feat: Initial Physics Code From Previous Repo

Engine.Physics2D/Primitives/Line.cs

@@ -0,0 +1,146 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics.CodeAnalysis;
+
+using Syntriax.Engine.Core;
+
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+public record Line(Vector2D From, Vector2D To)
+{
+    public Line Reversed => new(To, From);
+    public Vector2D Direction => Vector2D.Normalize(To - From);
+    public float Length => (From - To).Length();
+    public float LengthSquared => (From - To).LengthSquared();
+
+    public LineEquation LineEquation
+    {
+        get
+        {
+            Vector2D slopeVector = To - From;
+            float slope = slopeVector.Y / slopeVector.X;
+
+            float yOffset = From.Y - (slope * From.X);
+
+            return new LineEquation(slope, yOffset);
+        }
+    }
+
+    public bool Intersects(Vector2D point)
+        => Resolve(point.X).ApproximatelyEquals(point);
+
+    public float GetT(Vector2D point)
+    {
+        float fromX = MathF.Abs(From.X);
+        float toX = MathF.Abs(To.X);
+        float pointX = MathF.Abs(point.X);
+
+        float min = MathF.Min(fromX, toX);
+        float max = MathF.Max(fromX, toX) - min;
+
+        pointX -= min;
+
+        float t = pointX / max;
+
+        // FIXME
+        // I don't even know, apparently whatever I wrote up there doesn't take into account of the direction of the line
+        // Which... I can see how, but I am also not sure how I can make it take into account. Or actually I'm for some reason
+        // too unmotivated to find a solution. Future me, find a better way if possible, please.
+        if (!Lerp(t).ApproximatelyEquals(point))
+            return 1f - t;
+        return t;
+    }
+
+    public bool Exist(List<Vector2D> vertices)
+    {
+        for (int i = 0; i < vertices.Count - 1; i++)
+        {
+            Vector2D vertexCurrent = vertices[i];
+            Vector2D vertexNext = vertices[i];
+            if (From == vertexCurrent && To == vertexNext) return true;
+            if (From == vertexNext && To == vertexCurrent) return true;
+        }
+
+        Vector2D vertexFirst = vertices[0];
+        Vector2D vertexLast = vertices[^1];
+        if (From == vertexFirst && To == vertexLast) return true;
+        if (From == vertexLast && To == vertexFirst) return true;
+        return false;
+    }
+
+    public float IntersectionParameterT(Line other)
+    {
+        float numerator = (From.X - other.From.X) * (other.From.Y - other.To.Y) - (From.Y - other.From.Y) * (other.From.X - other.To.X);
+        float denominator = (From.X - To.X) * (other.From.Y - other.To.Y) - (From.Y - To.Y) * (other.From.X - other.To.X);
+
+        // Lines are parallel
+        if (denominator == 0)
+            return float.NaN;
+
+        return numerator / denominator;
+    }
+
+    public Vector2D Lerp(float t)
+        => new Vector2D(
+            From.X + (To.X - From.X) * t,
+            From.Y + (To.Y - From.Y) * t
+        );
+
+    public Vector2D Resolve(float x)
+        => new Vector2D(x, LineEquation.Resolve(x));
+
+    public Vector2D ClosestPointTo(Vector2D point)
+    {
+        // Convert edge points to vectors
+        var edgeVector = new Vector2D(To.X - From.X, To.Y - From.Y);
+        var pointVector = new Vector2D(point.X - From.X, point.Y - From.Y);
+
+        // Calculate the projection of pointVector onto edgeVector
+        float t = (pointVector.X * edgeVector.X + pointVector.Y * edgeVector.Y) / (edgeVector.X * edgeVector.X + edgeVector.Y * edgeVector.Y);
+
+        // Clamp t to the range [0, 1] to ensure the closest point is on the edge
+        t = MathF.Max(0, MathF.Min(1, t));
+
+        // Calculate the closest point on the edge
+        float closestX = From.X + t * edgeVector.X;
+        float closestY = From.Y + t * edgeVector.Y;
+
+        return new Vector2D((float)closestX, (float)closestY);
+    }
+
+    public Vector2D IntersectionPoint(Line other)
+        => Vector2D.Lerp(From, To, IntersectionParameterT(other));
+
+    public bool Intersects(Line other)
+    {
+        int o1 = PhysicsMath.Orientation(From, To, other.From);
+        int o2 = PhysicsMath.Orientation(From, To, other.To);
+        int o3 = PhysicsMath.Orientation(other.From, other.To, From);
+        int o4 = PhysicsMath.Orientation(other.From, other.To, To);
+
+        if (o1 != o2 && o3 != o4)
+            return true;
+
+        if (o1 == 0 && PhysicsMath.OnSegment(From, other.From, To)) return true;
+        if (o2 == 0 && PhysicsMath.OnSegment(From, other.To, To)) return true;
+        if (o3 == 0 && PhysicsMath.OnSegment(other.From, From, other.To)) return true;
+        if (o4 == 0 && PhysicsMath.OnSegment(other.From, To, other.To)) return true;
+
+        return false;
+    }
+
+    public bool Intersects(Line other, [NotNullWhen(returnValue: true)] out Vector2D? point)
+    {
+        point = null;
+
+        bool result = Intersects(other);
+
+        if (result)
+            point = IntersectionPoint(other);
+
+        return result;
+    }
+
+    public bool ApproximatelyEquals(Line other)
+        => From.ApproximatelyEquals(other.From) && To.ApproximatelyEquals(other.To);
+}