839 lines
37 KiB
C#
839 lines
37 KiB
C#
// Copyright (c) Xenko contributors (https://xenko.com) and Silicon Studio Corp. (https://www.siliconstudio.co.jp)
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// Distributed under the MIT license. See the LICENSE.md file in the project root for more information.
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//
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// -----------------------------------------------------------------------------
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// Original code from SlimMath project. http://code.google.com/p/slimmath/
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// Greetings to SlimDX Group. Original code published with the following license:
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// -----------------------------------------------------------------------------
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/*
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* Copyright (c) 2007-2011 SlimDX Group
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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using System;
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using System.Globalization;
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using System.Runtime.InteropServices;
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using System.Runtime.Serialization;
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namespace math
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{
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/// <summary>
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/// Represents a plane in three dimensional space.
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/// </summary>
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[DataContract]
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[StructLayout(LayoutKind.Sequential, Pack = 4)]
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public struct Plane : IEquatable<Plane>, IFormattable
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{
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/// <summary>
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/// The normal vector of the plane.
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/// </summary>
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public Vec3 Normal;
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/// <summary>
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/// The distance of the plane along its normal from the origin.
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/// </summary>
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public float D;
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Plane"/> struct.
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/// </summary>
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/// <param name="value">The value that will be assigned to all components.</param>
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public Plane(float value)
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{
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Normal.X = Normal.Y = Normal.Z = D = value;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Plane"/> struct.
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/// </summary>
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/// <param name="a">The X component of the normal.</param>
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/// <param name="b">The Y component of the normal.</param>
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/// <param name="c">The Z component of the normal.</param>
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/// <param name="d">The distance of the plane along its normal from the origin.</param>
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public Plane(float a, float b, float c, float d)
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{
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Normal.X = a;
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Normal.Y = b;
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Normal.Z = c;
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D = d;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="Plane"/> struct.
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/// </summary>
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/// <param name="point">Any point that lies along the plane.</param>
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/// <param name="normal">The normal vector to the plane.</param>
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public Plane(Vec3 point, Vec3 normal)
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{
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this.Normal = normal;
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this.D = Vec3.Dot(normal, point);
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Plane"/> struct.
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/// </summary>
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/// <param name="value">The normal of the plane.</param>
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/// <param name="d">The distance of the plane along its normal from the origin</param>
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public Plane(Vec3 value, float d)
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{
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Normal = value;
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D = d;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Plane"/> struct.
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/// </summary>
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/// <param name="point1">First point of a triangle defining the plane.</param>
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/// <param name="point2">Second point of a triangle defining the plane.</param>
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/// <param name="point3">Third point of a triangle defining the plane.</param>
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public Plane(Vec3 point1, Vec3 point2, Vec3 point3)
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{
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float x1 = point2.X - point1.X;
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float y1 = point2.Y - point1.Y;
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float z1 = point2.Z - point1.Z;
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float x2 = point3.X - point1.X;
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float y2 = point3.Y - point1.Y;
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float z2 = point3.Z - point1.Z;
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float yz = (y1 * z2) - (z1 * y2);
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float xz = (z1 * x2) - (x1 * z2);
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float xy = (x1 * y2) - (y1 * x2);
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float invPyth = 1.0f / (float)(Math.Sqrt((yz * yz) + (xz * xz) + (xy * xy)));
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Normal.X = yz * invPyth;
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Normal.Y = xz * invPyth;
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Normal.Z = xy * invPyth;
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D = -((Normal.X * point1.X) + (Normal.Y * point1.Y) + (Normal.Z * point1.Z));
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Plane"/> struct.
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/// </summary>
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/// <param name="values">The values to assign to the A, B, C, and D components of the plane. This must be an array with four elements.</param>
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/// <exception cref="ArgumentNullException">Thrown when <paramref name="values"/> is <c>null</c>.</exception>
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/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="values"/> contains more or less than four elements.</exception>
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public Plane(float[] values)
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{
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if (values == null)
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throw new ArgumentNullException("values");
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if (values.Length != 4)
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throw new ArgumentOutOfRangeException("values", "There must be four and only four input values for Plane.");
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Normal.X = values[0];
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Normal.Y = values[1];
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Normal.Z = values[2];
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D = values[3];
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}
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/// <summary>
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/// Gets or sets the component at the specified index.
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/// </summary>
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/// <value>The value of the A, B, C, or D component, depending on the index.</value>
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/// <param name="index">The index of the component to access. Use 0 for the A component, 1 for the B component, 2 for the C component, and 3 for the D component.</param>
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/// <returns>The value of the component at the specified index.</returns>
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/// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="index"/> is out of the range [0, 3].</exception>
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public float this[int index]
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{
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get
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{
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switch (index)
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{
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case 0: return Normal.X;
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case 1: return Normal.Y;
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case 2: return Normal.Z;
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case 3: return D;
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}
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throw new ArgumentOutOfRangeException("index", "Indices for Plane run from 0 to 3, inclusive.");
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}
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set
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{
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switch (index)
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{
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case 0: Normal.X = value; break;
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case 1: Normal.Y = value; break;
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case 2: Normal.Z = value; break;
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case 3: D = value; break;
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default: throw new ArgumentOutOfRangeException("index", "Indices for Plane run from 0 to 3, inclusive.");
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}
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}
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}
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/// <summary>
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/// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
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/// </summary>
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public void Negate()
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{
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Normal.X = -Normal.X;
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Normal.Y = -Normal.Y;
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Normal.Z = -Normal.Z;
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D = -D;
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}
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/// <summary>
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/// Changes the coefficients of the normal vector of the plane to make it of unit length.
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/// </summary>
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public void Normalize()
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{
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float magnitude = 1.0f / (float)(Math.Sqrt((Normal.X * Normal.X) + (Normal.Y * Normal.Y) + (Normal.Z * Normal.Z)));
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Normal.X *= magnitude;
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Normal.Y *= magnitude;
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Normal.Z *= magnitude;
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D *= magnitude;
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}
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/// <summary>
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/// Creates an array containing the elements of the plane.
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/// </summary>
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/// <returns>A four-element array containing the components of the plane.</returns>
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public float[] ToArray()
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{
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return new float[] { Normal.X, Normal.Y, Normal.Z, D };
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a point.
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/// </summary>
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/// <param name="point">The point to test.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public PlaneIntersectionType Intersects(ref Vec3 point)
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{
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return CollisionHelper.PlaneIntersectsPoint(ref this, ref point);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a <see cref="math.Ray"/>.
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/// </summary>
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/// <param name="ray">The ray to test.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public bool Intersects(ref Ray ray)
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{
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float distance;
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return CollisionHelper.RayIntersectsPlane(ref ray, ref this, out distance);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a <see cref="math.Ray"/>.
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/// </summary>
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/// <param name="ray">The ray to test.</param>
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/// <param name="distance">When the method completes, contains the distance of the intersection,
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/// or 0 if there was no intersection.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public bool Intersects(ref Ray ray, out float distance)
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{
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return CollisionHelper.RayIntersectsPlane(ref ray, ref this, out distance);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a <see cref="math.Ray"/>.
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/// </summary>
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/// <param name="ray">The ray to test.</param>
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/// <param name="point">When the method completes, contains the point of intersection,
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/// or <see cref="math.Vec3.Zero"/> if there was no intersection.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public bool Intersects(ref Ray ray, out Vec3 point)
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{
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return CollisionHelper.RayIntersectsPlane(ref ray, ref this, out point);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a <see cref="math.Plane"/>.
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/// </summary>
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/// <param name="plane">The plane to test.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public bool Intersects(ref Plane plane)
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{
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return CollisionHelper.PlaneIntersectsPlane(ref this, ref plane);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a <see cref="math.Plane"/>.
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/// </summary>
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/// <param name="plane">The plane to test.</param>
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/// <param name="line">When the method completes, contains the line of intersection
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/// as a <see cref="math.Ray"/>, or a zero ray if there was no intersection.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public bool Intersects(ref Plane plane, out Ray line)
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{
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return CollisionHelper.PlaneIntersectsPlane(ref this, ref plane, out line);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a triangle.
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/// </summary>
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/// <param name="vertex1">The first vertex of the triangle to test.</param>
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/// <param name="vertex2">The second vertex of the triagnle to test.</param>
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/// <param name="vertex3">The third vertex of the triangle to test.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public PlaneIntersectionType Intersects(ref Vec3 vertex1, ref Vec3 vertex2, ref Vec3 vertex3)
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{
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return CollisionHelper.PlaneIntersectsTriangle(ref this, ref vertex1, ref vertex2, ref vertex3);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a <see cref="math.BoundingBox"/>.
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/// </summary>
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/// <param name="box">The box to test.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public PlaneIntersectionType Intersects(ref BoundingBox box)
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{
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return CollisionHelper.PlaneIntersectsBox(ref this, ref box);
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}
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/// <summary>
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/// Determines if there is an intersection between the current object and a <see cref="math.BoundingSphere"/>.
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/// </summary>
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/// <param name="sphere">The sphere to test.</param>
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/// <returns>Whether the two objects intersected.</returns>
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public PlaneIntersectionType Intersects(ref BoundingSphere sphere)
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{
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return CollisionHelper.PlaneIntersectsSphere(ref this, ref sphere);
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}
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/// <summary>
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/// Scales the plane by the given scaling factor.
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/// </summary>
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/// <param name="value">The plane to scale.</param>
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/// <param name="scale">The amount by which to scale the plane.</param>
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/// <param name="result">When the method completes, contains the scaled plane.</param>
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public static void Multiply(ref Plane value, float scale, out Plane result)
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{
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result.Normal.X = value.Normal.X * scale;
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result.Normal.Y = value.Normal.Y * scale;
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result.Normal.Z = value.Normal.Z * scale;
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result.D = value.D * scale;
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}
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/// <summary>
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/// Scales the plane by the given scaling factor.
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/// </summary>
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/// <param name="value">The plane to scale.</param>
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/// <param name="scale">The amount by which to scale the plane.</param>
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/// <returns>The scaled plane.</returns>
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public static Plane Multiply(Plane value, float scale)
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{
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return new Plane(value.Normal.X * scale, value.Normal.Y * scale, value.Normal.Z * scale, value.D * scale);
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}
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/// <summary>
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/// Calculates the dot product of the specified vector and plane.
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/// </summary>
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/// <param name="left">The source plane.</param>
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/// <param name="right">The source vector.</param>
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/// <param name="result">When the method completes, contains the dot product of the specified plane and vector.</param>
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public static void Dot(ref Plane left, ref Vec4 right, out float result)
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{
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result = (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + (left.D * right.W);
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}
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/// <summary>
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/// Calculates the dot product of the specified vector and plane.
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/// </summary>
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/// <param name="left">The source plane.</param>
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/// <param name="right">The source vector.</param>
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/// <returns>The dot product of the specified plane and vector.</returns>
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public static float Dot(Plane left, Vec4 right)
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{
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return (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + (left.D * right.W);
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}
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/// <summary>
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/// Calculates the dot product of a specified vector and the normal of the plane plus the distance value of the plane.
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/// </summary>
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/// <param name="left">The source plane.</param>
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/// <param name="right">The source vector.</param>
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/// <param name="result">When the method completes, contains the dot product of a specified vector and the normal of the Plane plus the distance value of the plane.</param>
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public static void DotCoordinate(ref Plane left, ref Vec3 right, out float result)
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{
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result = (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + left.D;
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}
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/// <summary>
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/// Calculates the dot product of a specified vector and the normal of the plane plus the distance value of the plane.
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/// </summary>
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/// <param name="left">The source plane.</param>
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/// <param name="right">The source vector.</param>
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/// <returns>The dot product of a specified vector and the normal of the Plane plus the distance value of the plane.</returns>
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public static float DotCoordinate(Plane left, Vec3 right)
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{
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return (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z) + left.D;
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}
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/// <summary>
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/// Calculates the dot product of the specified vector and the normal of the plane.
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/// </summary>
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/// <param name="left">The source plane.</param>
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/// <param name="right">The source vector.</param>
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/// <param name="result">When the method completes, contains the dot product of the specified vector and the normal of the plane.</param>
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public static void DotNormal(ref Plane left, ref Vec3 right, out float result)
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{
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result = (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z);
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}
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/// <summary>
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/// Calculates the dot product of the specified vector and the normal of the plane.
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/// </summary>
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/// <param name="left">The source plane.</param>
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/// <param name="right">The source vector.</param>
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/// <returns>The dot product of the specified vector and the normal of the plane.</returns>
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public static float DotNormal(Plane left, Vec3 right)
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{
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return (left.Normal.X * right.X) + (left.Normal.Y * right.Y) + (left.Normal.Z * right.Z);
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}
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/// <summary>
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/// Projects a point onto a plane.
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/// </summary>
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/// <param name="plane">The plane to project the point to.</param>
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/// <param name="point">The point to project.</param>
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/// <param name="result">The projected point.</param>
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public static void Project(ref Plane plane, ref Vec3 point, out Vec3 result)
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{
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float distance;
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DotCoordinate(ref plane, ref point, out distance);
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// compute: point - distance * plane.Normal
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Vec3.Multiply(ref plane.Normal, distance, out result);
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Vec3.Subtract(ref point, ref result, out result);
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}
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/// <summary>
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/// Projects a point onto a plane.
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/// </summary>
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/// <param name="plane">The plane to project the point to.</param>
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/// <param name="point">The point to project.</param>
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/// <returns>The projected point.</returns>
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public static Vec3 Project(Plane plane, Vec3 point)
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{
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Vec3 result;
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Project(ref plane, ref point, out result);
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return result;
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}
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/// <summary>
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/// Changes the coefficients of the normal vector of the plane to make it of unit length.
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/// </summary>
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/// <param name="plane">The source plane.</param>
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/// <param name="result">When the method completes, contains the normalized plane.</param>
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public static void Normalize(ref Plane plane, out Plane result)
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{
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float magnitude = 1.0f / (float)(Math.Sqrt((plane.Normal.X * plane.Normal.X) + (plane.Normal.Y * plane.Normal.Y) + (plane.Normal.Z * plane.Normal.Z)));
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result.Normal.X = plane.Normal.X * magnitude;
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result.Normal.Y = plane.Normal.Y * magnitude;
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result.Normal.Z = plane.Normal.Z * magnitude;
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result.D = plane.D * magnitude;
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}
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/// <summary>
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/// Changes the coefficients of the normal vector of the plane to make it of unit length.
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/// </summary>
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/// <param name="plane">The source plane.</param>
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/// <returns>The normalized plane.</returns>
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public static Plane Normalize(Plane plane)
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{
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float magnitude = 1.0f / (float)(Math.Sqrt((plane.Normal.X * plane.Normal.X) + (plane.Normal.Y * plane.Normal.Y) + (plane.Normal.Z * plane.Normal.Z)));
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return new Plane(plane.Normal.X * magnitude, plane.Normal.Y * magnitude, plane.Normal.Z * magnitude, plane.D * magnitude);
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}
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/// <summary>
|
|
/// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
|
|
/// </summary>
|
|
/// <param name="plane">The source plane.</param>
|
|
/// <param name="result">When the method completes, contains the flipped plane.</param>
|
|
public static void Negate(ref Plane plane, out Plane result)
|
|
{
|
|
result.Normal.X = -plane.Normal.X;
|
|
result.Normal.Y = -plane.Normal.Y;
|
|
result.Normal.Z = -plane.Normal.Z;
|
|
result.D = -plane.D;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
|
|
/// </summary>
|
|
/// <param name="plane">The source plane.</param>
|
|
/// <returns>The flipped plane.</returns>
|
|
public static Plane Negate(Plane plane)
|
|
{
|
|
float magnitude = 1.0f / (float)(Math.Sqrt((plane.Normal.X * plane.Normal.X) + (plane.Normal.Y * plane.Normal.Y) + (plane.Normal.Z * plane.Normal.Z)));
|
|
return new Plane(plane.Normal.X * magnitude, plane.Normal.Y * magnitude, plane.Normal.Z * magnitude, plane.D * magnitude);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a normalized plane by a quaternion rotation.
|
|
/// </summary>
|
|
/// <param name="plane">The normalized source plane.</param>
|
|
/// <param name="rotation">The quaternion rotation.</param>
|
|
/// <param name="result">When the method completes, contains the transformed plane.</param>
|
|
public static void Transform(ref Plane plane, ref Quaternion rotation, out Plane result)
|
|
{
|
|
float x2 = rotation.X + rotation.X;
|
|
float y2 = rotation.Y + rotation.Y;
|
|
float z2 = rotation.Z + rotation.Z;
|
|
float wx = rotation.W * x2;
|
|
float wy = rotation.W * y2;
|
|
float wz = rotation.W * z2;
|
|
float xx = rotation.X * x2;
|
|
float xy = rotation.X * y2;
|
|
float xz = rotation.X * z2;
|
|
float yy = rotation.Y * y2;
|
|
float yz = rotation.Y * z2;
|
|
float zz = rotation.Z * z2;
|
|
|
|
float x = plane.Normal.X;
|
|
float y = plane.Normal.Y;
|
|
float z = plane.Normal.Z;
|
|
|
|
result.Normal.X = ((x * ((1.0f - yy) - zz)) + (y * (xy - wz))) + (z * (xz + wy));
|
|
result.Normal.Y = ((x * (xy + wz)) + (y * ((1.0f - xx) - zz))) + (z * (yz - wx));
|
|
result.Normal.Z = ((x * (xz - wy)) + (y * (yz + wx))) + (z * ((1.0f - xx) - yy));
|
|
result.D = plane.D;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a normalized plane by a quaternion rotation.
|
|
/// </summary>
|
|
/// <param name="plane">The normalized source plane.</param>
|
|
/// <param name="rotation">The quaternion rotation.</param>
|
|
/// <returns>The transformed plane.</returns>
|
|
public static Plane Transform(Plane plane, Quaternion rotation)
|
|
{
|
|
Plane result;
|
|
float x2 = rotation.X + rotation.X;
|
|
float y2 = rotation.Y + rotation.Y;
|
|
float z2 = rotation.Z + rotation.Z;
|
|
float wx = rotation.W * x2;
|
|
float wy = rotation.W * y2;
|
|
float wz = rotation.W * z2;
|
|
float xx = rotation.X * x2;
|
|
float xy = rotation.X * y2;
|
|
float xz = rotation.X * z2;
|
|
float yy = rotation.Y * y2;
|
|
float yz = rotation.Y * z2;
|
|
float zz = rotation.Z * z2;
|
|
|
|
float x = plane.Normal.X;
|
|
float y = plane.Normal.Y;
|
|
float z = plane.Normal.Z;
|
|
|
|
result.Normal.X = ((x * ((1.0f - yy) - zz)) + (y * (xy - wz))) + (z * (xz + wy));
|
|
result.Normal.Y = ((x * (xy + wz)) + (y * ((1.0f - xx) - zz))) + (z * (yz - wx));
|
|
result.Normal.Z = ((x * (xz - wy)) + (y * (yz + wx))) + (z * ((1.0f - xx) - yy));
|
|
result.D = plane.D;
|
|
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms an array of normalized planes by a quaternion rotation.
|
|
/// </summary>
|
|
/// <param name="planes">The array of normalized planes to transform.</param>
|
|
/// <param name="rotation">The quaternion rotation.</param>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="planes"/> is <c>null</c>.</exception>
|
|
public static void Transform(Plane[] planes, ref Quaternion rotation)
|
|
{
|
|
if (planes == null)
|
|
throw new ArgumentNullException("planes");
|
|
|
|
float x2 = rotation.X + rotation.X;
|
|
float y2 = rotation.Y + rotation.Y;
|
|
float z2 = rotation.Z + rotation.Z;
|
|
float wx = rotation.W * x2;
|
|
float wy = rotation.W * y2;
|
|
float wz = rotation.W * z2;
|
|
float xx = rotation.X * x2;
|
|
float xy = rotation.X * y2;
|
|
float xz = rotation.X * z2;
|
|
float yy = rotation.Y * y2;
|
|
float yz = rotation.Y * z2;
|
|
float zz = rotation.Z * z2;
|
|
|
|
for (int i = 0; i < planes.Length; ++i)
|
|
{
|
|
float x = planes[i].Normal.X;
|
|
float y = planes[i].Normal.Y;
|
|
float z = planes[i].Normal.Z;
|
|
|
|
/*
|
|
* Note:
|
|
* Factor common arithmetic out of loop.
|
|
*/
|
|
planes[i].Normal.X = ((x * ((1.0f - yy) - zz)) + (y * (xy - wz))) + (z * (xz + wy));
|
|
planes[i].Normal.Y = ((x * (xy + wz)) + (y * ((1.0f - xx) - zz))) + (z * (yz - wx));
|
|
planes[i].Normal.Z = ((x * (xz - wy)) + (y * (yz + wx))) + (z * ((1.0f - xx) - yy));
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a normalized plane by a matrix.
|
|
/// </summary>
|
|
/// <param name="plane">The normalized source plane.</param>
|
|
/// <param name="transformation">The transformation matrix.</param>
|
|
/// <param name="result">When the method completes, contains the transformed plane.</param>
|
|
public static void Transform(ref Plane plane, ref Matrix transformation, out Plane result)
|
|
{
|
|
float x = plane.Normal.X;
|
|
float y = plane.Normal.Y;
|
|
float z = plane.Normal.Z;
|
|
float d = plane.D;
|
|
|
|
Matrix inverse;
|
|
Matrix.Invert(ref transformation, out inverse);
|
|
|
|
result.Normal.X = (((x * inverse.M11) + (y * inverse.M12)) + (z * inverse.M13)) + (d * inverse.M14);
|
|
result.Normal.Y = (((x * inverse.M21) + (y * inverse.M22)) + (z * inverse.M23)) + (d * inverse.M24);
|
|
result.Normal.Z = (((x * inverse.M31) + (y * inverse.M32)) + (z * inverse.M33)) + (d * inverse.M34);
|
|
result.D = (((x * inverse.M41) + (y * inverse.M42)) + (z * inverse.M43)) + (d * inverse.M44);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a normalized plane by a matrix.
|
|
/// </summary>
|
|
/// <param name="plane">The normalized source plane.</param>
|
|
/// <param name="transformation">The transformation matrix.</param>
|
|
/// <returns>When the method completes, contains the transformed plane.</returns>
|
|
public static Plane Transform(Plane plane, Matrix transformation)
|
|
{
|
|
Plane result;
|
|
float x = plane.Normal.X;
|
|
float y = plane.Normal.Y;
|
|
float z = plane.Normal.Z;
|
|
float d = plane.D;
|
|
|
|
transformation.Invert();
|
|
result.Normal.X = (((x * transformation.M11) + (y * transformation.M12)) + (z * transformation.M13)) + (d * transformation.M14);
|
|
result.Normal.Y = (((x * transformation.M21) + (y * transformation.M22)) + (z * transformation.M23)) + (d * transformation.M24);
|
|
result.Normal.Z = (((x * transformation.M31) + (y * transformation.M32)) + (z * transformation.M33)) + (d * transformation.M34);
|
|
result.D = (((x * transformation.M41) + (y * transformation.M42)) + (z * transformation.M43)) + (d * transformation.M44);
|
|
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms an array of normalized planes by a matrix.
|
|
/// </summary>
|
|
/// <param name="planes">The array of normalized planes to transform.</param>
|
|
/// <param name="transformation">The transformation matrix.</param>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="planes"/> is <c>null</c>.</exception>
|
|
public static void Transform(Plane[] planes, ref Matrix transformation)
|
|
{
|
|
if (planes == null)
|
|
throw new ArgumentNullException("planes");
|
|
|
|
Matrix inverse;
|
|
Matrix.Invert(ref transformation, out inverse);
|
|
|
|
for (int i = 0; i < planes.Length; ++i)
|
|
{
|
|
Transform(ref planes[i], ref transformation, out planes[i]);
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scales a plane by the given value.
|
|
/// </summary>
|
|
/// <param name="scale">The amount by which to scale the plane.</param>
|
|
/// <param name="plane">The plane to scale.</param>
|
|
/// <returns>The scaled plane.</returns>
|
|
public static Plane operator *(float scale, Plane plane)
|
|
{
|
|
return new Plane(plane.Normal.X * scale, plane.Normal.Y * scale, plane.Normal.Z * scale, plane.D * scale);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scales a plane by the given value.
|
|
/// </summary>
|
|
/// <param name="plane">The plane to scale.</param>
|
|
/// <param name="scale">The amount by which to scale the plane.</param>
|
|
/// <returns>The scaled plane.</returns>
|
|
public static Plane operator *(Plane plane, float scale)
|
|
{
|
|
return new Plane(plane.Normal.X * scale, plane.Normal.Y * scale, plane.Normal.Z * scale, plane.D * scale);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
|
|
/// </summary>
|
|
/// <returns>The negated plane.</returns>
|
|
public static Plane operator -(Plane plane)
|
|
{
|
|
return new Plane(-plane.Normal.X, -plane.Normal.Y, -plane.Normal.Z, -plane.D);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Tests for equality between two objects.
|
|
/// </summary>
|
|
/// <param name="left">The first value to compare.</param>
|
|
/// <param name="right">The second value to compare.</param>
|
|
/// <returns><c>true</c> if <paramref name="left"/> has the same value as <paramref name="right"/>; otherwise, <c>false</c>.</returns>
|
|
public static bool operator ==(Plane left, Plane right)
|
|
{
|
|
return left.Equals(right);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Tests for inequality between two objects.
|
|
/// </summary>
|
|
/// <param name="left">The first value to compare.</param>
|
|
/// <param name="right">The second value to compare.</param>
|
|
/// <returns><c>true</c> if <paramref name="left"/> has a different value than <paramref name="right"/>; otherwise, <c>false</c>.</returns>
|
|
public static bool operator !=(Plane left, Plane right)
|
|
{
|
|
return !left.Equals(right);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public override string ToString()
|
|
{
|
|
return string.Format(CultureInfo.CurrentCulture, "A:{0} B:{1} C:{2} D:{3}", Normal.X, Normal.Y, Normal.Z, D);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="format">The format.</param>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public string ToString(string format)
|
|
{
|
|
return string.Format(CultureInfo.CurrentCulture, "A:{0} B:{1} C:{2} D:{3}", Normal.X.ToString(format, CultureInfo.CurrentCulture),
|
|
Normal.Y.ToString(format, CultureInfo.CurrentCulture), Normal.Z.ToString(format, CultureInfo.CurrentCulture), D.ToString(format, CultureInfo.CurrentCulture));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="formatProvider">The format provider.</param>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public string ToString(IFormatProvider formatProvider)
|
|
{
|
|
return string.Format(formatProvider, "A:{0} B:{1} C:{2} D:{3}", Normal.X, Normal.Y, Normal.Z, D);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="format">The format.</param>
|
|
/// <param name="formatProvider">The format provider.</param>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public string ToString(string format, IFormatProvider formatProvider)
|
|
{
|
|
return string.Format(formatProvider, "A:{0} B:{1} C:{2} D:{3}", Normal.X.ToString(format, formatProvider),
|
|
Normal.Y.ToString(format, formatProvider), Normal.Z.ToString(format, formatProvider), D.ToString(format, formatProvider));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a hash code for this instance.
|
|
/// </summary>
|
|
/// <returns>
|
|
/// A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.
|
|
/// </returns>
|
|
public override int GetHashCode()
|
|
{
|
|
return Normal.GetHashCode() + D.GetHashCode();
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="math.Vec4"/> is equal to this instance.
|
|
/// </summary>
|
|
/// <param name="value">The <see cref="math.Vec4"/> to compare with this instance.</param>
|
|
/// <returns>
|
|
/// <c>true</c> if the specified <see cref="math.Vec4"/> is equal to this instance; otherwise, <c>false</c>.
|
|
/// </returns>
|
|
public bool Equals(Plane value)
|
|
{
|
|
return Normal == value.Normal && D == value.D;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="object"/> is equal to this instance.
|
|
/// </summary>
|
|
/// <param name="value">The <see cref="object"/> to compare with this instance.</param>
|
|
/// <returns>
|
|
/// <c>true</c> if the specified <see cref="object"/> is equal to this instance; otherwise, <c>false</c>.
|
|
/// </returns>
|
|
public override bool Equals(object value)
|
|
{
|
|
if (value == null)
|
|
return false;
|
|
|
|
if (value.GetType() != GetType())
|
|
return false;
|
|
|
|
return Equals((Plane)value);
|
|
}
|
|
|
|
#if SlimDX1xInterop
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="math.Plane"/> to <see cref="SlimDX.Plane"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator SlimDX.Plane(Plane value)
|
|
{
|
|
return new SlimDX.Plane(value.Normal, value.D);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="SlimDX.Plane"/> to <see cref="math.Plane"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator Plane(SlimDX.Plane value)
|
|
{
|
|
return new Plane(value.Normal, value.D);
|
|
}
|
|
#endif
|
|
|
|
#if XnaInterop
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="math.Plane"/> to <see cref="Microsoft.Xna.Framework.Plane"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator Microsoft.Xna.Framework.Plane(Plane value)
|
|
{
|
|
return new Microsoft.Xna.Framework.Plane(value.Normal, value.D);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="Microsoft.Xna.Framework.Plane"/> to <see cref="math.Plane"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator Plane(Microsoft.Xna.Framework.Plane value)
|
|
{
|
|
return new Plane(value.Normal, value.D);
|
|
}
|
|
#endif
|
|
}
|
|
}
|