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Starters on the integral equation. Quite nice so far, I think.

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This commit is contained in:
That_One_Nerd 2024-03-19 10:22:00 -04:00
parent 762a5f5a32
commit 855a90b452
4 changed files with 138 additions and 36 deletions
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33
Base/Forms/GraphForm.cs
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@ -431,38 +431,7 @@ public partial class GraphForm : Form
}
private void EquationComputeIntegral_Click(Equation equation)
{
EquationDelegate equ = equation.GetDelegate();
string oldName = equation.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;
// TODO: anti-derive (maybe)
Graph(new Equation(x => Integrate(equ, 0, x))
{
Name = newName
});
static double Integrate(EquationDelegate e, double lower, double upper)
{
// TODO: a better rendering method could make this much faster.
const double step = 1e-2;
double factor = 1;
if (upper < lower)
{
factor = -1;
(lower, upper) = (upper, lower);
}
double sum = 0;
for (double x = lower; x <= upper; x += step)
{
sum += e(x) * step;
}
return sum * factor;
}
Graph(equation.Integrate());
}
private void MenuMiscCaches_Click(object? sender, EventArgs e)

2
Base/Graphables/Equation.cs
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@ -48,6 +48,8 @@ public class Equation : Graphable
return lines;
}
public IntegralEquation Integrate() => new(this);
public EquationDelegate GetDelegate() => equ;
public override void EraseCache() => cache.Clear();

133
Base/Graphables/IntegralEquation.cs Normal file
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@ -0,0 +1,133 @@
using Graphing.Forms;
using Graphing.Parts;
using System;
using System.Collections.Generic;
namespace Graphing.Graphables;
public class IntegralEquation : Graphable
{
protected readonly Equation baseEqu;
protected readonly EquationDelegate baseEquDel;
public IntegralEquation(Equation 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 = baseEquation;
baseEquDel = baseEquation.GetDelegate();
}
public override Graphable DeepCopy() => new IntegralEquation(baseEqu);
public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
{
const int step = 10;
double epsilon = Math.Abs(graph.ScreenSpaceToGraphSpace(new Int2(0, 0)).x
- graph.ScreenSpaceToGraphSpace(new Int2(step / 2, 0)).x) / 5;
epsilon *= graph.DpiFloat / 192;
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;
// Now we can start.
double previousX = start;
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;
}
}
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;
// Now we can start.
double previousX = start;
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;
}
}
else
{
// Origin is on-screen.
// We need to do two cycles.
// Start with right.
double start = 0, end = graph.MaxVisibleGraph.x;
double previousX = start;
double previousY = 0;
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;
}
// Now do left.
start = 0;
end = graph.MinVisibleGraph.x;
previousX = start;
previousY = 0;
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;
}
}
return lines;
}
public Equation AsEquation() => new(GetIntegralAtPoint);
// Standard integral method.
// Inefficient for successive calls.
public double GetIntegralAtPoint(double x)
{
EquationDelegate equ = baseEqu.GetDelegate();
double start = Math.Min(0, x), end = Math.Max(0, x);
const double step = 1e-3;
double sum = 0;
for (double t = start; t <= end; t += step) sum += equ(t) * step;
if (x < 0) sum = -sum;
return sum;
}
}

6
Testing/Program.cs
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@ -16,10 +16,8 @@ internal static class Program
GraphForm graph = new("One Of The Graphing Calculators Of All Time");
Equation equ = new(x => Math.Sin(x));
SlopeField sf = new(2, (x, y) => Math.Cos(x));
TangentLine tl = new(2, 2, equ);
graph.Graph(equ, sf, tl);
Equation equ = new(Math.Sin);
graph.Graph(equ);
// You can preload graphs in by going Misc > Preload Cache.
// Keep in mind this uses more memory than usual and can take