/// <summary>
/// Initializes a new instance of the Function class.
/// </summary>
/// <param name="identifier">The name of the function. The identifier is the following part of the
/// function: "_f_(x[,...])."</param>
/// <param name="expression">The expression this function should represent.</param>
/// <param name="arguments">The explicit arguments that should be specified whenever this function
/// is called. The order of the items in this parameter is the order in which the arguments should
/// be specified when calling <see cref="Evaluate"/>.</param>
public Function(string identifier, string expression, IList<string> arguments)
{
Id = _nextId++;
Identifier = identifier;
// Only optimize the graphing argument if there isn't an explicit argument
// with the same identifier
_expr = ExpressionCompiler.CompileInfix(expression,
!arguments.Any(arg => arg == Calculator.GraphingArgument));
if (arguments.Count == 0)
{
ExplicitArguments = new ReadOnlyCollection<string>(new List<string>());
return;
}
// The local indicies of the explicit arguments in the expression's arguments
_explicitArgIndices = new int[arguments.Count];
for (int i = 0; i < _explicitArgIndices.Length; i++)
{
bool found = false;
foreach (Argument arg in Expression.Arguments.Where(arg => arg.Identifier == arguments[i]))
{
_explicitArgIndices[i] = arg.Index;
found = true;
break;
}
if (!found)
{
// The argument is not used in the expression
_explicitArgIndices[i] = -1;
}
}
ExplicitArguments = arguments.ToList().AsReadOnly();
}
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>
/// Evaluates the specified expression using this instance's arguments and functions.
/// </summary>
/// <param name="expr">The expression to evaluate.</param>
/// <returns>A value that is the result of the evaluation of the specified expression.</returns>
public double Evaluate(CompiledExpression expr)
{
var args = new double[expr.ArgumentCount];
for (int i = 0; i < args.Length; i++)
{
Argument arg = expr.Arguments[i];
args[i] = GetArgument(arg.Identifier);
}
return expr.Evaluate(args, this);
}
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());
}
