Engine-Pong/Game/Physics2D/PhysicsMath.cs

using System;
using System.Collections.Generic;

using Microsoft.Xna.Framework;
using Syntriax.Engine.Core;
using Syntriax.Engine.Physics2D.Primitives;

namespace Syntriax.Engine.Physics2D;

public static class PhysicsMath
{
    public static Vector2D Scale(this Vector2D original, Vector2D scale)
        => new Vector2D(original.X * scale.X, original.Y * scale.Y);

    public static Triangle ToSuperTriangle(this IList<Vector2D> vertices)
    {
        float minX = float.MaxValue, minY = float.MaxValue;
        float maxX = float.MinValue, maxY = float.MinValue;

        foreach (Vector2D point in vertices)
        {
            minX = MathF.Min(minX, point.X);
            minY = MathF.Min(minY, point.Y);
            maxX = MathF.Max(maxX, point.X);
            maxY = MathF.Max(maxY, point.Y);
        }

        float dx = maxX - minX;
        float dy = maxY - minY;
        float deltaMax = MathF.Max(dx, dy);
        float midX = (minX + maxX) / 2;
        float midY = (minY + maxY) / 2;

        Vector2D p1 = new Vector2D((float)midX - 20f * (float)deltaMax, (float)midY - (float)deltaMax);
        Vector2D p2 = new Vector2D((float)midX, (float)midY + 20 * (float)deltaMax);
        Vector2D p3 = new Vector2D((float)midX + 20 * (float)deltaMax, (float)midY - (float)deltaMax);

        return new Triangle(p1, p2, p3);
    }

    public static IList<Line> ToLines(this IList<Vector2D> vertices)
    {
        List<Line> lines = new List<Line>(vertices.Count - 1);
        ToLines(vertices, lines);
        return lines;
    }

    public static void ToLines(this IList<Vector2D> vertices, IList<Line> lines)
    {
        lines.Clear();
        for (int i = 0; i < vertices.Count - 1; i++)
            lines.Add(new(vertices[i], vertices[i + 1]));
        lines.Add(new(vertices[^1], vertices[0]));
    }

    public static bool LaysOn(this Vector2D point, Line line)
        => line.Resolve(point.X).ApproximatelyEquals(point);


    // Given three collinear points p, q, r, the function checks if 
    // point q lies on line segment 'pr' 
    public static bool OnSegment(Vector2D p, Vector2D q, Vector2D r)
    {
        if (q.X <= MathF.Max(p.X, r.X) && q.X >= MathF.Min(p.X, r.X) &&
            q.Y <= MathF.Max(p.Y, r.Y) && q.Y >= MathF.Min(p.Y, r.Y))
            return true;

        return false;
    }

    // To find orientation of ordered triplet (p, q, r). 
    // The function returns following values 
    // 0 --> p, q and r are collinear 
    // 1 --> Clockwise 
    // 2 --> Counterclockwise 
    public static int Orientation(Vector2D p, Vector2D q, Vector2D r)
    {
        // See https://www.geeksforgeeks.org/orientation-3-ordered-points/ 
        // for details of below formula. 
        float val = (q.Y - p.Y) * (r.X - q.X) -
                (q.X - p.X) * (r.Y - q.Y);

        if (val == 0) return 0; // collinear 

        return (val > 0) ? 1 : 2; // clock or counterclock wise 
    }

    public static float IntersectionParameterT(Vector2D p0, Vector2D p1, Vector2D q0, Vector2D q1)
        => ((q0.X - p0.X) * (p1.Y - p0.Y) - (q0.Y - p0.Y) * (p1.X - p0.X)) /
            ((q1.Y - q0.Y) * (p1.X - p0.X) - (q1.X - q0.X) * (p1.Y - p0.Y));


    public static bool ApproximatelyEquals(this float a, float b)
        => ApproximatelyEquals(a, b, float.Epsilon);
    public static bool ApproximatelyEquals(this Vector2 a, Vector2 b)
        => ApproximatelyEquals(a, b, float.Epsilon);
    public static bool ApproximatelyEquals(this Vector2 a, Vector2 b, float epsilon)
        => ApproximatelyEquals(a.X, b.X, epsilon) && ApproximatelyEquals(a.Y, b.Y, epsilon);
    public static bool ApproximatelyEquals(this Vector2D a, Vector2D b)
        => ApproximatelyEquals(a, b, float.Epsilon);
    public static bool ApproximatelyEquals(this Vector2D a, Vector2D b, float epsilon)
        => ApproximatelyEquals(a.X, b.X, epsilon) && ApproximatelyEquals(a.Y, b.Y, epsilon);
    public static bool ApproximatelyEquals(this float a, float b, float epsilon)
    {
        if (a == b)
            return true;

        const float floatNormal = (1 << 23) * float.Epsilon;
        float absA = MathF.Abs(a);
        float absB = MathF.Abs(b);
        float diff = MathF.Abs(a - b);

        if (a == 0.0f || b == 0.0f || diff < floatNormal)
            return diff < (epsilon * floatNormal);

        return diff / MathF.Min(absA + absB, float.MaxValue) < epsilon;
    }
}