talipot-core/ParametricCurves: Remove caching of Bézier coefficients

It did not bring any significant performance improvements and cause
crashes when using OpenMP and MSVC so better removing that cache as
Bézier points are already computed in parallel to speedup curve
computation.

library/talipot-core/src/ParametricCurves.cpp

@@ -1,6 +1,6 @@
 /**
  *
- * Copyright (C) 2019-2021  The Talipot developers
+ * Copyright (C) 2019-2024  The Talipot developers
  *
  * Talipot is a fork of Tulip, created by David Auber
  * and the Tulip development Team from LaBRI, University of Bordeaux
@@ -112,36 +112,10 @@ static void computeCubicBezierPoints(const Coord &p0, const Coord &p1, const Coo
   curvePoints[nbCurvePoints - 1] = p3;
 }
 
-static map<double, vector<double>> tCoeffs;
-static map<double, vector<double>> sCoeffs;
-static map<uint, uint> computedCoefficients;
-
-static void computeCoefficients(double t, uint nbControlPoints) {
-  double s = (1.0 - t);
-  TLP_LOCK_SECTION(computeCoefficients) {
-    auto &tCoeff = tCoeffs[t];
-    auto &sCoeff = sCoeffs[t];
-    // preallocate vectors to avoid heap-use-after-free due to vectors growth
-    // when computing Bézier points with multiple threads
-    tCoeff.reserve(256);
-    sCoeff.reserve(256);
-    if (tCoeff.size() < nbControlPoints) {
-      size_t oldSize = tCoeff.size();
-      for (size_t i = oldSize; i < nbControlPoints; ++i) {
-        tCoeff.push_back(pow(t, double(i)));
-        sCoeff.push_back(pow(s, double(i)));
-      }
-    }
-  }
-  TLP_UNLOCK_SECTION(computeCoefficients);
-}
-
 Coord computeBezierPoint(const vector<Coord> &controlPoints, const float t) {
 
   size_t nbControlPoints = controlPoints.size();
 
-  computeCoefficients(t, nbControlPoints);
-
   Vec3d bezierPoint;
   bezierPoint[0] = bezierPoint[1] = bezierPoint[2] = 0;
   double curCoeff = 1.0;
@@ -152,8 +126,8 @@ Coord computeBezierPoint(const vector<Coord> &controlPoints, const float t) {
     controlPoint[0] = controlPoints[i][0];
     controlPoint[1] = controlPoints[i][1];
     controlPoint[2] = controlPoints[i][2];
-    bezierPoint += controlPoint * curCoeff * tCoeffs[double(t)][i] *
-                   sCoeffs[double(t)][nbControlPoints - 1 - i];
+    bezierPoint += controlPoint * curCoeff * pow(double(t), double(i)) *
+                   pow(1.0 - double(t), double(nbControlPoints - 1 - i));
     auto c = double(i + 1);
     curCoeff *= (r - c) / c;
   }