#ifndef MUSCLEFUNCTIONFACTORY_H_
#define MUSCLEFUNCTIONFACTORY_H_
/* -------------------------------------------------------------------------- *
 *   OpenSim:  SmoothSegmentedFunctionFactory.h                               *
 * -------------------------------------------------------------------------- *
 * The OpenSim API is a toolkit for musculoskeletal modeling and simulation.  *
 * See http://opensim.stanford.edu and the NOTICE file for more information.  *
 * OpenSim is developed at Stanford University and supported by the US        *
 * National Institutes of Health (U54 GM072970, R24 HD065690) and by DARPA    *
 * through the Warrior Web program.                                           *
 *                                                                            *
 * Copyright (c) 2005-2012 Stanford University and the Authors                *
 * Author(s): Matthew Millard                                                 *
 *                                                                            *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may    *
 * not use this file except in compliance with the License. You may obtain a  *
 * copy of the License at http://www.apache.org/licenses/LICENSE-2.0.         *
 *                                                                            *
 * Unless required by applicable law or agreed to in writing, software        *
 * distributed under the License is distributed on an "AS IS" BASIS,          *
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   *
 * See the License for the specific language governing permissions and        *
 * limitations under the License.                                             *
 * -------------------------------------------------------------------------- */
/*
  Update:
  This is a port of the original code so that it will work with
  the multibody code RBDL written by Martin Felis.
  
  Author:
  Matthew Millard
  
  Date:
  Nov 2015

*/
#include "../geometry/SmoothSegmentedFunction.h"
#include "../geometry/SegmentedQuinticBezierToolkit.h"

#include <cstdio>
#include <iostream>
#include <fstream>
#include <cmath>



/**
This is a class that acts as a user friendly wrapper to QuinticBezerCurveSet
to build specific kinds of physiologically plausible muscle curves using C2 
continuous sets of quintic Bezier curves. This class has been written there did 
not exist a set of curves describing muscle characteristics that was:

1. Physiologically Accurate
2. Continuous to the second derivative
3. Parameterized in a physically meaningful manner

For example, the curves employed by Thelen (Thelen DG(2003). Adjustment of 
Muscle Mechanics Model Parameters to Simulate Dynamic Contractions in Older 
Adults. ASME Journal of Biomechanical Engineering (125).) are parameterized in a 
physically meaningful manner, making them easy to use. However there are 
many shortcomings of these curves:

1.  The tendon and parallel element are not C2 continuous, making them slow to 
  simulate and likely not physiologically accurate. 
2.  The active force length curve approaches does not achieve its minimum value
  at a normalized fiber length of 0.5, and 1.5. 
3.  The force velocity curve is not C2 continuous at the origin. As it is 
  written in the paper the curve is impossible to use with an equilibrium model
  because it is not invertible. In addition the force-velocity curve actually 
  increases in stiffness as activation drops - a very undesirable property given
  that many muscles are inactive at any one time.

The muscle curves used in the literature until 2012 have been hugely influenced
by Thelen's work, and thus similar comments can easily be applied to just about
every other musculoskeletal simulation.

Another example is from Miller (Miller,RH(2011).Optimal Control of 
Human Running. PhD Thesis). On pg 149 a physiolgically plausible force velocity
curve is specified that gives the user the ability to change the concentric 
curvature to be consistent with a slow or a fast twitch musle. This curve is 
not C2 continuous at the origin, but even worse, it contains singularities in 
its parameter space. Since these parameters do not have a physical 
interpretation this model is difficult to use without accidentically creating a 
curve with a singularity.

With this motivation I set out to develop a class that could generate muscle
characteristic curves with the following properties:

1. Physiologically Accurate
2. Continuous to the second derivative
3. Parameterized in a physically meaningful manner
4. Monotonicity for monotonic curves
5. Computationally efficient

These goals were surprisingly time consuming achieve, but these goals have been 
achieved using sets of C2 continuous quintic Bezier curves. The resulting 
muscle curve functions in this class take parameters that would be intuitive to 
biomechanists who simulate human musculoskeletal systems, and returns a 
SmoothSegmentedFunction which is capable of evaluating the value, and
derivatives of the desired function (or actually relation as 
the case may be). 

Each curve is made up of one or more C2 quintic Bezier curves x(u), 
and y(u), with linearily extrapolated ends as shown in the figure below. These 
quintic curves span 2 points, and achieve the desired derivative at its end 
points. The degree of curviness can be varied from 0 to 1 (0, 0.75 and 1.0 are 
shown in the figure in grey, blue and black respectively), and will make the 
curve approximate a line when set to 0 (grey), and approximate a curve that 
hugs the intersection of the lines that are defined by the end points locations 
and the slopes at the end of each curve segment (red lines). Although you do 
not need to set all of this information directly, for some of the curves it is 
useful to know that both the slope and the curviness parameter may need to be 
altered to achieve the desired shape.


\image html fig_GeometryAddon_quinticCornerSections.png



<B>Computational Cost Details</B>
All computational costs assume the following operation costs:

\verbatim
Operation Type   : #flops
*,+,-,=,Boolean Op : 1 
   / : 10
   sqrt: 20
   trig: 40
\endverbatim

These relative weightings will vary processor to processor, and so any of 
the quoted computational costs are approximate.

<B> RBDL Port Notes </B>
The port of this code from OpenSim has been accompanied by a few changes:

1. The 'calcIntegral' method has been removed. Why? This function 
   relied on having access to a variable-step error controlled 
   integrator. There is no such integrator built into RBDL. Rather 
   than add a dependency (by using Boost perhaps) this functionality
   has been removed. 

2. The function name .printMuscleCurveToFile(...) has been changed
   to .printCurveToFile(). 



@author Matt Millard
@version 0.0

*/
namespace RigidBodyDynamics {
  namespace Addons {
  namespace Muscle{

class MuscleFunctionFactory
{


  public:

   // friend class SmoothSegmentedFunction;


  /**
  This is a function that will produce a C2 (continuous to the second
  derivative) active force length curve.


  @param lce0   Normalized fiber length at the left-most shoulder of the 
    active force-length curve. The value of the active force
    length curve for lce < lce0 will be equal to the value
    set in shoulderVal. Normally lce0 is approximately 0.5
  
  @param lce1   Normalized fiber length at the transition point between 
    the ascending limb and the plateau region of the active 
    force length curve.
  
  @param lce2   Normalized fiber length at the maximum active force length
    curve value of 1. Normally lce2 is by definition 1.
  
  @param lce3   Normalized fiber length of the at the right most shoulder
    of the active-force length curve. The value of the active
    force length curve for lce > lce2 will be equal to the 
    value of shoulderVal. Normally lce3 is approximately 1.5

  @param minActiveForceLengthValue
    The minimum value of the active force length 
    curve. A physiological non-equibrium muscle model
    would have this value set to 0. An equilibrium 
    muscle model would have a non-zero lower bound on 
    this value of 0.1 typically. shoulderVal must be 
    greater than, or equal to 0.
    
  @param plateauSlope   The slope of the plateau of the active force
    length curve between lce1 and lce2. This parameter
    can vary depending on the muscle model, but a 
    value of 0.8616 is a good place to start.

  @param curviness  The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow). A value of 0 will yield an active 
    force length curve that is composed of slightly curved 
    line segments. A value of 1 will yield an active force
    length curve that is smoothly rounded.


  @param curveName The name of the muscle this curve applies to. This 
    curve name should have the name of the muscle and the
    curve in it (e.g. "bicep_fiberActiveForceLengthCurve") 
    sothat if this curve ever causes an exception, a 
    userfriendly error message can be displayed to the
    end user to help them debug their model.

  @param smoothSegmentedFunctionToUpdate
      A SmoothSegmentedFunction object that will be erased and filled with 
      the coefficients that are defined by this curve.

  \b aborts \b 
  if these conditions aren't met
  -0 < lce0 < lce1 < lce2 < lce3 
  -shoulderVal >= 0
  -0 <= plateauSlope < (1/(lce3-lce2))
  -0 <= curviness <= 1


  \image html fig_MuscleAddon_MuscleFunctionFactory_falCurve.png

   
  <B>Conditions:</B>

  <B>Computational Costs</B>
  \verbatim 
  ~20,500 flops
  \endverbatim

  <B>Example:</B>
  @code
  double lce0 = 0.5;
  double lce1 = 0.75;
  double lce2 = 1;
  double lce3 = 1.5;
  double shoulderVal  = 0.1;
  double plateauSlope = 0.75;
  double curviness  = 0.9;

  SmoothSegmentedFunction fiberfalCurve = SmoothSegmentedFunction();
  MuscleFunctionFactory::
    createFiberActiveForceLengthCurve(lce0, lce1, lce2, lce3, 
        shoulderVal, plateauSlope, curviness,"test", fiberfalCurve);  
  fiberfalCurve.printCurveToFile();
  @endcode
  

  */
  static void createFiberActiveForceLengthCurve(
                  double lce0, 
                  double lce1, 
                  double lce2, 
                  double lce3, 
                  double minActiveForceLengthValue, 
                  double plateauSlope, 
                  double curviness, 
                  const std::string& curveName,
                  RigidBodyDynamics::Addons::Geometry
                    ::SmoothSegmentedFunction&
                    smoothSegmentedFunctionToUpdate);

  /**
  This function will generate a C2 continous (continuous to the second 
  derivative) force velocity curve of a single muscle fiber. The main 
  function of this element is to model the amount the force enhancement or 
  attenuation that is associated with contracting at a particular velocity.
  
  @param fmaxE  The normalized maximum force the fiber can generate when 
    is being stretched. This value is reported to range 
    between 1.1 and 1.8 in the literature, though all values
    are above 1.

  @param dydxC  The slope of the fv(dlce(t)/dt) curve at the maximum 
    normalized concentric contraction velocity. Although 
    physiologically the value of dydxC at the maximum 
    concentric contracton velocity is by definition 0, a value
    of 0 is often used. If you are using an equilbrium type 
    model this term must be positive and greater than zero so
    that the fv curve can be inverted.
    <br /><br />
    Minimum Value: 0
    Maximum Value: dydxC < 1 
    <br /><br />

  @param dydxNearC The slope of the force velocity curve as it approaches
     the maximum concentric (shortening) contraction velocity.
     <br /><br />
    Minimum Value: > dydxC
    Maximum Value: dydxNearC < 1 
    <br /><br />


  @param dydxIso  The slope of the fv curve when dlce(t)/dt = 0. 
    <br /><br />
    Minimim Value: dydxIso > 1.0
    Maximum Value: dydxIso < Inf
    
  @param dydxE  The analogous term of dydxC parameter but for the 
    eccentric portion of the force-velocity curve. As with
    the dydxC term, the physiologically accurate value for
    this parameter is 0, though a value of 0 is rarely used
    in muscle models.  If you are using an equilbrium type 
    model this term must be positive and greater than zero 
    so that the fv curve can be inverted. 
    <br /><br />
    Minimum Value: 0
    Maximum Value: dydxC < (fmaxE-1).
    <br /><br />
    As with the dydxC term, 
    the size of this term also affects the stiffness of the 
    integration problem for equilibrium-type muscle models: 
    the closer to zero this term is, the stiffer the model 
    will be (but only when (dlce(t)/dt)/vmax approaches 1.
  
  @param dydxNearE The slope of the force velocity curve as it approaches
     the maximum eccentric (lengthening) contraction velocity.
     <br /><br />
    Minimum Value: > dydxE
    Maximum Value: dydxNearE < (fmaxE-1)
    <br /><br />


  @param concCurviness  The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow). This parameter affects only
    the concentric side of the fv curve.

  @param eccCurviness   The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow). This parameter affects only 
    the eccentric side of the fv curve.


  @param curveName The name of the muscle this curve applies to. This 
    curve name should have the name of the muscle and the
    curve in it (e.g. "bicep_fiberForceVelocityCurve") 
    sothat if this curve ever causes an exception, a 
    userfriendly error message can be displayed to the
    end user to help them debug their model.

  @param smoothSegmentedFunctionToUpdate
      A SmoothSegmentedFunction object that will be erased and filled with 
      the coefficients that are defined by this curve.

  \b aborts \b 
  unless these conditions are met  
  -0 <= dydxC < 1
  -dydxC < dydxNearC < 1
  -1 < dydxIso
  -dydxE < (fmaxE-1) 
  -dydxE < dydxNearC < (fmaxE-1)
  -0<= concCurviness <=0
  -0 <= eccCurviness <= 0
  
  
  \image html fig_MuscleAddon_MuscleFunctionFactory_fvCurve.png



  <B>Computational Costs</B>
  \verbatim 
  ~8,200 flops
  \endverbatim

  <B>Example:</B>
  @code
  double fmaxE = 1.8;
  double dydxC = 0.1;
  double dydxNearC = 0.25;
  double dydxE = 0.1;
  double dydxNearE = 0.15;
  double dydxIso= 5;
  double concCurviness = 0.1;
  double eccCurviness = 0.75;
  
  SmoothSegmentedFunction fiberFVCurve = SmoothSegmentedFunction();
  MuscleFunctionFactory::
    createFiberForceVelocityCurve(fmaxE, 
      dydxC, dydxNearC, dydxIso, dydxE, dydxNearE,
      concCurviness,  eccCurviness,"test", fiberFVCurve);
  fiberFVCurve.printCurveToFile();
  @endcode   
  */
  static void createFiberForceVelocityCurve(
                  double fmaxE, 
                  double dydxC, 
                  double dydxNearC, 
                  double dydxIso, 
                  double dydxE, 
                  double dydxNearE,
                  double concCurviness, 
                  double eccCurviness,
                  const std::string& curveName,
                  RigidBodyDynamics::Addons::Geometry::
                    SmoothSegmentedFunction&
                    smoothSegmentedFunctionToUpdate);

  /**
  This function will generate a C2 continuous (continuous to the 2nd
  derivative) inverse curve that the function 
  createFiberForceVelocityCurve generates. The inverse force velocity 
  curve is required by every equilibrium muscle model in order to compute
  the derivative of fiber velocity. To generate the inverse force velocity
  curve simply call this function with EXACTLY the same parameter values
  that you used to generate the force velocity curve. See the parameter
  descriptions for createFiberForceVelocityCurve, as the parameters for
  the inverse function are identical. The curve name should be different,
  however, because this is an inverse curve 
  (e.g. "bicep_fiberForceVelocityInverseCurve")
  

  \image html fig_MuscleAddon_MuscleFunctionFactory_fvInvCurve.png

  */
  static void createFiberForceVelocityInverseCurve(
                  double fmaxE, 
                  double dydxC, 
                  double dydxNearC, 
                  double dydxIso, 
                  double dydxE, 
                  double dydxNearE,
                  double concCurviness, 
                  double eccCurviness, 
                  const std::string& muscleName,
                  RigidBodyDynamics::Addons::Geometry::
                    SmoothSegmentedFunction&
                    smoothSegmentedFunctionToUpdate);

  /**
  This element will generate a C2 continuous (continuous to the 2nd
  derivative) compressive force profile curve as a function of pennation.
  A muscle model with this element usually places this element parallel to
  the fiber.The main function of this element is to prevent the fiber from 
  achieving a pennation angle of pi/2 radians. This type of element is 
  necessary for a parallelogram pennated equilibrium muscle models because 
  without it, the muscle model can deform to the point where a pennation 
  angle of pi/2 radians is reached, which causes a singularity in the 
  model.


  @param phi0 The pennation angle at which the compressive force element
    starts to engage . When the pennation angle is greater than 
    phi0, the compressive element is generating a force. When the 
    pennation angle is less than phi0, the compressive element 
    generates no force.

  @param kiso This is the maximum stiffness of the compressive element, 
    which occurs when the fiber is pennated by 90 degrees

  @param curviness  The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow)

  @param curveName The name of the muscle this curve applies to. This 
    curve name should have the name of the muscle and the
    curve in it 
    (e.g. "bicep_fiberCompressiveForcePennationCurve") 
    sothat if this curve ever causes an exception, a 
    userfriendly error message can be displayed to the
    end user to help them debug their model.

  @param smoothSegmentedFunctionToUpdate
      A SmoothSegmentedFunction object that will be erased and filled with 
      the coefficients that are defined by this curve.

  \b aborts \b
  unless the following conditions are met
  -0 < phi0 < SimTK::Pi/2
  -kiso > 1/(SimTK::Pi/2-phi0)
  -0 <= curviness <= 1


  \image html fig_MuscleAddon_MuscleFunctionFactory_fcphiCurve.png

  <B>Computational Costs</B>
  \verbatim 
  ~4,100 flops
  \endverbatim

  <B>Example:</B>
  @code
  double phi0 = (SimTK::Pi/2)*(8.0/9.0);
  double kiso = 8.389863790885878;
  double c  = 0.0;

  SmoothSegmentedFunction fiberCEPhiCurve = SmoothSegmentedFunction();
  MuscleFunctionFactory::
  createFiberCompressiveForcePennationCurve(phi0,kiso,c,"test",fiberCEPhiCurve);
  fiberCEPhiCurve.printCurveToFile();
  @endcode
  */
  static void createFiberCompressiveForcePennationCurve(
                double phi0, 
                double kiso, 
                double curviness,   
                const std::string& curveName,
                RigidBodyDynamics::Addons::Geometry::
                  SmoothSegmentedFunction&
                  smoothSegmentedFunctionToUpdate);

  /**
  This element will generate a C2 continuous (continuous to the 2nd
  derivative) compressive force profile curve as a function of 
  cos(pennation).

  A muscle model with this element usually places this element in line 
  with the tendon. The main function of this element is to prevent the 
  fiber from achieving a pennation angle of pi/2 radians. This type of 
  element is necessary for a parallelogram pennated muscle models because 
  without it, the muscle model can deform to the point where a pennation 
  angle of pi/2 radians is reached, which causes a singularity in the 
  model.

  
  @param  cosPhi0 The cosine of the pennation angle at which the 
    compressive force element starts to engage. When the 
    cos of the pennation angle is greater than cosPhi0, the 
    compressive element generates no force. When cos of the
    pennation angle is less than cosPhi0, the compressive 
    element generates a compressive force.

  @param kiso This is the maximum stiffness of the compressive element, 
    which occurs when cosPhi is zero. This parameter must be
    negative
    cos
  @param curviness  The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow)


  @param curveName The name of the muscle this curve applies to. This 
    curve name should have the name of the muscle and the
    curve in it 
     (e.g. "bicep_fiberCompressiveForceCosPennationCurve") 
    sothat if this curve ever causes an exception, a 
    userfriendly error message can be displayed to the
    end user to help them debug their model.

  @param smoothSegmentedFunctionToUpdate
    A SmoothSegmentedFunction object that will be erased and filled with 
    the coefficients that are defined by this curve.

  \b aborts \b 
  unless the following conditions are met:
  -0 < cosPhi0
  -kiso > 1/(cosPhi0)
  -0 <= curviness <= 1
  
  \image html fig_MuscleAddon_MuscleFunctionFactory_fcCosPhiCurve.png

  <B>Computational Costs</B>
  \verbatim 
  ~4,100 flops
  \endverbatim

  <B>Example:</B>
  @code
  double cosPhi0 = cos( (80.0/90.0)*SimTK::Pi/2);
  double kiso  = -1.2/(cosPhi0);
  double c   = 0.5;

  SmoothSegmentedFunction fiberCECosPhiCurve = MuscleFunctionFactory::
  createFiberCompressiveForceCosPennationCurve(cosPhi0,kiso,c,"test");
  fiberCEPhiCurve.printCurveToFile();
  @endcode

  

  */
  static void createFiberCompressiveForceCosPennationCurve(
                double cosPhi0, 
                double kiso, 
                double curviness, 
                const std::string& curveName,
                RigidBodyDynamics::Addons::Geometry::
                  SmoothSegmentedFunction&
                  smoothSegmentedFunctionToUpdate);


  /**
  This element will generate a C2 continous (continuous to the second 
  derivative) curve that models a compressive force profile that is a 
  function of fiber length. The main function of
  this element is to prevent the fiber from achieving an unrealistically
  short length. This type of element is necessary for equilibrium-type 
  muscle models because of the editing that is done to the active force
  length curve that endows an equilibrium model fiber with the ability to
  to generate force when a physiological fiber cannot.



  @param l0   The normalized fiber length at which the compressive element 
    starts to engage. When the fiber is shorter than l0, the 
    compressive element is generating a force. When the fiber 
    length is longer than l0, the compressive element generates
    no force.

  @param kiso This is the maximum stiffness of the compressive element, 
    which occurs when the fiber has a length of 0, under a load 
    of 1 maximum isometric unit of force.

  @param curviness  The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow)

   @param curveName The name of the muscle this curve applies to. This 
    curve name should have the name of the muscle and the
    curve in it 
    (e.g. "bicep_fiberCompressiveForceLengthCurve") 
    sothat if this curve ever causes an exception, a 
    userfriendly error message can be displayed to the
    end user to help them debug their model.

  @param smoothSegmentedFunctionToUpdate
      A SmoothSegmentedFunction object that will be erased and filled with 
      the coefficients that are defined by this curve.

  \b aborts \b 
  unless the following conditions are met
  -e0 > 0
  -kiso > 1/(e0)
  -0 <= curviness <= 1


  \image html fig_MuscleAddon_MuscleFunctionFactory_fpeCurve.png


  <B>Computational Costs</B>
  \verbatim 
  ~4,100 flops
  \endverbatim

  <B>Example:</B>
  @code
  double lmax = 0.6;
  double kiso = -8.389863790885878;
  double c  = 0.1;//0.0;

  SmoothSegmentedFunction fiberCECurve = MuscleFunctionFactory::
  createFiberCompressiveForceLengthCurve(lmax,kiso,c,"test");
  fiberCECurve.printCurveToFile();
  @endcode

  */
  static void createFiberCompressiveForceLengthCurve(
                double l0, 
                double kiso, 
                double curviness,  
                const std::string& curveName,
                RigidBodyDynamics::Addons::Geometry::
                  SmoothSegmentedFunction&
                  smoothSegmentedFunctionToUpdate);

   /**
  This function will generate a C2 continuous curve that fits a fiber's 
  tensile force length curve.

  @param eZero The fiber strain at which the fiber begins to develop force.
     Thus an e0 of 0.0 means that the fiber will start to develop
     passive force when it has a normalized length of 1.0. Note
     that e0 can be postive or negative.

  @param eIso The fiber strain at which the fiber develops 1 unit of 
    normalized force (1 maximum isometric force). Note that the 
    '1' is left off. Thus an e0 of 0.6 means that the fiber 
    will develop an 1 normalized force unit when it is strained 
    by 60% of its resting length, or to a normalized length of 
    1.6

  @param kLow   The normalized stiffness (or slope) of the fiber curve 
    close to the location where the force-length curve 
    approaches a normalized force of 0. This is usually 
    chosen to be a small, but non-zero fraction of kIso 
    (kLow = 0.025 kIso is typical).

  @param kIso   The normalized stiffness (or slope) of the fiber curve 
    when the fiber is strained by eIso (or has a length of 
    1+eIso) under a load of 1 maximum isometric unit of force.


  @param curviness  The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow)

   @param curveName The name of the muscle this curve applies to. This 
    curve name should have the name of the muscle and the
    curve in it (e.g. "bicep_fiberForceLengthCurve") 
    sothat if this curve ever causes an exception, a 
    userfriendly error message can be displayed to the
    end user to help them debug their model.

  @param smoothSegmentedFunctionToUpdate
      A SmoothSegmentedFunction object that will be erased and filled with 
      the coefficients that are defined by this curve.

  \b aborts \b 
  unless the following conditions are met
  -eIso > eZero  
  -kIso > 1/(eIso-eZero)
  -0 < kLow < kIso
  -0 <= curviness <= 1

  \image html fig_MuscleAddon_MuscleFunctionFactory_fcLengthCurve.png


  <B>Computational Costs</B>
  \verbatim 
  ~4,100 flops
  \endverbatim

  <B>Example:</B>
  @code
  double eIso  = 0.6;
  double eZero   = 0.0;
  double kIso  = 4.0/(eIso-eZero);
  double kNearZero = 0.025*kIso
  double c   = 0.5;

  SmoothSegmentedFunction fiberFLCurve 
  = MuscleFunctionFactory::
  createFiberForceLengthCurve(eZero, eIso,
      kLow, kIso, c,"test");
  fiberFLCurve.printCurveToFile();
  @endcode

  */
  static void createFiberForceLengthCurve(
                 double eZero, 
                 double eIso,
                 double kLow, 
                 double kIso,
                 double curviness,
                 const std::string& curveName,
                 RigidBodyDynamics::Addons::Geometry::
                  SmoothSegmentedFunction&
                  smoothSegmentedFunctionToUpdate);

  /**
  Will generate a C2 continous (continuous to the second derivative) 
  curve in a MuscleFunctionObject object that fits a tendon's tensile 
  force length curve. 



  @param eIso   The tendon strain at which the tendon develops 1 unit
    of normalized force (1 maximum isometric force). Note that 
    the'1' is left off. Thus an e0 of 0.04 means that the tendon 
    will develop an 1 normalized force unit when it is strained 
    by 4% of its resting length, at a normalized length of 
    1.04

  @param kIso  The normalized stiffness (or slope) of the tendon
    curve when the tendon is strained by e0 
    (or has a length of 1+e0) under a load of 1 maximum
    isometric unit of force.  

  @param fToe  The normalized force at which the tendon smoothly
     transitions from the curved low stiffness region to 
     the linear stiffness region.

  @param curviness  The dimensionless 'curviness' parameter that 
    can vary between 0 (a line) to 1 (a smooth, but 
    sharply bent elbow)

   @param curveName The name of the muscle this curve applies to. This 
    curve name should have the name of the muscle and the
    curve in it (e.g. "bicep_tendonForceLengthCurve") 
    sothat if this curve ever causes an exception, a 
    userfriendly error message can be displayed to the
    end user to help them debug their model.
 
  @param smoothSegmentedFunctionToUpdate
      A SmoothSegmentedFunction object that will be erased and filled with 
      the coefficients that are defined by this curve.

  \b aborts \b 
  unless the following conditions are met:
  -0 < fToe < 1
  -e0 > 0
  -kiso > 1/e0
  -0 <= curviness <= 1


  \image html fig_MuscleAddon_MuscleFunctionFactory_fseCurve.png


  <B>Computational Costs</B>
  \verbatim 
  ~4,100 flops
  \endverbatim

  <B>Example:</B>
  @code
  double e0   = 0.04;
  double kiso = 42.79679348815859;
  double fToe = 1.0/3.0
  double c  = 0.75;
  
  SmoothSegmentedFunction* tendonCurve = MuscleFunctionFactory::
      createTendonForceLengthCurve(
        e0,kiso,fToe,c,"test");
  tendonCurve.printCurveToFile();  
  @endcode

  
  */
  static void createTendonForceLengthCurve(double eIso, 
                double kIso,
                double fToe, 
                double curviness,
                const std::string& curveName,
                RigidBodyDynamics::Addons::Geometry::
                  SmoothSegmentedFunction&
                  smoothSegmentedFunctionToUpdate);


  

};

}
}
}

#endif //MUSCLEFUNCTIONFACTORY_H_