// Draw the tangent and normal to the equation at diffAt
// Method takes a Graphics object to draw to the panel and the target of differention set by the user
private float DrawTangentAndNormalLines(Graphics g, float diffAt)
{
// Create a new object to allow the estimation of the derivative of the target equation TargetFunction at diffAt
var diff = new CentralDifferenceMethod(TargetFunction, diffAt);
// The gradient of the function at diffAt
double grad;
try
{
// Evaluate the target function at diffAt
float fa = TargetFunction.EvaluateF(diffAt.ToString(CultureInfo.InvariantCulture));
// Obtain the value of the first derivative of the functiona at diffAt
// This will become the gradient of the tangent line
grad = diff.DeriveFirst();
PointF originPoint = ToCartesianPoint(0, 0);
PointF widthPoint = ToCartesianPoint(Width, 0);
// If the gradient is defined
if (!Double.IsNaN(grad))
{
// Convert the gradient to a float to allow for drawing and get the normal gradient
float tangentGrad = Convert.ToSingle(grad);
float normalGrad = Convert.ToSingle(-1 / grad);
// Set the NormalGrad property to the gradient of the normal line, rounding to avoid innacuracies
NormalGrad = (float) Math.Round(normalGrad, 3);
// If the gradient is defined and can be drawn
if (Math.Abs(grad) < 1250)
{
// Draw the tangent to the function
DrawLine(g, Color.Red, 3F, originPoint.X, fa + tangentGrad * (originPoint.X - diffAt), widthPoint.X, fa + tangentGrad * (widthPoint.X - diffAt), false);
// If the normal is defined and can be drawn
if (Math.Abs(grad) > 0.010)
{
// Draw the normal with a dashed line
DrawLine(g, Color.Gray, 3F, originPoint.X, fa + normalGrad * (originPoint.X - diffAt), widthPoint.X, fa + normalGrad * (widthPoint.X - diffAt), true);
}
}
// Get the equations of the tangent and normal and set the corresponding fields to their values
Tangent = "y - " + Math.Round(fa, 3) + " = " + Math.Round(grad, 3) + " (x - " +
Math.Round(diffAt, 3) + ")";
Normal = "y - " + Math.Round(fa, 3) + " = " + NormalGrad + " (x - " + Math.Round(diffAt, 3) + ")";
}
else
{
// If the gradient is not defined return NaN
return Single.NaN;
}
}
catch (Exception)
{
// If any errors occured return NaN
return Single.NaN;
}
// Return the gradient of the function
return Convert.ToSingle(grad);
}
// Method tells the grapher to find any local extrema within the graph view
// Method returns a list of Extrema objects, each representing a local minimum or maximum
// A function has a minimum or maxmimum when the first derivative is zero
// If the second derivative at a minimum or maximum is negative, then the function is at a
// maximum. Otherwise the function is at a minimum
// Currently this method can produce repeated and innaccurate results due to innacuracies in the
// calculation of the derivatives
public List <Extrema> FindExtrema()
{
// Get the values of bounds of the current graph view
// These values will become the bounds of the searching radius
PointF min = ToCartesianPoint(0, 5);
PointF max = ToCartesianPoint(Width, 5);
// Set the current target and visible target to the minimum visible point on the graph
float currentTarget = min.X;
// The target variable defines the point visible to the user during the calculation
target = min.X;
// Set the finding field to true
finding = true;
// Obtain an object to estimate the derivatives of the target function
var m = new CentralDifferenceMethod(TargetFunction, currentTarget);
// Make a list object to hold the extrema that have been found
var ex = new List <Extrema>();
try
{
// While the target is still in the searching bounds
while (currentTarget < max.X)
{
// Estimate the first derivative
double res = m.DeriveFirst();
// If the first derivative is within a tolerance to zero
if (Math.Abs(Math.Round(res, 3)) < 0.0025)
{
// Calculate the second derivative
double second = m.DeriveSecond();
// If the function is at a maximum
if (second < 0)
{
// Add a new Extrema to the list with the current target point
ex = AddExtrema(ex, currentTarget, "Local Maximum");
}
else
{
// The function is at a minimum
// Add a new Extrema to the list with the current target point
ex = AddExtrema(ex, currentTarget, "Local Minimum");
}
}
// Increment the target points
currentTarget += 0.001F;
target += 0.08F;
// Set the target point of the differentiation object to get ready for thex next calculation
m.TargetPoint = currentTarget;
// If the grapher is still searching, repaint the graph to update the user on progress
if (target < max.X)
{
Invalidate();
Update();
}
}
}
catch (Exception)
{
// Prompt the user if any errors occur during the calculations
MessageBox.Show("Unable to find extrema", "Eror", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(null);
}
// Prompt the user that the grapher has finished searching
MessageBox.Show("Finished finding extrema", "Success", MessageBoxButtons.OK, MessageBoxIcon.Information);
// Reset variables and return the list of extrema found
finding = false;
target = max.X;
Invalidate();
return(ex);
}
// Method tells the grapher to find any local extrema within the graph view
// Method returns a list of Extrema objects, each representing a local minimum or maximum
// A function has a minimum or maxmimum when the first derivative is zero
// If the second derivative at a minimum or maximum is negative, then the function is at a
// maximum. Otherwise the function is at a minimum
// Currently this method can produce repeated and innaccurate results due to innacuracies in the
// calculation of the derivatives
public List<Extrema> FindExtrema()
{
// Get the values of bounds of the current graph view
// These values will become the bounds of the searching radius
PointF min = ToCartesianPoint(0, 5);
PointF max = ToCartesianPoint(Width, 5);
// Set the current target and visible target to the minimum visible point on the graph
float currentTarget = min.X;
// The target variable defines the point visible to the user during the calculation
target = min.X;
// Set the finding field to true
finding = true;
// Obtain an object to estimate the derivatives of the target function
var m = new CentralDifferenceMethod(TargetFunction, currentTarget);
// Make a list object to hold the extrema that have been found
var ex = new List<Extrema>();
try
{
// While the target is still in the searching bounds
while (currentTarget < max.X)
{
// Estimate the first derivative
double res = m.DeriveFirst();
// If the first derivative is within a tolerance to zero
if (Math.Abs(Math.Round(res, 3)) < 0.0025)
{
// Calculate the second derivative
double second = m.DeriveSecond();
// If the function is at a maximum
if (second < 0)
{
// Add a new Extrema to the list with the current target point
ex = AddExtrema(ex, currentTarget, "Local Maximum");
}
else
{
// The function is at a minimum
// Add a new Extrema to the list with the current target point
ex = AddExtrema(ex, currentTarget, "Local Minimum");
}
}
// Increment the target points
currentTarget += 0.001F;
target += 0.08F;
// Set the target point of the differentiation object to get ready for thex next calculation
m.TargetPoint = currentTarget;
// If the grapher is still searching, repaint the graph to update the user on progress
if (target < max.X)
{
Invalidate();
Update();
}
}
}
catch (Exception)
{
// Prompt the user if any errors occur during the calculations
MessageBox.Show("Unable to find extrema", "Eror", MessageBoxButtons.OK, MessageBoxIcon.Error);
return null;
}
// Prompt the user that the grapher has finished searching
MessageBox.Show("Finished finding extrema", "Success", MessageBoxButtons.OK, MessageBoxIcon.Information);
// Reset variables and return the list of extrema found
finding = false;
target = max.X;
Invalidate();
return ex;
}
// Draw the tangent and normal to the equation at diffAt
// Method takes a Graphics object to draw to the panel and the target of differention set by the user
private float DrawTangentAndNormalLines(Graphics g, float diffAt)
{
// Create a new object to allow the estimation of the derivative of the target equation TargetFunction at diffAt
var diff = new CentralDifferenceMethod(TargetFunction, diffAt);
// The gradient of the function at diffAt
double grad;
try
{
// Evaluate the target function at diffAt
float fa = TargetFunction.EvaluateF(diffAt.ToString(CultureInfo.InvariantCulture));
// Obtain the value of the first derivative of the functiona at diffAt
// This will become the gradient of the tangent line
grad = diff.DeriveFirst();
PointF originPoint = ToCartesianPoint(0, 0);
PointF widthPoint = ToCartesianPoint(Width, 0);
// If the gradient is defined
if (!Double.IsNaN(grad))
{
// Convert the gradient to a float to allow for drawing and get the normal gradient
float tangentGrad = Convert.ToSingle(grad);
float normalGrad = Convert.ToSingle(-1 / grad);
// Set the NormalGrad property to the gradient of the normal line, rounding to avoid innacuracies
NormalGrad = (float)Math.Round(normalGrad, 3);
// If the gradient is defined and can be drawn
if (Math.Abs(grad) < 1250)
{
// Draw the tangent to the function
DrawLine(g, Color.Red, 3F, originPoint.X, fa + tangentGrad * (originPoint.X - diffAt), widthPoint.X, fa + tangentGrad * (widthPoint.X - diffAt), false);
// If the normal is defined and can be drawn
if (Math.Abs(grad) > 0.010)
{
// Draw the normal with a dashed line
DrawLine(g, Color.Gray, 3F, originPoint.X, fa + normalGrad * (originPoint.X - diffAt), widthPoint.X, fa + normalGrad * (widthPoint.X - diffAt), true);
}
}
// Get the equations of the tangent and normal and set the corresponding fields to their values
Tangent = "y - " + Math.Round(fa, 3) + " = " + Math.Round(grad, 3) + " (x - " +
Math.Round(diffAt, 3) + ")";
Normal = "y - " + Math.Round(fa, 3) + " = " + NormalGrad + " (x - " + Math.Round(diffAt, 3) + ")";
}
else
{
// If the gradient is not defined return NaN
return(Single.NaN);
}
}
catch (Exception)
{
// If any errors occured return NaN
return(Single.NaN);
}
// Return the gradient of the function
return(Convert.ToSingle(grad));
}
