feat: added sphere primitive

Engine.Core/Primitives/AABB3D.cs

@@ -42,6 +42,8 @@ public readonly struct AABB3D(Vector3D lowerBoundary, Vector3D upperBoundary) :
     public static bool operator ==(AABB3D left, AABB3D right) => left.UpperBoundary == right.UpperBoundary && left.LowerBoundary == right.LowerBoundary;
     public static bool operator !=(AABB3D left, AABB3D right) => left.UpperBoundary != right.UpperBoundary || left.LowerBoundary != right.LowerBoundary;
 
+    public static implicit operator AABB3D(Sphere3D sphere) => new(sphere.Center - new Vector3D(sphere.Radius, sphere.Radius, sphere.Radius), sphere.Center + new Vector3D(sphere.Radius, sphere.Radius, sphere.Radius));
+
     /// <summary>
     /// Creates an <see cref="AABB3D"/> from a collection of <see cref="Vector3D"/>s.
     /// </summary>

Engine.Core/Primitives/Circle.cs

@@ -42,6 +42,8 @@ public readonly struct Circle(Vector2D center, float radius) : IEquatable<Circle
     public static bool operator ==(Circle left, Circle right) => left.Center == right.Center && left.Radius == right.Radius;
     public static bool operator !=(Circle left, Circle right) => left.Center != right.Center || left.Radius != right.Radius;
 
+    public static implicit operator Circle(Sphere3D sphere) => new(sphere.Center, sphere.Radius);
+
     /// <summary>
     /// Sets the center of the <see cref="Circle"/>.
     /// </summary>

Engine.Core/Primitives/Sphere3D.cs

@@ -0,0 +1,131 @@
+using System;
+using System.Diagnostics;
+
+namespace Engine.Core;
+
+/// <summary>
+/// Represents a 3D sphere.
+/// </summary>
+/// <param name="center">The center of the sphere.</param>
+/// <param name="radius">The radius of the sphere.</param>
+/// <remarks>
+/// Initializes a new instance of the <see cref="Sphere3D"/> struct with the specified center and radius.
+/// </remarks>
+[DebuggerDisplay("Center: {Center.ToString(),nq}, Radius: {Radius}")]
+public readonly struct Sphere3D(Vector3D center, float radius) : IEquatable<Sphere3D>
+{
+    /// <summary>
+    /// The center of the <see cref="Sphere3D"/>.
+    /// </summary>
+    public readonly Vector3D Center = center;
+
+    /// <summary>
+    /// The radius of the <see cref="Sphere3D"/>.
+    /// </summary>
+    public readonly float Radius = radius;
+
+    /// <summary>
+    /// Gets the squared radius of the <see cref="Sphere3D"/>.
+    /// </summary>
+    public readonly float RadiusSquared => Radius * Radius;
+
+    /// <summary>
+    /// Gets the diameter of the <see cref="Sphere3D"/>.
+    /// </summary>
+    public readonly float Diameter => 2f * Radius;
+
+    /// <summary>
+    /// A predefined unit <see cref="Sphere3D"/> with a center at the origin and a radius of 1.
+    /// </summary>
+    public static readonly Sphere3D UnitSphere = new(Vector3D.Zero, 1f);
+
+    public static bool operator ==(Sphere3D left, Sphere3D right) => left.Center == right.Center && left.Radius == right.Radius;
+    public static bool operator !=(Sphere3D left, Sphere3D right) => left.Center != right.Center || left.Radius != right.Radius;
+
+    /// <summary>
+    /// Sets the center of the <see cref="Sphere3D"/>.
+    /// </summary>
+    public static Sphere3D SetCenter(Sphere3D sphere, Vector3D center) => new(center, sphere.Radius);
+
+    /// <summary>
+    /// Sets the radius of the <see cref="Sphere3D"/>.
+    /// </summary>
+    public static Sphere3D SetRadius(Sphere3D sphere, float radius) => new(sphere.Center, radius);
+
+    /// <summary>
+    /// Displaces the <see cref="Sphere3D"/> by the specified <see cref="Vector3D"/>.
+    /// </summary>
+    public static Sphere3D Displace(Sphere3D sphere, Vector3D displaceVector) => new(sphere.Center + displaceVector, sphere.Radius);
+
+    /// <summary>
+    /// Projects the <see cref="Sphere3D"/> onto the specified <see cref="Vector3D"/>.
+    /// </summary>
+    public static Projection1D Project(Sphere3D sphere, Vector3D projectionVector)
+    {
+        float projectedCenter = sphere.Center.Dot(projectionVector);
+        return new(projectedCenter - sphere.Radius, projectedCenter + sphere.Radius);
+    }
+
+    /// <summary>
+    /// Transforms the <see cref="Sphere3D"/> by the specified <see cref="ITransform3D"/>.
+    /// </summary>
+    public static Sphere3D Transform(ITransform3D transform, Sphere3D sphere)
+        => new(transform.Transform(sphere.Center), sphere.Radius * (transform.Scale.Magnitude / Vector3D.One.Magnitude));
+
+    /// <summary>
+    /// Checks if two <see cref="Sphere3D"/>s are approximately equal.
+    /// </summary>
+    /// <param name="left">The first <see cref="Sphere3D"/>.</param>
+    /// <param name="right">The second <see cref="Sphere3D"/>.</param>
+    /// <param name="epsilon">The epsilon range.</param>
+    /// <returns><see cref="true"/> if the <see cref="Sphere3D"/>s are approximately equal; otherwise, <see cref="false"/>.</returns>
+    public static bool ApproximatelyEquals(Sphere3D left, Sphere3D right, float epsilon = float.Epsilon)
+        => left.Center.ApproximatelyEquals(right.Center, epsilon) && left.Radius.ApproximatelyEquals(right.Radius, epsilon);
+
+    /// <summary>
+    /// Determines whether the specified object is equal to the current <see cref="Sphere3D"/>.
+    /// </summary>
+    /// <param name="obj">The object to compare with the current <see cref="Sphere3D"/>.</param>
+    /// <returns><see cref="true"/> if the specified object is equal to the current <see cref="Sphere3D"/>; otherwise, <see cref="false"/>.</returns>
+    public override bool Equals(object? obj) => obj is Sphere3D sphere && this == sphere;
+    public bool Equals(Sphere3D other) => this == other;
+
+    /// <summary>
+    /// Generates a hash code for the <see cref="Sphere3D"/>.
+    /// </summary>
+    /// <returns>A hash code for the <see cref="Sphere3D"/>.</returns>
+    public override int GetHashCode() => System.HashCode.Combine(Center, Radius);
+
+    /// <summary>
+    /// Converts the <see cref="Sphere3D"/> to its string representation.
+    /// </summary>
+    /// <returns>A string representation of the <see cref="Sphere3D"/>.</returns>
+    public override string ToString() => $"{nameof(Sphere3D)}({Center}, {Radius})";
+}
+
+/// <summary>
+/// Provides extension methods for the <see cref="Sphere3D"/> struct.
+/// </summary>
+public static class SphereExtensions
+{
+    /// <inheritdoc cref="Sphere3D.SetCenter(Sphere3D, Vector3D)" />
+    public static Sphere3D SetCenter(this Sphere3D sphere, Vector3D center) => Sphere3D.SetCenter(sphere, center);
+
+    /// <inheritdoc cref="Sphere3D.SetRadius(Sphere3D, float)" />
+    public static Sphere3D SetRadius(this Sphere3D sphere, float radius) => Sphere3D.SetRadius(sphere, radius);
+
+    /// <inheritdoc cref="Sphere3D.Displace(Sphere3D, Vector3D)" />
+    public static Sphere3D Displace(this Sphere3D sphere, Vector3D displaceVector) => Sphere3D.Displace(sphere, displaceVector);
+
+    /// <inheritdoc cref="Sphere3D.Project(Sphere3D, Vector3D)" />
+    public static Projection1D ProjectTo(this Sphere3D sphere, Vector3D projectionVector) => Sphere3D.Project(sphere, projectionVector);
+
+    /// <inheritdoc cref="Sphere3D.Transform(ITransform3D, Sphere3D)" />
+    public static Sphere3D Transform(this ITransform3D transform, Sphere3D sphere) => Sphere3D.Transform(transform, sphere);
+
+    /// <inheritdoc cref="Sphere3D.Transform(ITransform3D, Sphere3D)" />
+    public static Sphere3D Transform(this Sphere3D sphere, ITransform3D transform) => Sphere3D.Transform(transform, sphere);
+
+    /// <inheritdoc cref="Sphere3D.ApproximatelyEquals(Sphere3D, Sphere3D, float)" />
+    public static bool ApproximatelyEquals(this Sphere3D left, Sphere3D right, float epsilon = float.Epsilon) => Sphere3D.ApproximatelyEquals(left, right, epsilon);
+}