// #include "res://addons/rokojori_action_library/Runtime/Shading/Library/Bezier.gdshaderinc"


float cubicBezier( float t, float p0, float p1, float p2, float p3  )
{
  float bp0 = ( 1.0 - t ) * ( 1.0 - t ) * ( 1.0 - t );
  float bp1 = 3.0 * ( 1.0 - t ) * ( 1.0 - t ) * t;
  float bp2 = 3.0 * ( 1.0 - t ) * t * t;
  float bp3 = t * t * t;

  return p0 * bp0 + p1 * bp1 + p2 * bp2 + p3 * bp3;
}  

vec2 cubicBezier( float t, vec2 p0, vec2 p1, vec2 p2, vec2 p3  )
{
  float bp0 = ( 1.0 - t ) * ( 1.0 - t ) * ( 1.0 - t );
  float bp1 = 3.0 * ( 1.0 - t ) * ( 1.0 - t ) * t;
  float bp2 = 3.0 * ( 1.0 - t ) * t * t;
  float bp3 = t * t * t;

  return p0 * bp0 + p1 * bp1 + p2 * bp2 + p3 * bp3;
}  


vec3 cubicBezier( float t, vec3 p0, vec3 p1, vec3 p2, vec3 p3  )
{
  float bp0 = ( 1.0 - t ) * ( 1.0 - t ) * ( 1.0 - t );
  float bp1 = 3.0 * ( 1.0 - t ) * ( 1.0 - t ) * t;
  float bp2 = 3.0 * ( 1.0 - t ) * t * t;
  float bp3 = t * t * t;

  return p0 * bp0 + p1 * bp1 + p2 * bp2 + p3 * bp3;
}  

vec3 cubicBezierDerivative( float t, vec3 p0, vec3 p1, vec3 p2, vec3 p3  )
{
  vec3 d0 = ( p1 - p0 );
  vec3 d1 = ( p2 - p1 );
  vec3 d2 = ( p3 - p2 );

  float bp0 = 3.0 * ( 1.0 - t ) * ( 1.0 - t );
  float bp1 = 6.0 * ( 1.0 - t ) * t;
  float bp2 = 3.0 * t * t;


  return d0 * bp0 + d1 * bp1 + d2 * bp2;
}


vec3 rationalCubicBezier( float t, 
      vec3 p0, vec3 p1, vec3 p2, vec3 p3, 
      float w0, float w1, float w2, float w3
    )
{
  float bp0 = ( 1.0 - t ) * ( 1.0 - t ) * ( 1.0 - t ) * w0;
  float bp1 = 3.0 * ( 1.0 - t ) * ( 1.0 - t ) * t * w1;
  float bp2 = 3.0 * ( 1.0 - t ) * t * t * w2;
  float bp3 = t * t * t * w3;

  vec3 weighted = p0 * bp0 + p1 * bp1 + p2 * bp2 + p3 * bp3;

  float projection = bp0 + bp1 + bp2 + bp3;

  return weighted / projection;
}