/// <summary>
/// Calculates the area between, in the case of this overload, two curves.
/// </summary>
/// <param name="calc">The <see cref="Calculator"/> to calculate the Y-values with.</param>
/// <param name="top">The curve that defines the top of the integral.</param>
/// <param name="bottom">The curve that defines the bottom of the integral.</param>
/// <param name="leftBound">The left bound of the integral.</param>
/// <param name="rightBound">The right bound of the integral.</param>
/// <returns>
/// The area between the curves <paramref name="top"/> and <paramref name="bottom"/>.
/// </returns>
public static double CalculateIntegral(Calculator calc, StandardExpression top, StandardExpression bottom, double leftBound, double rightBound)
{
Func<Calculator, double> distanceMethod;
// Optimize for anything that might be a constant here
if (top.Expression.IsConstant && bottom.Expression.IsConstant)
{
// The integral between two constants is just a rectangle
double topConstant = calc.Evaluate(top.Expression);
double bottomConstant = calc.Evaluate(bottom.Expression);
// Area = Width * Height
return (rightBound - leftBound) * (topConstant - bottomConstant);
}
if (top.Expression.IsConstant)
{
double topConstant = calc.Evaluate(top.Expression);
distanceMethod = c => topConstant - c.Evaluate(bottom.Expression);
}
else if (bottom.Expression.IsConstant)
{
double bottomConstant = calc.Evaluate(bottom.Expression);
distanceMethod = c => c.Evaluate(top.Expression) - bottomConstant;
}
else
{
distanceMethod = c => c.Evaluate(top.Expression) - c.Evaluate(bottom.Expression);
}
return CalculateIntegral(calc, distanceMethod, leftBound, rightBound);
}
public static double CalculateDerivative(Calculator calc, StandardExpression expr, double x, out double y)
{
calc.GraphingArgumentValue = x;
double y1 = calc.Evaluate(expr.Expression);
calc.GraphingArgumentValue = x + DeltaX;
double y2 = calc.Evaluate(expr.Expression);
y = y1;
// lim h -> 0 (f(x + h) - f(x)) / h = slope of the derivative
return (y2 - y1) / DeltaX;
}
private static PointD RefineIntersection(Calculator calc, StandardExpression expr1, StandardExpression expr2, IList<PointD> intersectionData)
{
// Whether or not expr1 starts out above expr2
bool oneOnTop = intersectionData[0].Y > intersectionData[2].Y;
double lo = intersectionData[0].X;
double hi = intersectionData[1].X;
double mid = (lo + hi) / 2;
double lastMid;
do
{
calc.GraphingArgumentValue = mid;
double y1 = calc.Evaluate(expr1.Expression);
double y2 = calc.Evaluate(expr2.Expression);
// Unlikely, but possible
if (y1 == y2)
{
break;
}
// Check to see if the current "on top" status (whether expr1
// is above expr2) is consistent with the initial "on top" status.
if ((y1 > y2) == oneOnTop)
{
lo = mid;
}
else
{
hi = mid;
}
lastMid = mid;
mid = (lo + hi) / 2;
}
while (mid != lastMid);
// Recalculate the Y value against both expressions and return the average
calc.GraphingArgumentValue = mid;
return new PointD(mid, (calc.Evaluate(expr1.Expression) + calc.Evaluate(expr2.Expression)) / 2).CorrectForGdiLimit();
}
public ExpressionInfo(UncompiledExpression expr, CompiledDomain domain = null)
{
if (expr is UncompiledStandardExpression)
{
var stdExpr = expr as UncompiledStandardExpression;
Expression = new StandardExpression(expr.Slot, expr.Type, stdExpr.Expression, domain);
}
else if (expr is UncompiledParametricExpression)
{
var paraExpr = expr as UncompiledParametricExpression;
Expression = new ParametricExpression(expr.Slot, paraExpr.XExpression, paraExpr.YExpression, domain);
}
else
{
throw new ArgumentException("expr");
}
OriginalUncompiled = expr;
Enabled = true;
}
private static PointD RefineZero(Calculator calc, StandardExpression expr, double lowerBound, double upperBound, Sign initialSign)
{
double lo = lowerBound;
double hi = upperBound;
double mid = (lo + hi) / 2;
double lastMid;
double y;
int i = 0;
do
{
calc.GraphingArgumentValue = mid;
y = calc.Evaluate(expr.Expression);
Sign currentSign = y < 0 ? Sign.Negative : Sign.Positive;
if (currentSign == initialSign)
{
lo = mid;
}
else
{
hi = mid;
}
lastMid = mid;
mid = (lo + hi) / 2;
// The "i < 100" below is only necessary when running in release mode, without a debugger attached.
// Otherwise, it goes into an infinite loop, even though mid and lastMid actually do equal eachother.
// I have no idea why that is (though its probably a race condition of some kind, despite the fact
// that I'm not doing any multithreading anywhere around here).
i++;
}
while (mid != lastMid && i < 100);
return new PointD(mid, y);
}
private PointF EvaluateExpression(StandardExpression expr, double xValue, bool scale = true, bool round = false)
{
Parent.Calculator.GraphingArgumentValue = xValue;
double y = Parent.Calculator.Evaluate(expr.Expression);
var point = new PointD(xValue, y);
return (scale ? point.ScaleUp(XScale, YScale, round) : point).AsSingle();
}
private IEnumerable<PointF> EnsureLineSpan(StandardExpression expr, IEnumerable<PointF> existingLine)
{
PointF left = EvaluateExpression(expr, LeftBound);
PointF right = EvaluateExpression(expr, RightBound);
return
new[] { left }.
Concat(existingLine).
Concat(new[] { right }).
ToArray();
}
public static double CalculateDerivative(Calculator calc, StandardExpression expr, double x)
{
double y;
return CalculateDerivative(calc, expr, x, out y);
}
/// <summary>
/// Calculates the area between, in the case of this overload, a curve and a horizontal line.
/// </summary>
/// <param name="calc">The <see cref="Calculator"/> to calculate the Y-values with.</param>
/// <param name="top">The curve that defines the top of the integral.</param>
/// <param name="bottomHorizontalLine">The horizontal line that defines the bottom of the
/// integral.</param>
/// <param name="leftBound">The left bound of the integral.</param>
/// <param name="rightBound">The right bound of the integral.</param>
/// <returns>
/// The area between the curve <paramref name="top"/> and the horizontal line
/// <paramref name="bottomHorizontalLine"/>.
/// </returns>
public static double CalculateIntegral(Calculator calc, StandardExpression top, double bottomHorizontalLine, double leftBound, double rightBound)
{
return CalculateIntegral(calc,
c => c.Evaluate(top.Expression) - bottomHorizontalLine,
leftBound,
rightBound);
}
/// <summary>
/// Calculates the area between, in the case of this overload, a horizontal line and a curve.
/// </summary>
/// <param name="calc">The <see cref="Calculator"/> to calculate the Y-values with.</param>
/// <param name="topHorizontalLine">The horizontal line that defines the top of the
/// integral.</param>
/// <param name="bottom">The curve that defines the bottom of the integral</param>
/// <param name="leftBound">The left bound of the integral.</param>
/// <param name="rightBound">The right bound of the integral.</param>
/// <returns>
/// The area between the horizontal line <paramref name="topHorizontalLine"/> and the curve
/// <paramref name="bottom"/>.
/// </returns>
public static double CalculateIntegral(Calculator calc, double topHorizontalLine, StandardExpression bottom, double leftBound, double rightBound)
{
return CalculateIntegral(calc,
c => topHorizontalLine - c.Evaluate(bottom.Expression),
leftBound,
rightBound);
}
/// <summary>
/// Determines whether the specified <see cref="StandardExpression"/> is equal to the
/// current <see cref="StandardExpression"/>.
/// </summary>
/// <param name="other">The <see cref="StandardExpression"/> to compare with the current
/// <see cref="StandardExpression"/>.</param>
/// <returns>
/// true if the specified <see cref="StandardExpression"/> is equal to the current
/// <see cref="StandardExpression"/>; otherwise, false.
/// </returns>
public bool Equals(StandardExpression other)
{
if (ReferenceEquals(null, other)) return false;
if (ReferenceEquals(this, other)) return true;
return Equals(other.Expression.OriginalExpression, Expression.OriginalExpression);
}
