You just need to fully compile your function:

fullycompiledBSplineSurf = 
  Hold@Compile[{{ctrlnets, _Real, 3}, {deg1, _Integer}, {deg2, _Integer}, {knots1, _Real,
         1}, {knots2, _Real, 1}, {u, _Real}, {v, _Real}}, 
      Module[{i, j, validnets, row, col}, i = searchSpan[{deg1, knots1}, u];
       j = searchSpan[{deg2, knots2}, v];
       validnets = Take[ctrlnets, {i - deg1 + 1, i + 1}, {j - deg2 + 1, j + 1}];
       row = optimizedNonzeroBasis[deg1, knots1, u];
       col = optimizedNonzeroBasis[deg2, knots2, v];
       row.Transpose[validnets, {1, 3, 2}].col], 
      CompilationOptions -> {"InlineExternalDefinitions" -> True}, 
      "RuntimeOptions" -> {"EvaluateSymbolically" -> False}, CompilationTarget -> C, 
       RuntimeOptions -> "Speed"] /. DownValues@searchSpan // ReleaseHold;

ParametricPlot3D[
  fullycompiledBSplineSurf[pts, 3, 3, k1, k2, u, v], {u, 0, 1}, {v, 0, 
   1}] // AbsoluteTiming

Now the function is about half as fast as the built-in:

ParametricPlot3D[f[u, v], {u, 0, 1}, {v, 0, 1}] // AbsoluteTiming

I think I don't need to make any explanation, because all the techniques above have been used in answering your previous questions.

You just need to fully compile your function:

fullycompiledBSplineSurf = 
  Hold@Compile[{{ctrlnets, _Real, 3}, {deg1, _Integer}, {deg2, _Integer}, 
                {knots1, _Real, 1}, {knots2, _Real, 1}, {u, _Real}, {v, _Real}}, 
      Module[{i, j, validnets, row, col}, 
        i = searchSpan[{deg1, knots1}, u];
        j = searchSpan[{deg2, knots2}, v];
        validnets = Take[ctrlnets, {i - deg1 + 1, i + 1}, {j - deg2 + 1, j + 1}];
        row = optimizedNonzeroBasis[i, deg1, knots1, u];
        col = optimizedNonzeroBasis[j, deg2, knots2, v];
        row.Transpose[validnets, {1, 3, 2}].col
      ], 
      CompilationOptions -> {"InlineExternalDefinitions" -> True}, 
      "RuntimeOptions" -> {"EvaluateSymbolically" -> False},  
      CompilationTarget -> C, RuntimeOptions -> "Speed"
  ] /. DownValues@searchSpan // ReleaseHold;

ParametricPlot3D[
  fullycompiledBSplineSurf[pts, 3, 3, k1, k2, u, v], 
  {u, 0, 1}, {v, 0, 1}] // AbsoluteTiming

Now the function is about half as fast as the built-in:

ParametricPlot3D[f[u, v], {u, 0, 1}, {v, 0, 1}] // AbsoluteTiming

I think I don't need to make any explanation, because all the techniques above have been used in answering your previous questions.

You just need to fully compile your function:

fullycompiledBSplineSurf = 
  Hold@Compile[{{ctrlnets, _Real, 3}, {deg1, _Integer}, {deg2, _Integer}, {knots1, _Real,
         1}, {knots2, _Real, 1}, {u, _Real}, {v, _Real}}, 
      Module[{i, j, validnets, row, col}, i = searchSpan[{deg1, knots1}, u];
       j = searchSpan[{deg2, knots2}, v];
       validnets = Take[ctrlnets, {i - deg1 + 1, i + 1}, {j - deg2 + 1, j + 1}];
       row = optimizedNonzeroBasis[deg1, knots1, u];
       col = optimizedNonzeroBasis[deg2, knots2, v];
       row.Transpose[validnets, {1, 3, 2}].col], 
      CompilationOptions -> {"InlineExternalDefinitions" -> True}, 
      "RuntimeOptions" -> {"EvaluateSymbolically" -> False}, CompilationTarget -> C, 
      RuntimeOptions -> "Speed"] /. DownValues@searchSpan // ReleaseHold;

ParametricPlot3D[
  fullycompiledBSplineSurf[pts, 3, 3, k1, k2, u, v], {u, 0, 1}, {v, 0, 
   1}] // AbsoluteTiming

I think I don't need to make any explanation, because all the techniques above have been used in answering your previous questions.

You just need to fully compile your function:

fullycompiledBSplineSurf = 
  Hold@Compile[{{ctrlnets, _Real, 3}, {deg1, _Integer}, {deg2, _Integer}, {knots1, _Real,
         1}, {knots2, _Real, 1}, {u, _Real}, {v, _Real}}, 
      Module[{i, j, validnets, row, col}, i = searchSpan[{deg1, knots1}, u];
       j = searchSpan[{deg2, knots2}, v];
       validnets = Take[ctrlnets, {i - deg1 + 1, i + 1}, {j - deg2 + 1, j + 1}];
       row = optimizedNonzeroBasis[deg1, knots1, u];
       col = optimizedNonzeroBasis[deg2, knots2, v];
       row.Transpose[validnets, {1, 3, 2}].col], 
      CompilationOptions -> {"InlineExternalDefinitions" -> True}, 
      "RuntimeOptions" -> {"EvaluateSymbolically" -> False}, CompilationTarget -> C, 
      RuntimeOptions -> "Speed"] /. DownValues@searchSpan // ReleaseHold;

ParametricPlot3D[
  fullycompiledBSplineSurf[pts, 3, 3, k1, k2, u, v], {u, 0, 1}, {v, 0, 
   1}] // AbsoluteTiming

Now the function is about half as fast as the built-in:

ParametricPlot3D[f[u, v], {u, 0, 1}, {v, 0, 1}] // AbsoluteTiming

I think I don't need to make any explanation, because all the techniques above have been used in answering your previous questions.