Proposal - 3.0 Additional types for Silk.NET.Maths

documentation/proposals/(WIP) Proposal - 3.0 Additional math types - Angle.md

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+# Summary
+Proposal API for additional math types to bring it up to feature parity with other popular math libraries i.e. `SlimDX`, `SharpDX`, or `Stride3D`. Leveraging modern .NET features such as `INumber<T>` and vectorization.
+
+# Contributors
+- Daniel Keenan (dfkeenan)
+
+# Current Status
+- [x] Proposed
+- [ ] Discussed with API Review Board (ARB)
+- [ ] Approved
+- [ ] Implemented
+
+# Design Decisions
+- This proposal should compliment/augment the proposed 3.0 implementation of `Silk.Net.Maths`, matching `System.Numerics` where possible, with concessions for design oversights in that api.
+- This proposal assumes no knowledge of the 2.x Math library.
+- Text herein marked **INFORMATIVE** does not form a normative part of this proposal, and is for background only.
+- Within this proposal, the key words **must**, **required**, **shall**, **should**, **recommended**, **may**, **could**, and **optional** are to be interpreted as described in [RFC 2119 - Key words for use in RFCs to Indicate Requirement Levels](https://www.ietf.org/rfc/rfc2119.txt). The additional key word **optionally** is an alternate form of **optional**, for use where grammatically appropriate. These key words are highlighted in the proposal for clarity.
+
+
+
+# Proposed API
+
+## Angle
+
+* `IParsable<TSelf>`, `ISpanParsable<TSelf>`, `IUtf8SpanParsable<TSelf>`
+    * must parse angle in degrees using `IParsable<TScalar>`, `ISpanParsable<TScalar>`, `IUtf8SpanParsable<TSelf>`
+    * optional handle `°` character
+
+* `IFormattable`, `IUtf8SpanFormattable`
+    * must produce text in degrees with default format of 2 decimal places. i.e. format string `0.##`
+    * optional include `°` character. i.e. format string `0.##°`
+
+Interface implementations not included for brevity.
+
+```csharp
+/// <summary>
+/// Represents a unit independant angle using a floating-point
+/// internal representation.
+/// </summary>
+public readonly struct Angle<TScalar> 
+    : IEquatable<Angle<TScalar>>
+    , IEqualityOperators<Angle<TScalar>,Angle<TScalar>, bool>
+    , IComparable<Angle<TScalar>>
+    , IComparisonOperators<Angle<TScalar>,Angle<TScalar>, bool>
+    , IAdditionOperators<Angle<TScalar>,Angle<TScalar>,Angle<TScalar>>
+    , IDivisionOperators<Angle<TScalar>, TScalar, Angle<TScalar>>
+    , IDivisionOperators<TScalar, Angle<TScalar>, Angle<TScalar>>
+    , IMultiplyOperators<Angle<TScalar>, TScalar, Angle<TScalar>>
+    , IMultiplyOperators<TScalar, Angle<TScalar>, Angle<TScalar>>
+    , IModulusOperators<Angle<TScalar>, Angle<TScalar>, Angle<TScalar>>
+    , ISubtractionOperators<Angle<TScalar>,Angle<TScalar>,Angle<TScalar>>
+    , IParsable<Angle<TScalar>>
+    , ISpanParsable<Angle<TScalar>>
+    , IUtf8SpanParsable<Angle<TScalar>>
+    , IFormattable
+    , IUtf8SpanFormattable
+    where TScalar : IFloatingPointIeee754<TScalar>
+{
+    internal Angle(TScalar radians) { }
+
+    /// <summary>Angle in degrees in the range [0, 360]. Without fractional component.</summary>
+    public TScalar Degrees { get; }
+
+    /// <summary>Angle in degrees in the range [0, 360]. With fractional component.</summary>
+    public TScalar TotalDegrees { get; }
+
+    /// <summary>Angle in radians in range [π, -π].</summary>
+    public TScalar Radians { get; }
+
+    /// <summary>Angle in radians in range [0, 2π].</summary>
+    public TScalar PositiveRadians { get; }
+
+    /// <summary>Gets or sets the minutes component of the degrees this Silk.NET.Maths.Angle<TScalar> represents.</summary>
+    public TScalar Minutes { get; }
+
+    /// <summary>Gets or sets the seconds of the degrees this Silk.NET.Maths.Angle<TScalar> represents.</summary>
+    public TScalar Seconds { get; }
+
+
+    /// <summary>
+    /// Gets a System.Boolean that determines whether this Silk.NET.Maths.Angle<TScalar>
+    /// is a right angle (i.e. 90° or π/2).
+    /// </summary>    
+    public bool IsRight { get; }
+
+    /// <summary>
+    /// Gets a System.Boolean that determines whether this Silk.NET.Maths.Angle<TScalar>
+    /// is a straight angle (i.e. 180° or π).
+    /// </summary>    
+    public bool IsStraight { get; }
+
+    /// <summary>
+    /// Gets a System.Boolean that determines whether this Silk.NET.Maths.Angle<TScalar>
+    /// is a full rotation angle (i.e. 360° or 2π).
+    /// </summary>    
+    public bool IsFullRotation { get; }
+
+    /// <summary>
+    /// Gets a System.Boolean that determines whether this Silk.NET.Maths.Angle<TScalar>
+    /// is an oblique angle (i.e. is not 90° or a multiple of 90°).
+    /// </summary>    
+    public bool IsOblique { get; }
+
+    /// <summary>
+    /// Gets a System.Boolean that determines whether this Silk.NET.Maths.Angle<TScalar>
+    /// is an acute angle (i.e. less than 90° but greater than 0°).
+    /// </summary>    
+    public bool IsAcute { get; }
+
+    /// <summary>
+    /// Gets a System.Boolean that determines whether this Silk.NET.Maths.Angle<TScalar>
+    /// is an obtuse angle (i.e. greater than 90° but less than 180°).
+    /// </summary>    
+    public bool IsObtuse { get; }
+
+    /// <summary>
+    /// Gets a System.Boolean that determines whether this Silk.NET.Maths.Angle<TScalar>
+    /// is a reflex angle (i.e. greater than 180° but less than 360°).
+    /// </summary>    
+    public bool IsReflex { get; }
+
+    /// <summary>
+    /// Gets a Silk.NET.Maths.Angle<TScalar> instance that complements this angle (i.e. the two angles add to 90°).
+    /// </summary>    
+    public Angle<TScalar> Complement { get; }
+
+    /// <summary>
+    /// Gets a Silk.NET.Maths.Angle<TScalar> instance that supplements this angle (i.e. the two angles add to 180°).
+    /// </summary>    
+    public Angle<TScalar> Supplement { get; }
+
+    /// <summary>Implicit cast in radians</summary>
+    public static implicit operator TScalar(Angle<TScalar> angle) => default;
+}
+
+```
+
+
+
+```csharp
+
+public static class Angle
+{
+    public static Angle<TScalar> FromRadians<TScalar>(TScalar radians)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> FromDegrees<TScalar>(TScalar degrees)
+        where TScalar : IFloatingPointIeee754<TScalar>
+         => default;
+
+    public static Angle<TScalar> FromDegrees<TScalar>(TScalar degrees, TScalar minutes, TScalar seconds)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Min<TScalar>(Angle<TScalar> left, Angle<TScalar> right) 
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Max<TScalar>(Angle<TScalar> left, Angle<TScalar> right)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Add<TScalar>(Angle<TScalar> left, Angle<TScalar> right)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Subtract<TScalar>(Angle<TScalar> left, Angle<TScalar> right)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Multiply<TScalar>(Angle<TScalar> left, TScalar right)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Divide<TScalar>(Angle<TScalar> left, TScalar right)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Clamp<TScalar>(Angle<TScalar> value, Angle<TScalar> min, Angle<TScalar> max)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> Atan2<TScalar>(TScalar y, TScalar x)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> ArcTan<TScalar>(TScalar y, TScalar x)
+        where TScalar : IFloatingPointIeee754<TScalar>
+        => default;
+
+    public static Angle<TScalar> ArcSin<TScalar>(TScalar sin)
+        where TScalar : IFloatingPointIeee754<TScalar>
+         => default;
+
+    public static Angle<TScalar> ArcCos<TScalar>(TScalar cos)
+        where TScalar : IFloatingPointIeee754<TScalar>
+         => default;
+
+    public static Angle<TScalar> Between<TScalar>(in Vector2F<TScalar> left, in Vector2F<TScalar> right)
+       where TScalar : IFloatingPointIeee754<TScalar>
+       => default;
+
+    public static Angle<TScalar> Between<TScalar>(in Vector3F<TScalar> left, in Vector3F<TScalar> right)
+       where TScalar : IFloatingPointIeee754<TScalar>
+       => default;
+
+    public static Angle<TScalar> ZeroAngle<TScalar>()
+        where TScalar : IFloatingPointIeee754<TScalar>
+         => default;
+
+    public static Angle<TScalar> RightAngle<TScalar>()
+        where TScalar : IFloatingPointIeee754<TScalar>
+         => default;
+
+    public static Angle<TScalar> StraightAngle<TScalar>()
+        where TScalar : IFloatingPointIeee754<TScalar>
+         => default;
+
+    public static Angle<TScalar> FullRotationAngle<TScalar>()
+        where TScalar : IFloatingPointIeee754<TScalar>
+         => default;
+}
+```
+
+# Meeting Agenda/Notes
+## TDB
+* Degrees, minutes and seconds are not fractional. Should they be changed to an integer type (`int`)?
+    *   ```csharp
+        public int Degrees { get; }
+        public int Minutes { get; }
+        public int Seconds { get; }
+
+        public static Angle<TScalar> FromDegrees<TScalar>(int degrees, int minutes, int seconds)
+            where TScalar : IFloatingPointIeee754<TScalar>
+            => default;
+        ```