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Math tools: a solver of triangles #42

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2 changes: 1 addition & 1 deletion AGENTS.md
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Expand Up @@ -19,7 +19,7 @@ generated parser, on netstandard2.0): keep it so, and keep containers and other
| `src/SharpEquations.Avalonia/` | The controls for Avalonia: `MathEditBox` (the editor), `MathView`; embeds Libertinus Math |
| `samples/SharpEquations.Avalonia.Demo/` | A window with the editor (`DemoView`, shared with the web demo) |
| `samples/SharpEquations.Avalonia.Browser.Demo/` | The same demo on WebAssembly (needs the `wasm-tools` workload, so not in the solution; `.github/workflows/demo.yml` publishes it to GitHub Pages) |
| `samples/SharpEquations.Avalonia.MathTools.Demo/` | A second app, math tools around the editor (`MathToolsView`, a page each: the scientific keypad, the library of formulas, the unit converter) |
| `samples/SharpEquations.Avalonia.MathTools.Demo/` | A second app, math tools around the editor (`MathToolsView`, a page each: the scientific keypad, the library of formulas, the unit converter, the solver of triangles) |
| `samples/SharpEquations.Avalonia.Browser.MathTools.Demo/` | The math tools on WebAssembly (as the web demo, not in the solution build; `demo.yml` publishes them under `math/`) |
| `benchmarks/SharpEquations.Benchmarks/` | BenchmarkDotNet benchmarks of reading, writing and converting the corpora |
| `tests/SharpEquations.Tests/` | TUnit tests, in folders by subject (PublicApi, MathML, Omml, Mtef, UnicodeMath, LaTeX, Property, Regression) |
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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -89,7 +89,7 @@ UnicodeMath and LaTeX, and `samples/SharpEquations.Avalonia.Browser.Demo` the sa
(published to GitHub Pages from `main`; to run it locally: `dotnet workload install wasm-tools`, then
`dotnet run --project samples/SharpEquations.Avalonia.Browser.Demo`). `samples/SharpEquations.Avalonia.MathTools.Demo` is a
second app around the editor, a set of math tools (a scientific keypad that types into the editor, a library of
formulas, a unit converter), with
formulas, a unit converter, a solver of triangles), with
`samples/SharpEquations.Avalonia.Browser.MathTools.Demo` in the browser (published under `math/` of the same site).

## Architecture
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9 changes: 7 additions & 2 deletions samples/SharpEquations.Avalonia.MathTools.Demo/MathToolsView.cs
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Expand Up @@ -9,8 +9,8 @@ namespace SharpEquations.Avalonia.MathTools
using SharpEquations;

/// <summary>
/// The math tools, a page each: the scientific keypad around the equation editor, the library of formulas and the
/// unit converter. The desktop window and the WebAssembly page show the same view.
/// The math tools, a page each: the scientific keypad around the equation editor, the library of formulas, the
/// unit converter and the solver of triangles. The desktop window and the WebAssembly page show the same view.
/// </summary>
public sealed class MathToolsView : UserControl
{
Expand All @@ -21,6 +21,7 @@ public MathToolsView()
Ui.AddBrushes(Resources);
Calculator = new CalculatorPage();
Converter = new UnitsPage();
TriangleSolver = new TrianglePage();
Tabs = new TabControl { Margin = new Thickness(20, 12, 20, 0) };
FormulaLibrary = new FormulasPage(equation =>
{
Expand All @@ -33,6 +34,7 @@ public MathToolsView()
Tab("Calculator", Calculator),
Tab("Formulas", FormulaLibrary),
Tab("Units", Converter),
Tab("Triangles", TriangleSolver),
};

var root = new DockPanel { Children = { Ui.Docked(Header(), Dock.Top), Tabs } };
Expand All @@ -49,6 +51,9 @@ public MathToolsView()
/// <summary>The page of the unit converter.</summary>
public UnitsPage Converter { get; }

/// <summary>The page of the solver of triangles.</summary>
public TrianglePage TriangleSolver { get; }

/// <summary>The tabs of the pages.</summary>
public TabControl Tabs { get; }

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294 changes: 294 additions & 0 deletions samples/SharpEquations.Avalonia.MathTools.Demo/TrianglePage.cs
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@@ -0,0 +1,294 @@
namespace SharpEquations.Avalonia.MathTools
{
using System;
using System.Collections.Generic;
using System.Linq;
using global::Avalonia;
using global::Avalonia.Controls;
using global::Avalonia.Controls.Shapes;
using global::Avalonia.Layout;
using global::Avalonia.Media;
using SharpEquations;

/// <summary>
/// The solver of triangles: three of the sides and angles give the others, the area, the perimeter and the radii of
/// the circles, with the laws used, written in UnicodeMath and drawn by <see cref="MathView"/>s, and the triangle
/// drawn to scale.
/// </summary>
public sealed class TrianglePage : UserControl
{
private const double DrawingWidth = 300;
private const double DrawingHeight = 210;

private static readonly Color Accent = Color.FromRgb(0x0D, 0x94, 0x88);

private static readonly (string Name, string[] Values)[] Examples =
{
("3, 4, 5", new[] { "3", "4", "5", "", "", "" }),
("SAS", new[] { "7", "", "9", "", "60", "" }),
("ASA", new[] { "", "", "10", "45", "75", "" }),
("Two triangles", new[] { "6", "8", "", "40", "", "" }),
("No triangle", new[] { "1", "2", "4", "", "", "" }),
};

private static readonly string[] Empty = { "", "", "", "", "", "" };

private readonly StackPanel results = new StackPanel { Spacing = 18 };
private readonly StackPanel steps = new StackPanel { Spacing = 10 };
private bool updating;

public TrianglePage()
{
Inputs = Triangles.SideNames.Concat(Triangles.AngleNames).Select(_ => new TextBox { Width = 92, PlaceholderText = "?" }).ToArray();
foreach (var input in Inputs)
{
input.PropertyChanged += (_, e) =>
{
if (e.Property == TextBox.TextProperty)
Solve();
};
}

var clear = new Button { Content = "Clear", CornerRadius = new CornerRadius(8) };
clear.Click += (_, _) => Fill(Empty);
var examples = new List<Control> { Ui.Muted("Examples", 12.5) };
foreach (var (name, values) in Examples)
{
var button = new Button { Content = name, CornerRadius = new CornerRadius(8), Padding = new Thickness(10, 4) };
button.Click += (_, _) => Fill(values);
examples.Add(button);
}
examples.Add(clear);

var sides = Ui.Row(Enumerable.Range(0, 3).Select(i => Field(Triangles.SideNames[i], Inputs[i], "")).ToArray());
var angles = Ui.Row(Enumerable.Range(0, 3).Select(i => Field(Triangles.AngleNames[i], Inputs[i + 3], "°")).ToArray());

Content = new StackPanel
{
Spacing = 20,
Children =
{
Ui.Card("Triangles", "Three of the sides and angles, at least one of them a side; each angle is opposite the side of its letter", new StackPanel
{
Spacing = 14,
Children =
{
new Grid
{
ColumnDefinitions = new ColumnDefinitions("Auto,*"),
RowDefinitions = new RowDefinitions("Auto,Auto"),
ColumnSpacing = 14,
RowSpacing = 10,
Children = { Label("Sides", 0), At(sides, 0, 1), Label("Angles", 1), At(angles, 1, 1) },
},
Ui.Row(examples.ToArray()),
},
}),
Ui.Card("Solution", "The values found, the area, the perimeter and the radii of the circles through the vertices and inside", results),
Ui.Card("How", "The laws that give the values found", steps),
},
};
Fill(Examples[0].Values);
}

/// <summary>The fields of a, b, c, α, β and γ.</summary>
public IReadOnlyList<TextBox> Inputs { get; }

/// <summary>The solution of the values in the fields.</summary>
public TriangleSolution? Solution { get; private set; }

/// <summary>Fills the fields, as the examples do.</summary>
public void Fill(IReadOnlyList<string> values)
{
updating = true;
for (var i = 0; i < Inputs.Count; i++)
Inputs[i].Text = values[i];
updating = false;
Solve();
}

/// <summary>The values of a triangle as UnicodeMath: <c>a=3, b=4, c=5</c> and <c>α=36.8699°, β=53.1301°, γ=90°</c>.</summary>
public static (string Sides, string Angles) Describe(Triangle triangle) => (
string.Join(", ", Enumerable.Range(0, 3).Select(i => Triangles.SideNames[i] + "=" + Units.Format(triangle.Side(i)))),
string.Join(", ", Enumerable.Range(0, 3).Select(i => Triangles.AngleNames[i] + "=" + Units.Format(triangle.Angle(i)) + "°")));

private void Solve()
{
if (updating)
return;

var values = new double?[Inputs.Count];
for (var i = 0; i < Inputs.Count; i++)
{
var text = Inputs[i].Text;
if (string.IsNullOrWhiteSpace(text))
continue;
if (!Units.TryParse(text!.TrimEnd('°', ' '), out var value))
{
Show(new TriangleSolution(null, Array.Empty<Triangle>(), Array.Empty<string>(), "“" + text + "” is not a number."));
return;
}
values[i] = value;
}
Show(Triangles.Solve(values[0], values[1], values[2], values[3], values[4], values[5]));
}

private void Show(TriangleSolution solution)
{
Solution = solution;
results.Children.Clear();
steps.Children.Clear();

if (solution.Error != null)
results.Children.Add(Ui.Muted(solution.Error, 14));
if (solution.Triangles.Count == 2)
results.Children.Add(Ui.Muted("The angle given is opposite the shorter side: two triangles have these values.", 13));
foreach (var (triangle, index) in solution.Triangles.Select((t, i) => (t, i)))
results.Children.Add(Result(triangle, solution.Triangles.Count == 2 ? "Triangle " + (index + 1) : null));

if (solution.Case != null)
steps.Children.Add(Ui.Muted("Case " + solution.Case + " (" + CaseName(solution.Case) + ")", 13));
foreach (var step in solution.Steps)
{
var math = Ui.Math(step, 19);
math.HorizontalAlignment = HorizontalAlignment.Left;
steps.Children.Add(math);
}
if (solution.Steps.Count == 0)
steps.Children.Add(Ui.Muted("Give three values, at least one of them a side.", 13));
}

private static Grid Result(Triangle triangle, string? title)
{
var (sides, angles) = Describe(triangle);
var values = new StackPanel { Spacing = 10, VerticalAlignment = VerticalAlignment.Center };
if (title != null)
values.Children.Add(Ui.Small(title));
values.Children.Add(Left(Ui.Math(sides, 21)));
values.Children.Add(Left(Ui.Math(angles, 21)));
values.Children.Add(Measures(triangle));

var drawing = Drawing(triangle);
Grid.SetColumn(values, 1);
return new Grid { ColumnDefinitions = new ColumnDefinitions("Auto,*"), ColumnSpacing = 24, Children = { drawing, values } };
}

private static Grid Measures(Triangle triangle)
{
var rows = new (string Name, string Value)[]
{
("Area", Units.Format(triangle.Area)),
("Perimeter", Units.Format(triangle.Perimeter)),
("Circumradius", "R=" + Units.Format(triangle.Circumradius)),
("Inradius", "r=" + Units.Format(triangle.Inradius)),
};
var grid = new Grid { ColumnDefinitions = new ColumnDefinitions("130,*"), RowSpacing = 8, Margin = new Thickness(0, 6, 0, 0) };
foreach (var (row, (name, value)) in rows.Select((r, i) => (i, r)))
{
grid.RowDefinitions.Add(new RowDefinition(GridLength.Auto));
var label = Ui.Muted(name, 13);
label.VerticalAlignment = VerticalAlignment.Center;
grid.Children.Add(At(label, row, 0));
grid.Children.Add(At(Left(Ui.Math(value, 17)), row, 1));
}
return grid;
}

/// <summary>The triangle to scale: A at the left of the base c, B at its right, C above.</summary>
private static Border Drawing(Triangle triangle)
{
var alpha = Triangles.Radians(triangle.Alpha);
var points = new[] { (X: 0.0, Y: 0.0), (X: triangle.C, Y: 0.0), (X: triangle.B * Math.Cos(alpha), Y: triangle.B * Math.Sin(alpha)) };
double minX = points.Min(p => p.X), maxX = points.Max(p => p.X), maxY = points.Max(p => p.Y);
const double margin = 26;
var scale = Math.Min((DrawingWidth - 2 * margin) / (maxX - minX), (DrawingHeight - 2 * margin) / maxY);
var offsetX = (DrawingWidth - (maxX - minX) * scale) / 2;
var offsetY = (DrawingHeight + maxY * scale) / 2;
var screen = points.Select(p => new Point(offsetX + (p.X - minX) * scale, offsetY - p.Y * scale)).ToArray();

var canvas = new Canvas { Width = DrawingWidth, Height = DrawingHeight };
var shape = new Polygon
{
Points = screen,
StrokeThickness = 2,
StrokeJoin = PenLineJoin.Round,
Stroke = new SolidColorBrush(Accent),
Fill = new SolidColorBrush(Accent, 0.14),
};
canvas.Children.Add(shape);

var center = new Point(screen.Average(p => p.X), screen.Average(p => p.Y));
for (var i = 0; i < 3; i++)
{
// the vertex, away from the center, and the side opposite it, at its middle, away from the center too
Label(canvas, ((char)('A' + i)).ToString(), Away(screen[i], center, 14), FontWeight.SemiBold);
var middle = (screen[(i + 1) % 3] + screen[(i + 2) % 3]) / 2;
Label(canvas, Triangles.SideNames[i], Away(middle, center, 12), FontWeight.Normal);
}

var frame = new Border { CornerRadius = new CornerRadius(12), Child = canvas, VerticalAlignment = VerticalAlignment.Top };
frame.Bind(Border.BackgroundProperty, frame.GetResourceObservable("CodeBrush"));
return frame;
}

private static Point Away(Point point, Point center, double distance)
{
var direction = point - center;
var length = Math.Sqrt(direction.X * direction.X + direction.Y * direction.Y);
return length < 1e-9 ? point : point + direction * (distance / length);
}

private static void Label(Canvas canvas, string text, Point at, FontWeight weight)
{
var label = new TextBlock { Text = text, FontStyle = FontStyle.Italic, FontSize = 15, FontWeight = weight };
label.Measure(Size.Infinity);
Canvas.SetLeft(label, at.X - label.DesiredSize.Width / 2);
Canvas.SetTop(label, at.Y - label.DesiredSize.Height / 2);
canvas.Children.Add(label);
}

private static string CaseName(string kind) => kind switch
{
"SSS" => "three sides",
"SAS" => "two sides and the angle between them",
"SSA" => "two sides and an angle not between them",
"ASA" => "two angles and the side between them",
_ => "two angles and a side not between them",
};

private static StackPanel Field(string name, TextBox input, string unit)
{
var label = Ui.Math(name, 19);
label.VerticalAlignment = VerticalAlignment.Center;
label.Width = 18;
var panel = new StackPanel { Orientation = Orientation.Horizontal, Spacing = 8, Children = { label, input } };
if (unit.Length > 0)
panel.Children.Add(new TextBlock { Text = unit, VerticalAlignment = VerticalAlignment.Center, Margin = new Thickness(-4, 0, 6, 0) });
else
panel.Margin = new Thickness(0, 0, 12, 0);
return panel;
}

private static TextBlock Label(string text, int row)
{
var label = Ui.Small(text);
label.VerticalAlignment = VerticalAlignment.Center;
return At(label, row, 0);
}

private static T Left<T>(T control)
where T : Control
{
control.HorizontalAlignment = HorizontalAlignment.Left;
return control;
}

private static T At<T>(T control, int row, int column)
where T : Control
{
Grid.SetRow(control, row);
Grid.SetColumn(control, column);
return control;
}
}
}
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