How to draw a colored curved shape

Question

I can draw a polygon with a curved edge using B-splines or Bézier curves:

Graphics[{Line[{{-1, -1}, {1, 2}, {3, -2}, {1, -4}}],
          BSplineCurve[{{-1, -1}, {1, -3}, {-0.75, -2}, {1, -4}}]}]

My question is: how can I then color the inside of this polygon with a color of my choosing?

Answer 1

g1 = Graphics[{Line[{{-1, -1}, {1, 2}, {3, -2}, {1, -4}}], 
    BSplineCurve[{{-1, -1}, {1, -3}, {-0.75, -2}, {1, -4}}]}];

BoundaryDiscretizeGraphics[g1, MeshCellStyle -> {1 -> Red, 2 -> LightYellow}]

Also

g1 /. {Line[x_], BSplineCurve[y_]} :> 
  Module[{ls = Join[x, BSplineFunction[y] /@ Subdivide[50]]},
   {EdgeForm[Red], LightGreen, Polygon[ls[[First@FindCurvePath[ls]]]]}]

and

Graphics[{EdgeForm[Red], LightCyan, 
  FilledCurve[{BSplineCurve[{{-1, -1}, {1, -3}, {-0.75, -2}, {1, -4}}], 
    Line[Reverse @ {{-1, -1}, {1, 2}, {3, -2}, {1, -4}}]}]}]