float min_param_a = 0.0 + epsilon;
  float max_param_a = 1.0 - epsilon;
  float min_param_b = 0.0;
  float max_param_b = 1.0; 
  a = clamp(a, min_param_a, max_param_a);
  b = clamp(b, min_param_b, max_param_b);

  float p = 2.*n + 1.;
  if (x <= a){
    return b - b*pow(1.-x/a, p);
  }
  return b + (1.-b)*pow((x-a)/(1.-a), p);
}

float double_poly_sigmoid(float x, float a, float b, float n) {
  if(mod(n, 2.) == 0.) {
    if(x <= 0.5) {
      return pow(2.0*x, n)/2.0;
    }
    return 1.0 - pow(2.*(x-1.), n)/2.0;
  } else {
    if (x<=0.5){
      return pow(2.0*x, n)/2.0;
    }
    return 1.0 + pow(2.0*(x-1.), n)/2.0;
  }
}

float quad_through_point(float x, vec2 ab) {
  float epsilon = 0.00001;
  float min_param_a = 0.0 + epsilon;
  float max_param_a = 1.0 - epsilon;
  float min_param_b = 0.0;
  float max_param_b = 1.0;
  float a = clamp(ab.x, min_param_a, max_param_a);
  float b = clamp(ab.y, min_param_b, max_param_b);

  float A = (1.-b)/(1.-a) - (b/a);
  float B = (A*(a*a)-b)/a;
  float y = A*(x*x) - B*(x);
  y = clamp(0., 1., y);

  return y;
}

// exponential shaping

float exp_easing(float x, float a) {
  float e = 0.00001;
  a = clamp(a, 0.+e, 1.-e);

  if (a < 0.5) {
    a = 2.0*(a);
    return pow(x, a);
  }
  a = 2.*(a-.5);
  return pow(x, 1./(1.-a));
}

float double_exp_seat(float x, float a) {
  float e = 0.00001;
  a = clamp(a, .0+e, 1.-e);

  if (x<=0.5) {
    return pow(2.*x, 1.-a)/2.0;
  }
  return 1. - pow(2.*(1.-x), 1.-a)/2.;
}

float double_exp_sigmoid(float x, float a) {
  float e = 0.00001;
  a = 1.-clamp(a, .0+e, 1.-e);

  if (x<=0.5){
    return pow(2.0*x, 1.0/a)/2.0;
  }
  return 1.0 - (pow(2.0*(1.0-x), 1.0/a))/2.0;
}

float normalized_log_sigmoid(float x, float a) {
  float e = 0.0001;
  a = 1./(1.-clamp(a, 0.+e, 1.-e)) - 1.;

  float b = 1.0 / (1.0 + exp(a));
  float c = 1.0 / (1.0 + exp(0.-a));
  a = 1. / (1. + exp(0. -((x-.5)*a*2.)));
  return (a-b)/(c-b);
}

// bezier shaping

float quad_bezier(float x, vec2 ab) {
  float e = 0.00001;
  float a = clamp(ab.x, 0., 1.);
  float b = clamp(ab.y, 0., 1.);
  if (a == 0.5) a += e;

  float om2a = 1. - 2.*a;
  float t = (sqrt(a*a + om2a*x) - a)/om2a;
  return (1.-2.*b)*(t*t) + (2.*b)*t;
}


// cubic bezier begin
float slope_from_t(float t, float A, float B, float C) {
  return 1.0/(3.0*A*t*t + 2.0*B*t + C);
}

float x_from_t(float t, float A, float B, float C, float D) {
  return A*(t*t*t) + B*(t*t) + C*t + D;
}

float y_from_t(float t, float E, float F, float G, float H) {
  return E*(t*t*t) + F*(t*t) + G*t + H;
}

float cubic_bezier(float x, vec2 a, vec2 b) {
  float y0a = 0.00;
  float x0a = 0.00;
  float y1a = a.y;
  float x1a = a.x;
  float y2a = b.y;
  float x2a = b.x;
  float y3a = 1.00;
  float x3a = 1.00;

  float A = x3a - 3.*x2a + 3.*x1a - x0a;
  float B = 3.*x2a - 6.*x1a + 3.*x0a;
  float C = 3.*x1a - 3.*x0a;
  float D = x0a;

  float E = y3a - 3.*y2a + 3.*y1a - y0a;
  float F = 3.*y2a - 6.*y1a + 3.*y0a;
  float G = 3.*y1a - 3.*y0a;
  float H = y0a;

  float currentt = x;
  for (int i=0; i < 5; i++){
    float currentx = x_from_t(currentt, A, B, C, D);
    float currentslope = slope_from_t(currentt, A, B, C);
    currentt -= (currentx - x)*(currentslope);
    currentt = clamp(currentt, 0., 1.);
  }

  float y = y_from_t(currentt, E, F, G, H);
  return y;
}
// cubic bezier end

// cubic bezier through points (requires cubic bezier) begin
float b0 (float t){
  return (1.-t)*(1.-t)*(1.-t);
}
float b1 (float t){
  return  3.*t* (1.-t)*(1.-t);
}
float b2 (float t){
  return 3.*t*t* (1.-t);
}
float b3 (float t){
  return t*t*t;
}
float  findx(float t, float x0, float x1, float x2, float x3) {
  return x0*b0(t) + x1*b1(t) + x2*b2(t) + x3*b3(t);
}
float findy(float t, float y0, float y1, float y2, float y3) {
  return y0*b0(t) + y1*b1(t) + y2*b2(t) + y3*b3(t);
}

float cubic_bezier_through(float x, vec2 a, vec2 b) {
  float y = 0.;
  float e = 0.00001;
  float minp = 0. + e;
  float maxp = 1. - e;
  a = clamp(a, minp, maxp);
  b = clamp(b, minp, maxp);

  float x0 = 0.;
  float y0 = 0.;
  float x4 = a.x;
  float y4 = a.y;
  float x5 = b.x;
  float y5 = b.y;
  float x3 = 1.;
  float y3 = 1.;
  float x1,y1,x2,y2;

  // arbitrary but reasonable
  float t1 = 0.3;
  float t2 = 0.7;

  float b0t1 = b0(t1);
  float b1t1 = b1(t1);
  float b2t1 = b2(t1);
  float b3t1 = b3(t1);
  float b0t2 = b0(t2);
  float b1t2 = b1(t2);
  float b2t2 = b2(t2);
  float b3t2 = b3(t2);

  float ccx = x4 - x0*b0t1 - x3*b3t1;
  float ccy = y4 - y0*b0t1 - y3*b3t1;
  float ffx = x5 - x0*b0t2 - x3*b3t2;
  float ffy = y5 - y0*b0t2 - y3*b3t2;

  x2 = (ccx - (ffx*b1t1)/b1t2) / (b2t1 - (b1t1*b2t2)/b1t2);
  y2 = (ccy - (ffy*b1t1)/b1t2) / (b2t1 - (b1t1*b2t2)/b1t2);
  x1 = (ccx - x2*b2t1) / b1t1;
  y1 = (ccy - y2*b2t1) / b1t1;

  x1 = clamp(x1, minp, maxp);
  x2 = clamp(x2, minp, maxp);

  y = cubic_bezier(x, vec2(x1,y1), vec2(x2,y2));
  return clamp(y, 0., 1.);
}
// cubic bezier through points end

// Circular shaping

float circ_ease_in (float x){
  return 1. - sqrt(1. - x*x);
}

float circ_ease_out (float x){
  return sqrt(1. - pow(1. - x, 2.));
}

float double_circ_seat(float x, float a) {
  a = clamp(a, 0., 1.); 

  if (x<=a){
    return sqrt(pow(a, 2.) - pow(x-a, 2.));
  }
  return 1. - sqrt(pow(1.-a, 2.) - pow(x-a, 2.));
}

float double_circ_sigmoid(float x, float a) {
  a = clamp(a, 0., 1.);

  if (x<=a){
    return a - sqrt(pow(a, 2.) - pow(x, 2.));
  }
  return a + sqrt(pow(1.-a, 2.) - pow(x-1., 2.));
}

float double_ellip_seat(float x, vec2 ab) {
  float e = 0.00001;
  float a = clamp(ab.x, 0.+e, 1.+e);
  float b = clamp(ab.y, 0., 1.);

  if (x<=a){
    return (b/a) * sqrt(pow(a, 2.) - pow(x-a, 2.));
  }
  return 1.-((1.-b)/(1.-a))*sqrt(pow(1.-a, 2.)-pow(x-a,2.));
}

float double_ellip_sigmoid(float x, vec2 ab) {
  float e = 0.00001;
  float a = clamp(ab.x, 0.+e, 1.+e);
  float b = clamp(ab.y, 0., 1.);

  if (x<=a){
    return b * (1. - (sqrt(pow(a, 2.) - pow(x, 2.))/a));
  }
  return b+((1.-b)/(1.-a))*sqrt(pow(1.-a,2.)-pow(x-1.,2.));
}