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 => From.FromTo(To).Normalize(); public float Length => From.FromTo(To).Length(); public float LengthSquared => From.FromTo(To).LengthSquared(); public static LineEquation GetLineEquation(Line line) { Vector2D slopeVector = line.From.FromTo(line.To); float slope = slopeVector.Y / slopeVector.X; float yOffset = line.From.Y - (slope * line.From.X); return new LineEquation(slope, yOffset); } public static bool Intersects(Line line, Vector2D point) => LineEquation.Resolve(GetLineEquation(line), point.X).ApproximatelyEquals(point.Y); public static float GetT(Line line, Vector2D point) { float fromX = MathF.Abs(line.From.X); float toX = MathF.Abs(line.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(line, t).ApproximatelyEquals(point)) return 1f - t; return t; } public static bool Exist(Line line, List vertices) { for (int i = 0; i < vertices.Count - 1; i++) { Vector2D vertexCurrent = vertices[i]; Vector2D vertexNext = vertices[i]; if (line.From == vertexCurrent && line.To == vertexNext) return true; if (line.From == vertexNext && line.To == vertexCurrent) return true; } Vector2D vertexFirst = vertices[0]; Vector2D vertexLast = vertices[^1]; if (line.From == vertexFirst && line.To == vertexLast) return true; if (line.From == vertexLast && line.To == vertexFirst) return true; return false; } public static float IntersectionParameterT(Line left, Line right) { float numerator = (left.From.X - right.From.X) * (right.From.Y - right.To.Y) - (left.From.Y - right.From.Y) * (right.From.X - right.To.X); float denominator = (left.From.X - left.To.X) * (right.From.Y - right.To.Y) - (left.From.Y - left.To.Y) * (right.From.X - right.To.X); // Lines are parallel if (denominator == 0) return float.NaN; return numerator / denominator; } public static Vector2D Lerp(Line line, float t) => new Vector2D( line.From.X + (line.To.X - line.From.X) * t, line.From.Y + (line.To.Y - line.From.Y) * t ); public static Vector2D ClosestPointTo(Line line, Vector2D point) { // Convert edge points to vectors var edgeVector = new Vector2D(line.To.X - line.From.X, line.To.Y - line.From.Y); var pointVector = new Vector2D(point.X - line.From.X, point.Y - line.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 = line.From.X + t * edgeVector.X; float closestY = line.From.Y + t * edgeVector.Y; return new Vector2D((float)closestX, (float)closestY); } public static Vector2D IntersectionPoint(Line left, Line right) => Vector2D.Lerp(left.From, left.To, IntersectionParameterT(left, right)); public static bool Intersects(Line left, Line right) { int o1 = Vector2D.Orientation(left.From, left.To, right.From); int o2 = Vector2D.Orientation(left.From, left.To, right.To); int o3 = Vector2D.Orientation(right.From, right.To, left.From); int o4 = Vector2D.Orientation(right.From, right.To, left.To); if (o1 != o2 && o3 != o4) return true; if (o1 == 0 && OnSegment(left, right.From)) return true; if (o2 == 0 && OnSegment(left, right.To)) return true; if (o3 == 0 && OnSegment(right, left.From)) return true; if (o4 == 0 && OnSegment(right, left.To)) return true; return false; } public static bool OnSegment(Line line, Vector2D point) { if (point.X <= MathF.Max(line.From.X, line.To.X) && point.X >= MathF.Min(line.From.X, line.To.X) && point.Y <= MathF.Max(line.From.Y, line.To.Y) && point.Y >= MathF.Min(line.From.Y, line.To.Y)) return true; return false; } public static bool Intersects(Line left, Line right, [NotNullWhen(returnValue: true)] out Vector2D? point) { point = null; bool result = Intersects(left, right); if (result) point = IntersectionPoint(left, right); return result; } public static bool ApproximatelyEquals(Line left, Line right) => left.From.ApproximatelyEquals(right.From) && left.To.ApproximatelyEquals(right.To); } public static class LineExtensions { public static bool ApproximatelyEquals(this Line left, Line right) => Line.ApproximatelyEquals(left, right); }