Engine-Pong/Game/Physics2D/PhysicsMath.cs

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using System;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
using Microsoft.Xna.Framework;
namespace Syntriax.Engine.Physics2D;
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public record Line(Vector2 From, Vector2 To)
{
public Vector2 Direction => Vector2.Normalize(To - From);
public float Length => (From - To).Length();
public float LengthSquared => (From - To).LengthSquared();
}
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public record LineEquation(float Slope, float OffsetY);
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public record Triangle(Vector2 A, Vector2 B, Vector2 C);
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public record Circle(Vector2 Position, float Radius);
public record AABB(Vector2 LowerBoundary, Vector2 UpperBoundary);
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public static class PhysicsMath
{
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public static Vector2 Scale(this Vector2 original, Vector2 scale)
=> new Vector2(original.X * scale.X, original.Y * scale.Y);
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public static Vector2 ClosestPointTo(this Line line, Vector2 point)
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{
// Convert edge points to vectors
var edgeVector = new Vector2(line.To.X - line.From.X, line.To.Y - line.From.Y);
var pointVector = new Vector2(point.X - line.From.X, point.Y - line.From.Y);
// Calculate the projection of pointVector onto edgeVector
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float t = (pointVector.X * edgeVector.X + pointVector.Y * edgeVector.Y) / (edgeVector.X * edgeVector.X + edgeVector.Y * edgeVector.Y);
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// Clamp t to the range [0, 1] to ensure the closest point is on the edge
t = Math.Max(0, Math.Min(1, t));
// Calculate the closest point on the edge
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float closestX = line.From.X + t * edgeVector.X;
float closestY = line.From.Y + t * edgeVector.Y;
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return new Vector2((float)closestX, (float)closestY);
}
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public static float GetArea(this Triangle triangle)
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{
return Math.Abs((triangle.A.X * (triangle.B.Y - triangle.C.Y) +
triangle.B.X * (triangle.C.Y - triangle.A.Y) +
triangle.C.X * (triangle.A.Y - triangle.B.Y)) * .5f);
}
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public static Circle ToCircumCircle(this Triangle triangle)
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{
Vector2 midAB = (triangle.A + triangle.B) / 2;
Vector2 midBC = (triangle.B + triangle.C) / 2;
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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);
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Vector2 center;
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if (Math.Abs(slopeAB - slopeBC) > float.Epsilon)
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{
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float x = (slopeAB * slopeBC * (triangle.A.Y - triangle.C.Y) + slopeBC * (triangle.A.X + triangle.B.X) - slopeAB * (triangle.B.X + triangle.C.X)) / (2 * (slopeBC - slopeAB));
float y = -(x - (triangle.A.X + triangle.B.X) / 2) / slopeAB + (triangle.A.Y + triangle.B.Y) / 2;
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center = new Vector2((float)x, (float)y);
}
else
center = (midAB + midBC) * .5f;
return new(center, Vector2.Distance(center, triangle.A));
}
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public static Triangle ToSuperTriangle(IList<Vector2> vertices)
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{
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float minX = float.MaxValue, minY = float.MaxValue;
float maxX = float.MinValue, maxY = float.MinValue;
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foreach (Vector2 point in vertices)
{
minX = Math.Min(minX, point.X);
minY = Math.Min(minY, point.Y);
maxX = Math.Max(maxX, point.X);
maxY = Math.Max(maxY, point.Y);
}
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float dx = maxX - minX;
float dy = maxY - minY;
float deltaMax = Math.Max(dx, dy);
float midX = (minX + maxX) / 2;
float midY = (minY + maxY) / 2;
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Vector2 p1 = new Vector2((float)midX - 20f * (float)deltaMax, (float)midY - (float)deltaMax);
Vector2 p2 = new Vector2((float)midX, (float)midY + 20 * (float)deltaMax);
Vector2 p3 = new Vector2((float)midX + 20 * (float)deltaMax, (float)midY - (float)deltaMax);
return new Triangle(p1, p2, p3);
}
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public static IList<Line> ToLines(this IList<Vector2> vertices)
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{
List<Line> lines = new List<Line>(vertices.Count - 1);
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ToLines(vertices, lines);
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return lines;
}
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public static void ToLines(this IList<Vector2> vertices, IList<Line> lines)
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{
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]));
}
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public static bool ExistIn(Line lineToCheck, List<Vector2> vertices)
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{
for (int i = 0; i < vertices.Count - 1; i++)
{
Vector2 vertexCurrent = vertices[i];
Vector2 vertexNext = vertices[i];
if (lineToCheck.From == vertexCurrent && lineToCheck.To == vertexNext) return true;
if (lineToCheck.From == vertexNext && lineToCheck.To == vertexCurrent) return true;
}
Vector2 vertexFirst = vertices[0];
Vector2 vertexLast = vertices[^1];
if (lineToCheck.From == vertexFirst && lineToCheck.To == vertexLast) return true;
if (lineToCheck.From == vertexLast && lineToCheck.To == vertexFirst) return true;
return false;
}
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public static bool LaysOn(this Vector2 point, Line line)
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=> ApproximatelyEqualEpsilon(line.Resolve(point.X), point, float.Epsilon);
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public static LineEquation ToLineEquation(this Line line)
{
Vector2 slopeVector = line.To - line.From;
float slope = slopeVector.Y / slopeVector.X;
float yOffset = line.From.Y - (slope * line.From.X);
return new LineEquation(slope, yOffset);
}
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// Given three collinear points p, q, r, the function checks if
// point q lies on line segment 'pr'
public static bool OnSegment(Vector2 p, Vector2 q, Vector2 r)
{
if (q.X <= Math.Max(p.X, r.X) && q.X >= Math.Min(p.X, r.X) &&
q.Y <= Math.Max(p.Y, r.Y) && q.Y >= Math.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(Vector2 p, Vector2 q, Vector2 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(Vector2 p0, Vector2 p1, Vector2 q0, Vector2 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 float IntersectionParameterT(this Line l0, Line l1)
=> ((l1.From.X - l0.From.X) * (l0.To.Y - l0.From.Y) - (l1.From.Y - l0.From.Y) * (l0.To.X - l0.From.X)) /
((l1.To.Y - l1.From.Y) * (l0.To.X - l0.From.X) - (l1.To.X - l1.From.X) * (l0.To.Y - l0.From.Y));
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public static float GetT(this Line line, Vector2 point)
{
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// if (!point.LaysOn(line))
// throw new Exception("Point does not lay on Line");
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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;
return pointX / max;
}
public static Vector2 Resolve(this Line line, float x)
{
LineEquation lineEquation = line.ToLineEquation();
// y = mx + b
float y = lineEquation.Slope * x + lineEquation.OffsetY;
return new Vector2(x, y);
}
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public static Vector2 IntersectionPoint(this Line l1, Line l2)
=> Vector2.Lerp(l1.From, l1.To, IntersectionParameterT(l1, l2));
public static bool Intersects(this Line l1, Line l2)
{
int o1 = Orientation(l1.From, l1.To, l2.From);
int o2 = Orientation(l1.From, l1.To, l2.To);
int o3 = Orientation(l2.From, l2.To, l1.From);
int o4 = Orientation(l2.From, l2.To, l1.To);
if (o1 != o2 && o3 != o4)
return true;
if (o1 == 0 && OnSegment(l1.From, l2.From, l1.To)) return true;
if (o2 == 0 && OnSegment(l1.From, l2.To, l1.To)) return true;
if (o3 == 0 && OnSegment(l2.From, l1.From, l2.To)) return true;
if (o4 == 0 && OnSegment(l2.From, l1.To, l2.To)) return true;
return false;
}
public static bool Intersects(this Line l1, Line l2, [NotNullWhen(returnValue: true)] out Vector2? point)
{
point = null;
bool result = Intersects(l1, l2);
if (result)
point = IntersectionPoint(l1, l2);
return result;
}
public static bool Intersects(this Circle circle, Circle circleOther)
{
float distanceSquared = (circle.Position - circleOther.Position).LengthSquared();
float radiusSumSquared = circle.Radius * circle.Radius + circleOther.Radius * circleOther.Radius;
return distanceSquared < radiusSumSquared;
}
public static bool Inside(this Triangle triangle, Vector2 point)
{
float originalTriangleArea = GetArea(triangle);
float pointTriangleArea1 = GetArea(new Triangle(point, triangle.B, triangle.C));
float pointTriangleArea2 = GetArea(new Triangle(triangle.A, point, triangle.C));
float pointTriangleArea3 = GetArea(new Triangle(triangle.A, triangle.B, point));
float pointTriangleAreasSum = pointTriangleArea1 + pointTriangleArea2 + pointTriangleArea3;
return originalTriangleArea >= pointTriangleAreasSum;
}
public static bool Inside(this AABB aabb, Vector2 point)
=> point.X >= aabb.LowerBoundary.X && point.X <= aabb.UpperBoundary.X &&
point.Y >= aabb.LowerBoundary.Y && point.Y <= aabb.UpperBoundary.Y;
public static bool Inside(this Circle circle, Vector2 point)
=> (circle.Position - point).LengthSquared() <= circle.Radius * circle.Radius;
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public static bool ApproximatelyEqualEpsilon(float a, float b, float epsilon)
{
if (a == b)
return true;
const float floatNormal = (1 << 23) * float.Epsilon;
float absA = Math.Abs(a);
float absB = Math.Abs(b);
float diff = Math.Abs(a - b);
if (a == 0.0f || b == 0.0f || diff < floatNormal)
return diff < (epsilon * floatNormal);
return diff / Math.Min((absA + absB), float.MaxValue) < epsilon;
}
public static bool ApproximatelyEqualEpsilon(Vector2 a, Vector2 b, float epsilon)
{
return ApproximatelyEqualEpsilon(a.X, b.X, epsilon) && ApproximatelyEqualEpsilon(a.Y, b.Y, epsilon);
}
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}