638 lines
20 KiB
C#
638 lines
20 KiB
C#
/*
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* Farseer Physics Engine based on Box2D.XNA port:
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* Copyright (c) 2010 Ian Qvist
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*
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* Box2D.XNA port of Box2D:
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* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
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*
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* Original source Box2D:
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* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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using System;
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using System.Diagnostics;
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using System.Runtime.InteropServices;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Common
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{
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public static class MathUtils
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{
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public static float Cross(Vector2 a, Vector2 b)
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{
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return a.X * b.Y - a.Y * b.X;
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}
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public static Vector2 Cross(Vector2 a, float s)
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{
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return new Vector2(s * a.Y, -s * a.X);
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}
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public static Vector2 Cross(float s, Vector2 a)
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{
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return new Vector2(-s * a.Y, s * a.X);
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}
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public static Vector2 Abs(Vector2 v)
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{
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return new Vector2(Math.Abs(v.X), Math.Abs(v.Y));
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}
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public static Vector2 Multiply(ref Mat22 A, Vector2 v)
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{
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return Multiply(ref A, ref v);
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}
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public static Vector2 Multiply(ref Mat22 A, ref Vector2 v)
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{
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return new Vector2(A.Col1.X * v.X + A.Col2.X * v.Y, A.Col1.Y * v.X + A.Col2.Y * v.Y);
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}
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public static Vector2 MultiplyT(ref Mat22 A, Vector2 v)
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{
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return MultiplyT(ref A, ref v);
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}
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public static Vector2 MultiplyT(ref Mat22 A, ref Vector2 v)
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{
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return new Vector2(v.X * A.Col1.X + v.Y * A.Col1.Y, v.X * A.Col2.X + v.Y * A.Col2.Y);
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}
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public static Vector2 Multiply(ref Transform T, Vector2 v)
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{
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return Multiply(ref T, ref v);
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}
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public static Vector2 Multiply(ref Transform T, ref Vector2 v)
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{
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return new Vector2(T.Position.X + T.R.Col1.X * v.X + T.R.Col2.X * v.Y,
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T.Position.Y + T.R.Col1.Y * v.X + T.R.Col2.Y * v.Y);
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}
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public static Vector2 MultiplyT(ref Transform T, Vector2 v)
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{
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return MultiplyT(ref T, ref v);
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}
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public static Vector2 MultiplyT(ref Transform T, ref Vector2 v)
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{
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Vector2 tmp = Vector2.Zero;
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tmp.X = v.X - T.Position.X;
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tmp.Y = v.Y - T.Position.Y;
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return MultiplyT(ref T.R, ref tmp);
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}
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// A^T * B
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public static void MultiplyT(ref Mat22 A, ref Mat22 B, out Mat22 C)
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{
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C = new Mat22();
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C.Col1.X = A.Col1.X * B.Col1.X + A.Col1.Y * B.Col1.Y;
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C.Col1.Y = A.Col2.X * B.Col1.X + A.Col2.Y * B.Col1.Y;
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C.Col2.X = A.Col1.X * B.Col2.X + A.Col1.Y * B.Col2.Y;
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C.Col2.Y = A.Col2.X * B.Col2.X + A.Col2.Y * B.Col2.Y;
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}
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// v2 = A.R' * (B.R * v1 + B.p - A.p) = (A.R' * B.R) * v1 + (B.p - A.p)
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public static void MultiplyT(ref Transform A, ref Transform B, out Transform C)
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{
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C = new Transform();
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MultiplyT(ref A.R, ref B.R, out C.R);
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C.Position.X = B.Position.X - A.Position.X;
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C.Position.Y = B.Position.Y - A.Position.Y;
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}
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public static void Swap<T>(ref T a, ref T b)
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{
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T tmp = a;
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a = b;
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b = tmp;
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}
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/// <summary>
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/// This function is used to ensure that a floating point number is
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/// not a NaN or infinity.
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/// </summary>
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/// <param name="x">The x.</param>
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/// <returns>
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/// <c>true</c> if the specified x is valid; otherwise, <c>false</c>.
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/// </returns>
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public static bool IsValid(float x)
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{
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if (float.IsNaN(x))
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{
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// NaN.
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return false;
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}
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return !float.IsInfinity(x);
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}
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public static bool IsValid(this Vector2 x)
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{
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return IsValid(x.X) && IsValid(x.Y);
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}
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/// <summary>
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/// This is a approximate yet fast inverse square-root.
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/// </summary>
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/// <param name="x">The x.</param>
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/// <returns></returns>
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public static float InvSqrt(float x)
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{
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FloatConverter convert = new FloatConverter();
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convert.x = x;
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float xhalf = 0.5f * x;
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convert.i = 0x5f3759df - (convert.i >> 1);
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x = convert.x;
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x = x * (1.5f - xhalf * x * x);
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return x;
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}
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public static int Clamp(int a, int low, int high)
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{
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return Math.Max(low, Math.Min(a, high));
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}
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public static float Clamp(float a, float low, float high)
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{
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return Math.Max(low, Math.Min(a, high));
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}
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public static Vector2 Clamp(Vector2 a, Vector2 low, Vector2 high)
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{
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return Vector2.Max(low, Vector2.Min(a, high));
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}
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public static void Cross(ref Vector2 a, ref Vector2 b, out float c)
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{
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c = a.X * b.Y - a.Y * b.X;
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}
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/// <summary>
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/// Return the angle between two vectors on a plane
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/// The angle is from vector 1 to vector 2, positive anticlockwise
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/// The result is between -pi -> pi
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/// </summary>
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public static double VectorAngle(ref Vector2 p1, ref Vector2 p2)
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{
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double theta1 = Math.Atan2(p1.Y, p1.X);
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double theta2 = Math.Atan2(p2.Y, p2.X);
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double dtheta = theta2 - theta1;
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while (dtheta > Math.PI)
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dtheta -= (2 * Math.PI);
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while (dtheta < -Math.PI)
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dtheta += (2 * Math.PI);
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return (dtheta);
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}
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public static double VectorAngle(Vector2 p1, Vector2 p2)
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{
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return VectorAngle(ref p1, ref p2);
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}
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/// <summary>
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/// Returns a positive number if c is to the left of the line going from a to b.
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/// </summary>
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/// <returns>Positive number if point is left, negative if point is right,
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/// and 0 if points are collinear.</returns>
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public static float Area(Vector2 a, Vector2 b, Vector2 c)
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{
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return Area(ref a, ref b, ref c);
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}
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/// <summary>
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/// Returns a positive number if c is to the left of the line going from a to b.
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/// </summary>
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/// <returns>Positive number if point is left, negative if point is right,
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/// and 0 if points are collinear.</returns>
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public static float Area(ref Vector2 a, ref Vector2 b, ref Vector2 c)
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{
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return a.X * (b.Y - c.Y) + b.X * (c.Y - a.Y) + c.X * (a.Y - b.Y);
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}
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/// <summary>
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/// Determines if three vertices are collinear (ie. on a straight line)
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/// </summary>
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/// <param name="a">First vertex</param>
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/// <param name="b">Second vertex</param>
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/// <param name="c">Third vertex</param>
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/// <returns></returns>
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public static bool Collinear(ref Vector2 a, ref Vector2 b, ref Vector2 c)
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{
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return Collinear(ref a, ref b, ref c, 0);
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}
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public static bool Collinear(ref Vector2 a, ref Vector2 b, ref Vector2 c, float tolerance)
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{
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return FloatInRange(Area(ref a, ref b, ref c), -tolerance, tolerance);
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}
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public static void Cross(float s, ref Vector2 a, out Vector2 b)
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{
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b = new Vector2(-s * a.Y, s * a.X);
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}
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public static bool FloatEquals(float value1, float value2)
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{
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return Math.Abs(value1 - value2) <= Settings.Epsilon;
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}
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/// <summary>
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/// Checks if a floating point Value is equal to another,
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/// within a certain tolerance.
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/// </summary>
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/// <param name="value1">The first floating point Value.</param>
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/// <param name="value2">The second floating point Value.</param>
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/// <param name="delta">The floating point tolerance.</param>
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/// <returns>True if the values are "equal", false otherwise.</returns>
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public static bool FloatEquals(float value1, float value2, float delta)
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{
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return FloatInRange(value1, value2 - delta, value2 + delta);
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}
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/// <summary>
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/// Checks if a floating point Value is within a specified
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/// range of values (inclusive).
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/// </summary>
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/// <param name="value">The Value to check.</param>
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/// <param name="min">The minimum Value.</param>
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/// <param name="max">The maximum Value.</param>
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/// <returns>True if the Value is within the range specified,
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/// false otherwise.</returns>
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public static bool FloatInRange(float value, float min, float max)
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{
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return (value >= min && value <= max);
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}
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#region Nested type: FloatConverter
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[StructLayout(LayoutKind.Explicit)]
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private struct FloatConverter
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{
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[FieldOffset(0)]
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public float x;
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[FieldOffset(0)]
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public int i;
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}
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#endregion
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}
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/// <summary>
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/// A 2-by-2 matrix. Stored in column-major order.
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/// </summary>
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public struct Mat22
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{
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public Vector2 Col1, Col2;
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/// <summary>
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/// Construct this matrix using columns.
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/// </summary>
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/// <param name="c1">The c1.</param>
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/// <param name="c2">The c2.</param>
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public Mat22(Vector2 c1, Vector2 c2)
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{
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Col1 = c1;
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Col2 = c2;
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}
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/// <summary>
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/// Construct this matrix using scalars.
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/// </summary>
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/// <param name="a11">The a11.</param>
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/// <param name="a12">The a12.</param>
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/// <param name="a21">The a21.</param>
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/// <param name="a22">The a22.</param>
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public Mat22(float a11, float a12, float a21, float a22)
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{
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Col1 = new Vector2(a11, a21);
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Col2 = new Vector2(a12, a22);
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}
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/// <summary>
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/// Construct this matrix using an angle. This matrix becomes
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/// an orthonormal rotation matrix.
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/// </summary>
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/// <param name="angle">The angle.</param>
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public Mat22(float angle)
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{
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// TODO_ERIN compute sin+cos together.
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float c = (float)Math.Cos(angle), s = (float)Math.Sin(angle);
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Col1 = new Vector2(c, s);
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Col2 = new Vector2(-s, c);
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}
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/// <summary>
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/// Extract the angle from this matrix (assumed to be
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/// a rotation matrix).
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/// </summary>
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/// <value></value>
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public float Angle
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{
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get { return (float)Math.Atan2(Col1.Y, Col1.X); }
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}
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public Mat22 Inverse
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{
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get
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{
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float a = Col1.X, b = Col2.X, c = Col1.Y, d = Col2.Y;
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float det = a * d - b * c;
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if (det != 0.0f)
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{
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det = 1.0f / det;
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}
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Mat22 result = new Mat22();
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result.Col1.X = det * d;
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result.Col1.Y = -det * c;
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result.Col2.X = -det * b;
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result.Col2.Y = det * a;
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return result;
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}
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}
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/// <summary>
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/// Initialize this matrix using columns.
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/// </summary>
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/// <param name="c1">The c1.</param>
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/// <param name="c2">The c2.</param>
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public void Set(Vector2 c1, Vector2 c2)
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{
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Col1 = c1;
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Col2 = c2;
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}
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/// <summary>
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/// Initialize this matrix using an angle. This matrix becomes
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/// an orthonormal rotation matrix.
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/// </summary>
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/// <param name="angle">The angle.</param>
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public void Set(float angle)
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{
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float c = (float)Math.Cos(angle), s = (float)Math.Sin(angle);
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Col1.X = c;
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Col2.X = -s;
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Col1.Y = s;
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Col2.Y = c;
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}
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/// <summary>
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/// Set this to the identity matrix.
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/// </summary>
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public void SetIdentity()
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{
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Col1.X = 1.0f;
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Col2.X = 0.0f;
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Col1.Y = 0.0f;
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Col2.Y = 1.0f;
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}
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/// <summary>
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/// Set this matrix to all zeros.
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/// </summary>
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public void SetZero()
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{
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Col1.X = 0.0f;
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Col2.X = 0.0f;
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Col1.Y = 0.0f;
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Col2.Y = 0.0f;
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}
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/// <summary>
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/// Solve A * x = b, where b is a column vector. This is more efficient
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/// than computing the inverse in one-shot cases.
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/// </summary>
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/// <param name="b">The b.</param>
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/// <returns></returns>
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public Vector2 Solve(Vector2 b)
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{
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float a11 = Col1.X, a12 = Col2.X, a21 = Col1.Y, a22 = Col2.Y;
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float det = a11 * a22 - a12 * a21;
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if (det != 0.0f)
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{
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det = 1.0f / det;
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}
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return new Vector2(det * (a22 * b.X - a12 * b.Y), det * (a11 * b.Y - a21 * b.X));
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}
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public static void Add(ref Mat22 A, ref Mat22 B, out Mat22 R)
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{
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R.Col1 = A.Col1 + B.Col1;
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R.Col2 = A.Col2 + B.Col2;
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}
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}
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/// <summary>
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/// A 3-by-3 matrix. Stored in column-major order.
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/// </summary>
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public struct Mat33
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{
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public Vector3 Col1, Col2, Col3;
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/// <summary>
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/// Construct this matrix using columns.
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/// </summary>
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/// <param name="c1">The c1.</param>
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/// <param name="c2">The c2.</param>
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/// <param name="c3">The c3.</param>
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public Mat33(Vector3 c1, Vector3 c2, Vector3 c3)
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{
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Col1 = c1;
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Col2 = c2;
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Col3 = c3;
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}
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/// <summary>
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/// Set this matrix to all zeros.
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/// </summary>
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public void SetZero()
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{
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Col1 = Vector3.Zero;
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Col2 = Vector3.Zero;
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Col3 = Vector3.Zero;
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}
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/// <summary>
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/// Solve A * x = b, where b is a column vector. This is more efficient
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/// than computing the inverse in one-shot cases.
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/// </summary>
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/// <param name="b">The b.</param>
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/// <returns></returns>
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public Vector3 Solve33(Vector3 b)
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{
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float det = Vector3.Dot(Col1, Vector3.Cross(Col2, Col3));
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if (det != 0.0f)
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{
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det = 1.0f / det;
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}
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return new Vector3(det * Vector3.Dot(b, Vector3.Cross(Col2, Col3)),
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det * Vector3.Dot(Col1, Vector3.Cross(b, Col3)),
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det * Vector3.Dot(Col1, Vector3.Cross(Col2, b)));
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}
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/// <summary>
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/// Solve A * x = b, where b is a column vector. This is more efficient
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/// than computing the inverse in one-shot cases. Solve only the upper
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/// 2-by-2 matrix equation.
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/// </summary>
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/// <param name="b">The b.</param>
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/// <returns></returns>
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public Vector2 Solve22(Vector2 b)
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{
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float a11 = Col1.X, a12 = Col2.X, a21 = Col1.Y, a22 = Col2.Y;
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float det = a11 * a22 - a12 * a21;
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if (det != 0.0f)
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{
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det = 1.0f / det;
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}
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return new Vector2(det * (a22 * b.X - a12 * b.Y), det * (a11 * b.Y - a21 * b.X));
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}
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}
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/// <summary>
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/// A transform contains translation and rotation. It is used to represent
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/// the position and orientation of rigid frames.
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/// </summary>
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public struct Transform
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{
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public Vector2 Position;
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public Mat22 R;
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/// <summary>
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/// Initialize using a position vector and a rotation matrix.
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/// </summary>
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/// <param name="position">The position.</param>
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/// <param name="r">The r.</param>
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public Transform(ref Vector2 position, ref Mat22 r)
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{
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Position = position;
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R = r;
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}
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/// <summary>
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/// Calculate the angle that the rotation matrix represents.
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/// </summary>
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/// <value></value>
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public float Angle
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{
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get { return (float)Math.Atan2(R.Col1.Y, R.Col1.X); }
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}
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/// <summary>
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/// Set this to the identity transform.
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/// </summary>
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public void SetIdentity()
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{
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Position = Vector2.Zero;
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R.SetIdentity();
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}
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/// <summary>
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/// Set this based on the position and angle.
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/// </summary>
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/// <param name="position">The position.</param>
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/// <param name="angle">The angle.</param>
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public void Set(Vector2 position, float angle)
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{
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Position = position;
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R.Set(angle);
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}
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}
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/// <summary>
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/// This describes the motion of a body/shape for TOI computation.
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/// Shapes are defined with respect to the body origin, which may
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/// no coincide with the center of mass. However, to support dynamics
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/// we must interpolate the center of mass position.
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/// </summary>
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public struct Sweep
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{
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/// <summary>
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/// World angles
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/// </summary>
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public float A;
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public float A0;
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/// <summary>
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/// Fraction of the current time step in the range [0,1]
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/// c0 and a0 are the positions at alpha0.
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/// </summary>
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public float Alpha0;
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/// <summary>
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/// Center world positions
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/// </summary>
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public Vector2 C;
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public Vector2 C0;
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/// <summary>
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/// Local center of mass position
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/// </summary>
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public Vector2 LocalCenter;
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/// <summary>
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/// Get the interpolated transform at a specific time.
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/// </summary>
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/// <param name="xf">The transform.</param>
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/// <param name="beta">beta is a factor in [0,1], where 0 indicates alpha0.</param>
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public void GetTransform(out Transform xf, float beta)
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{
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xf = new Transform();
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xf.Position.X = (1.0f - beta) * C0.X + beta * C.X;
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xf.Position.Y = (1.0f - beta) * C0.Y + beta * C.Y;
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float angle = (1.0f - beta) * A0 + beta * A;
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xf.R.Set(angle);
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// Shift to origin
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xf.Position -= MathUtils.Multiply(ref xf.R, ref LocalCenter);
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}
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/// <summary>
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/// Advance the sweep forward, yielding a new initial state.
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/// </summary>
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/// <param name="alpha">new initial time..</param>
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public void Advance(float alpha)
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{
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Debug.Assert(Alpha0 < 1.0f);
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float beta = (alpha - Alpha0) / (1.0f - Alpha0);
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C0.X = (1.0f - beta) * C0.X + beta * C.X;
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C0.Y = (1.0f - beta) * C0.Y + beta * C.Y;
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A0 = (1.0f - beta) * A0 + beta * A;
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Alpha0 = alpha;
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}
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/// <summary>
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/// Normalize the angles.
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/// </summary>
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public void Normalize()
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|
{
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float d = MathHelper.TwoPi * (float)Math.Floor(A0 / MathHelper.TwoPi);
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A0 -= d;
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A -= d;
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}
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}
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} |