public CalculateMinMax(Calculator calc, IEnumerable<Expression> criteria, bool isMax)
{
InitializeComponent();
_calc = calc;
string operationType = isMax ? "maximum" : "minimum";
Text = string.Format(Text, operationType);
instructions.Text = string.Format(instructions.Text, operationType);
var buttons = from expr in criteria
select new RadioButton
{
Text = expr.ToString(),
Tag = expr,
AutoSize = true
};
_checkables = buttons.ToArray();
if (_checkables.Length == 0)
{
throw new ArgumentException("Must contain at least one expression.", "criteria");
}
_checkables[0].Checked = true;
flowLayoutPanel1.Controls.AddRange(_checkables);
OnManualBoundsRadioCheckedChanged(null, null);
}
/// <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 List<IntersectionInfo> CalculateIntersections(Calculator calc, IList<CalculatedLine> exprs)
{
// Find each possible pair of each line with no repeats
// Asked how to do this in LINQ here: "http://stackoverflow.com/questions/3479980"
var range = Enumerable.Range(0, exprs.Count).ToArray();
var pairs = from i in range
from second in range.Skip(i + 1)
select new
{
First = exprs[i],
Second = exprs[second]
};
// Calculate and refine each intersection in each pair
var intrs = from pair in pairs.AsParallel().AsOrdered()
let unrefined = FindRoughIntersections(pair.First, pair.Second)
select from intersection in unrefined
let refined = RefineIntersection(new Calculator(calc),
(StandardExpression)pair.First.Expression,
(StandardExpression)pair.Second.Expression,
intersection)
select new IntersectionInfo(pair.First.Expression.ToString(),
pair.Second.Expression.ToString(),
refined);
return intrs.SelectMany(p => p).Distinct().ToList();
}
private void OnLoad(object sender, EventArgs e)
{
Application.Idle += OnApplicationIdle;
GL.ClearColor(Color.CornflowerBlue);
GL.Enable(EnableCap.DepthTest);
SetupViewport();
Context.VSync = true;
_window = new Window3D(-50, 50, -50, 50, -50, 50);
Calculator calc = new Calculator();
CompiledExpression expr = ExpressionCompiler.CompileInfix("sin(x)+cos(y)", false);
var mesh = LineCalculator3D.Calculate(calc, expr, _window, 0.5F);
// Vertices
GL.GenBuffers(1, out _bufferInfo.VertexId);
GL.BindBuffer(BufferTarget.ArrayBuffer, _bufferInfo.VertexId);
GL.BufferData(BufferTarget.ArrayBuffer, mesh.VertexArraySize, mesh.Vertices, BufferUsageHint.StaticDraw);
// Indices
GL.GenBuffers(1, out _bufferInfo.IndexId);
GL.BindBuffer(BufferTarget.ElementArrayBuffer, _bufferInfo.IndexId);
GL.BufferData(BufferTarget.ElementArrayBuffer, mesh.IndexArraySize, mesh.Indices, BufferUsageHint.StaticDraw);
// Colors
GL.GenBuffers(1, out _bufferInfo.ColorId);
GL.BindBuffer(BufferTarget.ArrayBuffer, _bufferInfo.ColorId);
GL.BufferData(BufferTarget.ArrayBuffer, mesh.ColorArraySize, mesh.Colors, BufferUsageHint.StaticDraw);
_bufferInfo.IndexCount = mesh.Indices.Length;
}
/// <summary>
/// Initializes a new instance of the Calculator class using data from another <see cref="Calculator"/>
/// instance.
/// </summary>
/// <param name="calcToCopy">The <see cref="Calculator"/> instance to copy data from into this new
/// instance.</param>
public Calculator(Calculator calcToCopy)
{
// Copy the dictionaries into a new instance
_arguments = calcToCopy._arguments.ToDictionary(pair => pair.Key,
pair => pair.Value);
_funcs = calcToCopy._funcs.ToDictionary(pair => pair.Key,
pair => pair.Value);
}
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;
}
public static CompiledDomain CompileDomain(Calculator calc, IList<Constraint> domain)
{
// Signature: bool Domain(CompiledExpression[] leftRightExprs, Calculator calc)
DynamicMethod method = GetDomainDynamicMethod();
ILGenerator il = method.GetILGenerator();
if (domain == null || domain.Count == 0)
{
return EmptyDomain;
}
List<CompiledExpression> expressions = new List<CompiledExpression>();
foreach (Constraint constraint in domain)
{
CompiledExpression left = ExpressionCompiler.CompileInfix(constraint.LeftValue);
CompiledExpression right = ExpressionCompiler.CompileInfix(constraint.RightValue);
Label success = il.DefineLabel();
PushExpressionValue(il, left, expressions, calc);
PushExpressionValue(il, right, expressions, calc);
// Check for the equality to be true
OpCode op = GetOpCodeFromEquality(constraint.Equality);
if (op == default(OpCode))
{
// Not equal to
il.Emit(OpCodes.Ceq);
il.Emit(OpCodes.Brfalse, success);
}
else
{
il.Emit(op, success);
}
// Left side was not true, return false
il.Emit(OpCodes.Ldc_I4_0); // Push 0 (represents false)
il.Emit(OpCodes.Ret); // Return
// Left side was true, test the right side now
il.MarkLabel(success);
}
// Left and right (if there was a right side) were right, return true
il.Emit(OpCodes.Ldc_I4_1); // Push 1 (represents true)
il.Emit(OpCodes.Ret); // Return
return new CompiledDomain(method, expressions.ToArray(), domain);
}
private static PointD FindMostSignificant(Calculator calc, CalculatedLine line, double leftBound, double rightBound, Mode mode)
{
if (line.Expression.Type != ExpressionType.Linear)
{
throw new ArgumentException("The line must be a linear one.");
}
if (line.PointData.Count == 0)
{
throw new ArgumentException("The calculated line must contain at least one line segment.");
}
RoughSignificant roughMax = GetRoughSignificant(line, calc, leftBound, rightBound, mode);
return RefineSignificant(calc, line, roughMax, mode);
}
/// <summary>
/// Initializes a new instance of the Graph class.
/// </summary>
public Graph()
{
_drawHelper = new GraphDrawingHelper(this);
_integralDrawHelper = new IntegralDrawingHelper(this);
_resolution = 1;
_window = Window.Standard;
Calculator = new Calculator();
_zoom = new ZoomMouseAdapter(this);
_zoom.Zoom +=
delegate(object sender, GenericEventArgs<Window> e)
{
Window = e.Data;
RestoreDefaultAdapter();
var handler = WindowChanged;
if (handler != null)
{
handler(this, EventArgs.Empty);
}
};
_xRange = new XRangeMouseAdapter(this);
_xRange.XRangeCreated +=
delegate(object sender, XRangeCreatedEventArgs e)
{
RestoreDefaultAdapter();
var handler = XRangeCreated;
if (handler != null)
{
handler(this, e);
}
};
_dragging = new DraggingMouseAdapter(this);
_current = _dragging;
// Prevents flickering
DoubleBuffered = true;
ResizeRedraw = true;
}
public static double CalculateDerivative(Calculator calc, ParametricExpression expr, double t, out PointD result)
{
calc.GraphingArgumentValue = t;
double x1 = calc.Evaluate(expr.XExpression);
double y1 = calc.Evaluate(expr.YExpression);
calc.GraphingArgumentValue = t + DeltaX;
double x2 = calc.Evaluate(expr.XExpression);
double y2 = calc.Evaluate(expr.YExpression);
double fPrime1 = (x2 - x1) / DeltaX;
double fPrime2 = (y2 - y1) / DeltaX;
result = new PointD(x1, y1);
return fPrime2 / fPrime1;
}
public SelectValue(Calculator calc, IEnumerable<Expression> criteria)
{
InitializeComponent();
_calc = calc;
foreach (Expression expr in criteria)
{
listboxLines.Items.Add(expr);
_exprs.Add(expr);
}
if (listboxLines.Items.Count == 0)
{
throw new Exception();
}
listboxLines.SelectedIndex = 0;
}
private static PointD[] CalculateLine(Calculator calc, CalculatedLine line, double end, ref double pos)
{
if (pos > end)
{
throw new ArgumentException("The current position is greater than the end.");
}
int i = 0;
var filled = new PointD[(int)Math.Round(Math.Abs(end - pos) / line.Increment)];
while (end - pos > 1E-10 || pos < end)
{
calc.GraphingArgumentValue = pos;
filled[i++] = new PointD(pos * line.XScale,
calc.Evaluate(((StandardExpression)line.Expression).Expression) * line.YScale);
pos += line.Increment;
}
return filled;
}
public CalculateIntegral(Calculator calc, IEnumerable<StandardExpression> exprs)
{
InitializeComponent();
_calc = calc;
_exprs = new List<StandardExpression>();
foreach (var expr in exprs)
{
listboxDefiniteIntegralList.Items.Add(expr);
_exprs.Add(expr);
}
OnRadioButtonCheckedChanged(null, EventArgs.Empty);
if (listboxDefiniteIntegralList.Items.Count > 0)
{
listboxDefiniteIntegralList.SelectedIndex = 0;
textboxLeftBound.Select();
}
}
/// <summary>
/// Finds every point on the specified line where that line crosses the X axis.
/// </summary>
/// <param name="calc">The calculator used to evaluate the expression.</param>
/// <param name="line">The line to test for zeros.</param>
/// <returns>
/// A list of points where the specified line crosses the X axis. If the line does not
/// cross the X axis at any point, the list will be empty.
/// </returns>
/// <remarks><para>
/// The algorithm used to find the zeros of a line is similar to the binary search
/// algorithm.
/// </para><para>
/// First, each point on the line is iterated through. In each iteration, it checks if the
/// sign of the Y values of the current point and the last point on the line are different.
/// For example, if we are iterating through the line "5x + 5," once we iterate through the
/// point (-1.5, -2.5) and (-0.5, 2.5), we find that the Y values have changed from negative
/// to positive. Those two points are then stored for later use. We repeat this process until
/// we reach the end of the line.
/// </para><para>
/// After we store each place where the Y values change signs, the binary search begins.
/// In a single iteration, we first determine if the left point of the pair (the minimum)
/// begins in the negative or positive side of the X axis. If it begins in the negative, it
/// is said to be moving "upward." Otherwise, it is moving "downward." This is important
/// because it determines what values are set to the high and low values for the binary
/// search. One of two things then happen:
/// </para><para>
/// In the case of the line going upward, if the sign of the middle value is negative, then
/// the low value becomes the middle value for the next iteration. Otherwise, the high value
/// becomes the middle value.
/// </para><para>
/// In the case of the line going downward, if the sign of the middle value is positive, then
/// the low value becomes the middle value for the next iteration. Otherwise, the high value
/// becomes the middle value.
/// </para><para>
/// This continues until the middle values for two consecutive iterations are the same value.
/// Once this happens, the limits of the precision and accuracy of the datatype we are using
/// (64-bit floating point in this specific implementation's case) has been reached, and the
/// search stops. The final middle value is the X value of the zero.
/// </para></remarks>
public static List<PointD> FindZeros(Calculator calc, CalculatedLine line)
{
if (line.Expression.Type != ExpressionType.Linear)
{
throw new ArgumentException("The expression type must be Linear.");
}
// Each PointF array represents the two points where the
// sign changes from positive to negative or vice versa
var signChanges = from roughZero in line.PointData.SelectMany(FindRoughZero)
select new
{
LowerBound = roughZero[0].X / line.XScale,
UpperBound = roughZero[1].X / line.XScale,
InitialSign = roughZero[0].Y < 0 ? Sign.Negative : Sign.Positive
};
// Find the corresponding zero for each sign change
var zeros = from change in signChanges
select RefineZero(calc, (StandardExpression)line.Expression, change.LowerBound, change.UpperBound, change.InitialSign);
return zeros.ToList();
}
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);
}
public static PointD FindMinimum(Calculator calc, CalculatedLine line, double leftBound, double rightBound)
{
return FindMostSignificant(calc, line, leftBound, rightBound, Mode.Minimum);
}
private static PointD RefineSignificant(Calculator calc, CalculatedLine line, RoughSignificant roughSig, Mode mode)
{
double lo = roughSig.Left.X / line.XScale;
double hi = roughSig.Right.X / line.XScale;
double mid = (lo + hi) / 2;
double lastMid = double.NaN;
var stdExpr = (StandardExpression)line.Expression;
Func<double, int> derivComparer = mode == Mode.Maximum ? _maxDerivComparer : _minDerivComparer;
double y;
while (lastMid != mid)
{
double deriv = DerivativeCalculator.CalculateDerivative(calc, stdExpr, mid, out y);
int result = derivComparer(deriv);
if (result == -1)
{
lo = mid;
}
else if (result == 1)
{
hi = mid;
}
else
{
// Unlikely, but possible
break;
}
lastMid = mid;
mid = (lo + hi) / 2;
}
mid = Math.Round(mid, DerivativeCalculator.DeltaXPrecision);
calc.GraphingArgumentValue = mid;
y = calc.Evaluate(stdExpr.Expression);
return new PointD(mid, y);
}
private static RoughSignificant GetRoughSignificant(CalculatedLine line, Calculator calc, double leftBound, double rightBound, Mode mode)
{
IList<IList<PointD>> segments = line.PointData.Count > 1 ? GetCompleteLine(calc, line) : line.PointData;
double scaledLeftBound = leftBound * line.XScale;
double scaledRightBound = rightBound * line.XScale;
Func<double, double, bool> comparer = mode == Mode.Maximum ? _maxValComparer : _minValComparer;
var significant = new PointD(0, mode == Mode.Maximum ? double.MinValue : double.MaxValue);
int signifSegment = -1, signifPoint = -1;
for (int i = 0; i < segments.Count; i++)
{
var segment = segments[i];
for (int j = 0; j < segment.Count; j++)
{
var point = segment[j];
if (comparer(significant.Y, point.Y) && point.X >= scaledLeftBound && point.X <= scaledRightBound)
{
significant = point;
signifSegment = i;
signifPoint = j;
}
}
}
if (signifSegment == -1 || signifPoint == -1)
{
throw new Exception("No significant value could be found.");
}
// Get the points to the left and right of the rough maximum
PointD left;
PointD right;
GetSurroundingPoints(segments, signifSegment, signifPoint, out left, out right);
return new RoughSignificant(left, right);
}
/// <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);
}
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();
}
private static double CalculateAreaChunk(Calculator calc, Func<Calculator, double> distanceMethod, double start, double rightBound, int iterCount)
{
iterCount++;
double totalArea = 0;
double lastX = start;
calc.GraphingArgumentValue = start;
// The left side of the trapezoid
double a = distanceMethod(calc);
bool calcEnd = false;
for (int i = 1; i < iterCount; i++)
{
double x = lastX + Increment;
if (x > rightBound)
{
x = rightBound;
calcEnd = true;
}
// Height of a sideways trapezoid
calc.GraphingArgumentValue = x;
double b = distanceMethod(calc);
// Area of trapezoid = (a + b) / 2 * h
// In this case, the trapezoid is sideways, so the height is the
// increment, or the space between the previous and current iteration
totalArea += (a + b) / 2 * (x - lastX);
lastX = x;
a = b;
if (calcEnd)
{
break;
}
}
return totalArea;
}
private static double CalculateIntegral(Calculator calc, Func<Calculator, double> distanceMethod, double leftBound, double rightBound)
{
// Protip: the Wolfram Alpha way of verifying the results from this is:
// "integral of (<<top>> - <<bottom>>)dx between <<start>> and <<stop>>"
int numCores = Environment.ProcessorCount;
int iterCount = (int)Math.Ceiling((rightBound - leftBound) / Increment);
int itersPerCore = (int)Math.Floor((double)iterCount / numCores);
// The number of iterations that the last thread should do (to accomodate for rounding errors)
int lastCoreIters = itersPerCore + (iterCount % numCores);
// Assemble the worker threads
Task<double>[] tasks = new Task<double>[numCores];
int core = 0;
bool lastTask = false;
while (!lastTask)
{
lastTask = core + 1 >= numCores;
double start = leftBound + ((core * itersPerCore) * Increment);
int numIters = (lastTask ? lastCoreIters : itersPerCore);
tasks[core++] = new Task<double>(() => CalculateAreaChunk(new Calculator(calc), distanceMethod, start, rightBound, numIters));
}
foreach (Task<double> t in tasks)
{
t.Start();
}
Task.WaitAll(tasks);
double totalArea = tasks.Sum(t => t.Result);
// Find the number of decimal places the increment goes to
int decPlace = 0;
double slicedIncrement = Increment;
// Move the decimal point of the increment to the right on each iteration. We keep
// moving the decimal over until the first significant digit of the increment is found
while ((int)(slicedIncrement *= 10) == 0)
{
decPlace++;
}
// Assume the area is only accurate to the number of decimal places that the increment has
return Math.Round(totalArea, decPlace + 1);
}
public bool Evaluate(Calculator calc)
{
return _compiledDomain(calc);
}
/// <summary>
/// Evalutes the compiled expression with the specified arguments.
/// </summary>
/// <returns></returns>
public double Evaluate(double[] arguments, Calculator calc)
{
return _compiled(arguments, calc);
}
private static void PushExpressionValue(ILGenerator il, CompiledExpression left, List<CompiledExpression> expressions, Calculator calc)
{
if (left.Arguments.Count > 0 || left.GraphingArgumentPresent)
{
// Push the Calculator
il.Emit(OpCodes.Ldarg_1);
// Evaluate and push the left side of the equality
il.Emit(OpCodes.Ldarg_0); // Push the expression array
int index;
if ((index = expressions.IndexOf(left)) != -1)
{
il.Emit(OpCodes.Ldelem, index);
}
else
{
il.Emit(OpCodes.Ldc_I4, expressions.Count);
il.Emit(OpCodes.Ldelem, typeof(CompiledExpression)); // Push the left expression
expressions.Add(left);
}
il.Emit(OpCodes.Call, _evaluateInfo); // Call Calculator.Evaluate(), pushing the result
}
else
{
// Push the static result of the left side's evaluation
il.Emit(OpCodes.Ldc_R8, calc.Evaluate(left));
}
}
/// <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>
/// Evaluates the expression represented by this function using the specified arguments.
/// </summary>
/// <param name="localArgs">The arguments used to evaluate the expression. The order of the values in the
/// array should be the same as those in <see cref="ExplicitArguments"/>.</param>
/// <param name="calc">The calculator used to evaluate the function.</param>
/// <returns>The result of the evaluation of the expression this function represents.</returns>
/// <exception cref="ArgumentException">Thrown when the number of values in <paramref name="localArgs"/>
/// does not match the number of values in <see cref="ExplicitArguments"/>.</exception>
public double Evaluate(double[] localArgs, Calculator calc)
{
if (localArgs.Length != ExplicitArguments.Count)
{
throw new ArgumentException("The size of the arguments must match the size of ExplicitArguments.");
}
double[] args = new double[Expression.ArgumentCount];
// Set all the local arguments
for (int i = 0; i < localArgs.Length; i++)
{
int argIndex = _explicitArgIndices[i];
if (argIndex == -1)
{
// The argument is not used in the expression
continue;
}
args[argIndex] = localArgs[i];
}
return Expression.Evaluate(args, calc);
}
public static double CalculateDerivative(Calculator calc, StandardExpression expr, double x)
{
double y;
return CalculateDerivative(calc, expr, x, out y);
}
private static IList<IList<PointD>> GetCompleteLine(Calculator calc, CalculatedLine line)
{
var regions = new List<IList<PointD>>();
double xScale = line.XScale;
double yScale = line.YScale;
int segmentIndex = 1;
int projSegments = line.PointData.Count - 1;
double pos = line.Window.MinimumX;
if (Math.Abs(line.PointData[0][0].X / xScale - pos) > 1E-10)
{
// There is a void region between the left side of the window and the first segment
segmentIndex = 0;
projSegments++;
}
for (int i = 0; i < projSegments; i++)
{
PointD[] filled = CalculateLine(calc,
line,
line.PointData[segmentIndex][0].X / xScale,
ref pos);
regions.Add(filled);
regions.Add(line.PointData[segmentIndex]);
pos = line.PointData[segmentIndex++].Last().X / xScale + line.Increment;
}
IList<PointD> lastSegment = line.PointData.Last();
if (Math.Abs(line.Window.MaximumX - lastSegment.Last().X / xScale) > 1E-10)
{
// There is a void region between the last segment and the right side of the window
regions.Add(CalculateLine(calc, line, line.Window.MaximumX, ref pos));
}
return regions;
}
public static ConstructedMatrix Calculate(Calculator calc, CompiledExpression expr, Window3D window, float step)
{
float lowZ = float.MaxValue, highZ = float.MinValue;
List<Vector3> results = new List<Vector3>();
List<int> startPoints = new List<int>();
int i = 0;
for (float x = window.MinimumX; x < window.MaximumX; x += step)
{
startPoints.Add(i);
calc.SetArgument("x", x);
bool outsideGraph = true;
Vector3? last = null;
for (float y = window.MinimumY; y < window.MaximumY; y += step)
{
calc.SetArgument("y", y);
float z = (float)calc.Evaluate(expr);
Vector3 result = new Vector3(x, y, z);
results.Add(result);
bool includeResult = false, includeLast = false;
if (z > window.MaximumZ || z < window.MinimumZ)
{
// Outside the window
if (!outsideGraph)
{
// First point outside the window
includeResult = true;
outsideGraph = true;
}
}
else
{
// Inside the window
if (outsideGraph)
{
// First point inside the window, include the last vertex as well
includeLast = true;
}
includeResult = true;
outsideGraph = false;
}
if (includeResult)
{
if (z < lowZ)
{
lowZ = includeLast && last.HasValue ? Math.Min(z, last.Value.Z) : z;
}
if (z > highZ)
{
highZ = includeLast && last.HasValue ? Math.Max(z, last.Value.Z) : z;
}
}
last = result;
i++;
}
}
List<int> indices = new List<int>();
for (int x = 0; x < startPoints.Count - 1; x++)
{
int currentX = startPoints[x];
int nextX = startPoints[x + 1];
for (int y = 0; y < startPoints[x + 1] - startPoints[x] - 1; y++)
{
indices.AddRange(new[] { currentX + y, nextX + y, nextX + y + 1, currentX + y, nextX + y + 1, currentX + y + 1 });
}
}
int[] colors = new int[results.Count];
float absLowZ = Math.Abs(lowZ);
float mulFactor = 255F / (absLowZ + Math.Abs(highZ));
for (int j = 0; j < results.Count; j++)
{
float z = results[j].Z;
int normalized = Math.Max(0, Math.Min(255, (int)Math.Round((z + absLowZ) * mulFactor)));
colors[j] = Color.FromArgb(normalized, normalized, normalized).ToArgb();
}
return new ConstructedMatrix(results.ToArray(), indices.ToArray(), colors.ToArray());
}