text: 
  //~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~~//
  // Arcane-FX for MIT Licensed Open Source version of Torque 3D from GarageGames
  // Copyright (C) 2015 Faust Logic, Inc.
  //
  // Permission is hereby granted, free of charge, to any person obtaining a copy
  // of this software and associated documentation files (the "Software"), to
  // deal in the Software without restriction, including without limitation the
  // rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
  // sell copies of the Software, and to permit persons to whom the Software is
  // furnished to do so, subject to the following conditions:
  //
  // The above copyright notice and this permission notice shall be included in
  // all copies or substantial portions of the Software.
  //
  // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
  // IN THE SOFTWARE.
  //
  //~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~~//
  
  #include "afx/arcaneFX.h"
  #include "afx/util/afxCurveEval.h"
  
  Point2F afxHermiteEval::evaluateCurve( Point2F &v0, Point2F &v1,
                                           Point2F &t0, Point2F &t1, F32 t )
  {
    F32 t_3 = t*t*t;
    F32 t_2 = t*t;
    F32 h1 = ( 2.0f * t_3 ) - ( 3.0f * t_2 ) + 1;
    F32 h2 = (-2.0f * t_3 ) + ( 3.0f * t_2 );
    F32 h3 = t_3 - ( 2.0f * t_2 ) + t;
    F32 h4 = t_3 - t_2;
  
    Point2F v( 
      (h1*v0.x)+(h2*v1.x)+(h3*t0.x)+(h4*t1.x),
      (h1*v0.y)+(h2*v1.y)+(h3*t0.y)+(h4*t1.y) );
  
    return v;
  }
  
  Point2F afxHermiteEval::evaluateCurve( Point2F &v0, Point2F &v1, F32 t )
  {
    Point2F tangent( 1, 0 );
    return( evaluateCurve( v0, v1, tangent, tangent, t ) );
  }
  
  Point2F afxHermiteEval::evaluateCurveTangent( Point2F &v0, Point2F &v1,
                                                  Point2F &t0, Point2F &t1, F32 t )
  {
    F32 t_2 = t*t;
    F32 h1_der = ( 6.0f * t_2 ) - ( 6.0f * t );
    F32 h2_der = (-6.0f * t_2 ) + ( 6.0f * t );
    F32 h3_der = ( 3.0f * t_2 ) - ( 4.0f * t ) + 1;
    F32 h4_der = ( 3.0f * t_2 ) - ( 2.0f * t );
  
    Point2F tangent( 
      (h1_der*v0.x)+(h2_der*v1.x)+(h3_der*t0.x)+(h4_der*t1.x),
      (h1_der*v0.y)+(h2_der*v1.y)+(h3_der*t0.y)+(h4_der*t1.y) );
  
    return tangent;
  }
  
  Point2F afxHermiteEval::evaluateCurveTangent( Point2F &v0, Point2F &v1, F32 t )
  {
    Point2F tangent( 1, 0 );
    return( evaluateCurveTangent( v0, v1, tangent, tangent, t ) );
  }
  
  Point3F afxHermiteEval::evaluateCurve( Point3F &v0, Point3F &v1,
                                           Point3F &t0, Point3F &t1, F32 t )
  {
    F32 t_3 = t*t*t;
    F32 t_2 = t*t;
    F32 h1 = ( 2.0f * t_3 ) - ( 3.0f * t_2 ) + 1;
    F32 h2 = (-2.0f * t_3 ) + ( 3.0f * t_2 );
    F32 h3 = t_3 - ( 2.0f * t_2 ) + t;
    F32 h4 = t_3 - t_2;
  
    Point3F v( 
      (h1*v0.x)+(h2*v1.x)+(h3*t0.x)+(h4*t1.x),
      (h1*v0.y)+(h2*v1.y)+(h3*t0.y)+(h4*t1.y),
      (h1*v0.z)+(h2*v1.z)+(h3*t0.z)+(h4*t1.z) );
  
    return v;
  }
  
  Point3F afxHermiteEval::evaluateCurve( Point3F &v0, Point3F &v1, F32 t )
  {
    Point3F tangent( 1, 0, 0 );
    return( evaluateCurve( v0, v1, tangent, tangent, t ) );
  }
  
  Point3F afxHermiteEval::evaluateCurveTangent( Point3F &v0, Point3F &v1,
                                                  Point3F &t0, Point3F &t1, F32 t )
  {
    F32 t_2 = t*t;
    F32 h1_der = ( 6.0f * t_2 ) - ( 6.0f * t );
    F32 h2_der = (-6.0f * t_2 ) + ( 6.0f * t );
    F32 h3_der = ( 3.0f * t_2 ) - ( 4.0f * t ) + 1;
    F32 h4_der = ( 3.0f * t_2 ) - ( 2.0f * t );
  
    Point3F tangent( 
      (h1_der*v0.x)+(h2_der*v1.x)+(h3_der*t0.x)+(h4_der*t1.x),
      (h1_der*v0.y)+(h2_der*v1.y)+(h3_der*t0.y)+(h4_der*t1.y),
      (h1_der*v0.z)+(h2_der*v1.z)+(h3_der*t0.z)+(h4_der*t1.z) );
  
    return tangent;
  }
  
  Point3F afxHermiteEval::evaluateCurveTangent( Point3F &v0, Point3F &v1, F32 t )
  {
    Point3F tangent( 1, 0, 0 );
    return( evaluateCurveTangent( v0, v1, tangent, tangent, t ) );
  }
  
  //~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~//~~~~~~~~~~~~~~~~~~~~~//
  
  