Syntriax.Engine/Engine.Physics2D/Primitives/Triangle.cs

using System;

using Syntriax.Engine.Core;

namespace Syntriax.Engine.Physics2D.Primitives;

public record Triangle(Vector2D A, Vector2D B, Vector2D C)
{
    public float Area
        => .5f * MathF.Abs(
                A.X * (B.Y - C.Y) +
                B.X * (C.Y - A.Y) +
                C.X * (A.Y - B.Y)
            );

    public static Circle GetCircumCircle(Triangle triangle)
    {
        Vector2D midAB = (triangle.A + triangle.B) / 2f;
        Vector2D midBC = (triangle.B + triangle.C) / 2f;

        float slopeAB = (triangle.B.Y - triangle.A.Y) / (triangle.B.X - triangle.A.X);
        float slopeBC = (triangle.C.Y - triangle.B.Y) / (triangle.C.X - triangle.B.X);

        Vector2D center;
        if (MathF.Abs(slopeAB - slopeBC) > float.Epsilon)
        {
            float x = (slopeAB * slopeBC * (triangle.A.Y - triangle.C.Y) + slopeBC * (triangle.A.X + triangle.B.X) - slopeAB * (triangle.B.X + triangle.C.X)) / (2f * (slopeBC - slopeAB));
            float y = -(x - (triangle.A.X + triangle.B.X) / 2f) / slopeAB + (triangle.A.Y + triangle.B.Y) / 2f;
            center = new Vector2D(x, y);
        }
        else
            center = (midAB + midBC) * .5f;

        return new(center, Vector2D.Distance(center, triangle.A));
    }

    public static bool ApproximatelyEquals(Triangle left, Triangle right)
        => left.A.ApproximatelyEquals(right.A) && left.B.ApproximatelyEquals(right.B) && left.C.ApproximatelyEquals(right.C);
}

public static class TriangleExtensions
{
    public static bool ApproximatelyEquals(this Triangle left, Triangle right) => Triangle.ApproximatelyEquals(left, right);
}