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Higher-order integrals are now supported.

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This commit is contained in:
That_One_Nerd 2024-03-19 12:34:31 -04:00
parent f5107b7238
commit 9b4905233c
6 changed files with 132 additions and 46 deletions
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2
Base/Abstract/IDerivable.cs
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@ -4,5 +4,5 @@ namespace Graphing.Abstract;
public interface IDerivable
{
public Equation Derive();
public Graphable Derive();
}

2
Base/Abstract/IIntegrable.cs
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@ -4,5 +4,5 @@ namespace Graphing.Abstract;
public interface IIntegrable
{
public IntegralEquation Integrate();
public Graphable Integrate();
}

1
Base/Forms/GraphForm.cs
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@ -1,5 +1,4 @@
using Graphing.Abstract;
using Graphing.Graphables;
using Graphing.Parts;
using System;
using System.Collections.Generic;

6
Base/Graphables/Equation.cs
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@ -49,12 +49,12 @@ public class Equation : Graphable, IIntegrable, IDerivable
return lines;
}
public Equation Derive() => new(x =>
public Graphable Derive() => new Equation(x =>
{
const double step = 1e-3;
return (equ(x + step) - equ(x)) / step;
});
public IntegralEquation Integrate() => new(this);
public Graphable Integrate() => new IntegralEquation(this);
public EquationDelegate GetDelegate() => equ;
@ -71,8 +71,6 @@ public class Equation : Graphable, IIntegrable, IDerivable
}
}
// Pretty sure this works. Certainly works pretty well with "hard-to-compute"
// equations.
protected (double dist, double y, int index) NearestCachedPoint(double x)
{
if (cache.Count == 0) return (double.PositiveInfinity, double.NaN, -1);

161
Base/Graphables/IntegralEquation.cs
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@ -3,13 +3,18 @@ using Graphing.Forms;
using Graphing.Parts;
using System;
using System.Collections.Generic;
using System.ComponentModel.Design;
namespace Graphing.Graphables;
public class IntegralEquation : Graphable, IIntegrable, IDerivable
{
protected readonly Equation baseEqu;
protected readonly EquationDelegate baseEquDel;
protected readonly Equation? baseEqu;
protected readonly EquationDelegate? baseEquDel;
protected readonly IntegralEquation? altBaseEqu;
protected readonly bool usingAlt;
public IntegralEquation(Equation baseEquation)
{
@ -22,9 +27,27 @@ public class IntegralEquation : Graphable, IIntegrable, IDerivable
baseEqu = baseEquation;
baseEquDel = baseEquation.GetDelegate();
altBaseEqu = null;
usingAlt = false;
}
public IntegralEquation(IntegralEquation baseEquation)
{
string oldName = baseEquation.Name, newName;
if (oldName.StartsWith("Integral of ")) newName = "Second Integral of " + oldName[12..];
else if (oldName.StartsWith("Second Integral of ")) newName = "Third Integral of " + oldName[19..];
else newName = "Integral of " + oldName;
Name = newName;
baseEqu = null;
baseEquDel = null;
altBaseEqu = baseEquation;
usingAlt = true;
}
public override Graphable DeepCopy() => new IntegralEquation(baseEqu);
public override Graphable DeepCopy() => new IntegralEquation(this);
public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
{
@ -35,45 +58,42 @@ public class IntegralEquation : Graphable, IIntegrable, IDerivable
List<IGraphPart> lines = [];
Int2 originLocation = graph.GraphSpaceToScreenSpace(new Float2(0, 0));
if (originLocation.x < 0)
{
// Origin is off the left side of the screen.
// Get to the left side from the origin.
double previousY = 0;
double start = graph.MinVisibleGraph.x, end = graph.MaxVisibleGraph.x;
for (double x = 0; x <= start; x += epsilon) previousY += baseEquDel(x) * epsilon;
SetInternalStepper(start, epsilon, null);
// Now we can start.
double previousX = start;
double previousX = stepX;
double previousY = stepY;
for (double x = start; x <= end; x += epsilon)
{
double currentX = x, currentY = previousY + baseEquDel(x) * epsilon;
lines.Add(new GraphLine(new Float2(previousX, previousY), new Float2(currentX, currentY)));
previousX = currentX;
previousY = currentY;
MoveInternalStepper(epsilon);
lines.Add(new GraphLine(new Float2(previousX, previousY),
new Float2(stepX, stepY)));
previousX = stepX;
previousY = stepY;
}
}
else if (originLocation.x > graph.ClientRectangle.Width)
{
// Origin is off the right side of the screen.
// Get to the right side of the origin.
double previousY = 0;
double start = graph.MaxVisibleGraph.x, end = graph.MinVisibleGraph.x;
for (double x = 0; x >= start; x -= epsilon) previousY -= baseEquDel(x) * epsilon;
SetInternalStepper(start, epsilon, null);
// Now we can start.
double previousX = start;
double previousX = stepX;
double previousY = stepY;
for (double x = start; x >= end; x -= epsilon)
{
double currentX = x, currentY = previousY - baseEquDel(x) * epsilon;
lines.Add(new GraphLine(new Float2(previousX, previousY), new Float2(currentX, currentY)));
previousX = currentX;
previousY = currentY;
MoveInternalStepper(-epsilon);
lines.Add(new GraphLine(new Float2(previousX, previousY),
new Float2(stepX, stepY)));
previousX = stepX;
previousY = stepY;
}
}
else
@ -83,45 +103,93 @@ public class IntegralEquation : Graphable, IIntegrable, IDerivable
// Start with right.
double start = 0, end = graph.MaxVisibleGraph.x;
double previousX = start;
double previousY = 0;
SetInternalStepper(start, epsilon, null);
double previousX = stepX;
double previousY = stepY;
for (double x = start; x <= end; x += epsilon)
{
double currentX = x, currentY = previousY + baseEquDel(x) * epsilon;
lines.Add(new GraphLine(new Float2(previousX, previousY), new Float2(currentX, currentY)));
previousX = currentX;
previousY = currentY;
MoveInternalStepper(epsilon);
lines.Add(new GraphLine(new Float2(previousX, previousY),
new Float2(stepX, stepY)));
previousX = stepX;
previousY = stepY;
}
// Now do left.
start = 0;
end = graph.MinVisibleGraph.x;
previousX = start;
previousY = 0;
SetInternalStepper(start, epsilon, null);
previousX = stepX;
previousY = stepY;
for (double x = start; x >= end; x -= epsilon)
{
double currentX = x, currentY = previousY - baseEquDel(x) * epsilon;
lines.Add(new GraphLine(new Float2(previousX, previousY), new Float2(currentX, currentY)));
previousX = currentX;
previousY = currentY;
MoveInternalStepper(-epsilon);
lines.Add(new GraphLine(new Float2(previousX, previousY),
new Float2(stepX, stepY)));
previousX = stepX;
previousY = stepY;
}
}
return lines;
}
private double stepX = 0;
private double stepY = 0;
private void SetInternalStepper(double x, double dX, Action<double, double>? stepCallback)
{
stepX = 0;
stepY = 0;
if (usingAlt) altBaseEqu!.SetInternalStepper(0, dX, null);
if (x > 0)
{
while (stepX < x)
{
MoveInternalStepper(dX);
stepCallback?.Invoke(stepX, stepY);
}
}
else if (x < 0)
{
while (x < stepX)
{
MoveInternalStepper(-dX);
stepCallback?.Invoke(stepX, stepY);
}
}
}
private void MoveInternalStepper(double dX)
{
stepX += dX;
if (usingAlt)
{
altBaseEqu!.MoveInternalStepper(dX);
stepY += altBaseEqu!.stepY * dX;
}
else
{
stepY += baseEquDel!(stepX) * dX;
}
}
// Try to avoid using this, as it converts the integral into a
// far less efficient format (uses the `IntegralAtPoint` method).
public Equation AsEquation() => new(IntegralAtPoint)
{
Name = Name,
Color = Color
};
public Equation Derive() => (Equation)baseEqu.DeepCopy();
public IntegralEquation Integrate() => AsEquation().Integrate();
public Graphable Derive()
{
if (usingAlt) return altBaseEqu!.DeepCopy();
else return (Equation)baseEqu!.DeepCopy();
}
public Graphable Integrate() => new IntegralEquation(this);
// Standard integral method.
// Inefficient for successive calls.
@ -138,4 +206,21 @@ public class IntegralEquation : Graphable, IIntegrable, IDerivable
return sum;
}
public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
{
Int2 screenMousePos = graph.GraphSpaceToScreenSpace(graphMousePos);
Int2 screenPos = graph.GraphSpaceToScreenSpace(new Float2(graphMousePos.x,
IntegralAtPoint(graphMousePos.x)));
double allowedDist = factor * graph.DpiFloat * 80 / 192;
Int2 dist = new(screenPos.x - screenMousePos.x,
screenPos.y - screenMousePos.y);
double totalDist = Math.Sqrt(dist.x * dist.x + dist.y * dist.y);
return totalDist <= allowedDist;
}
public override Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos) =>
new(graphMousePos.x, IntegralAtPoint(graphMousePos.x));
}

6
Testing/Program.cs
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@ -17,7 +17,9 @@ internal static class Program
GraphForm graph = new("One Of The Graphing Calculators Of All Time");
Equation equ = new(Math.Sin);
graph.Graph(equ);
SlopeField sf = new(2, (x, y) => Math.Cos(x));
TangentLine tl = new(2, 2, equ);
graph.Graph(equ, sf, tl);
// You can preload graphs in by going Misc > Preload Cache.
// Keep in mind this uses more memory than usual and can take
@ -26,6 +28,8 @@ internal static class Program
// Integrating equations is now much smoother and less intensive.
// Try it out!
// You can click and drag on an equation to select specific points.
Application.Run(graph);
}
}