323 lines
14 KiB
C#
323 lines
14 KiB
C#
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using System;
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using System.Runtime.CompilerServices;
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using Unity.IL2CPP.CompilerServices;
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using static Unity.Mathematics.math;
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namespace Unity.Mathematics.Geometry
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{
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/// <summary>
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/// Axis aligned bounding box (AABB) stored in min and max form.
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/// </summary>
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/// <remarks>
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/// Axis aligned bounding boxes (AABB) are boxes where each side is parallel with one of the Cartesian coordinate axes
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/// X, Y, and Z. AABBs are useful for approximating the region an object (or collection of objects) occupies and quickly
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/// testing whether or not that object (or collection of objects) is relevant. Because they are axis aligned, they
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/// are very cheap to construct and perform overlap tests with them.
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/// </remarks>
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[System.Serializable]
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[Il2CppEagerStaticClassConstruction]
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public struct MinMaxAABB : IEquatable<MinMaxAABB>
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{
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/// <summary>
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/// The minimum point contained by the AABB.
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/// </summary>
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/// <remarks>
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/// If any component of <see cref="Min"/> is greater than <see cref="Max"/> then this AABB is invalid.
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/// </remarks>
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/// <seealso cref="IsValid"/>
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public float3 Min;
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/// <summary>
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/// The maximum point contained by the AABB.
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/// </summary>
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/// <remarks>
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/// If any component of <see cref="Max"/> is less than <see cref="Min"/> then this AABB is invalid.
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/// </remarks>
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/// <seealso cref="IsValid"/>
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public float3 Max;
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/// <summary>
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/// Constructs the AABB with the given minimum and maximum.
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/// </summary>
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/// <remarks>
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/// If you have a center and extents, you can call <see cref="CreateFromCenterAndExtents"/> or <see cref="CreateFromCenterAndHalfExtents"/>
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/// to create the AABB.
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/// </remarks>
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/// <param name="min">Minimum point inside AABB.</param>
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/// <param name="max">Maximum point inside AABB.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public MinMaxAABB(float3 min, float3 max)
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{
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Min = min;
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Max = max;
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}
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/// <summary>
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/// Creates the AABB from a center and extents.
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/// </summary>
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/// <remarks>
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/// This function takes full extents. It is the distance between <see cref="Min"/> and <see cref="Max"/>.
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/// If you have half extents, you can call <see cref="CreateFromCenterAndHalfExtents"/>.
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/// </remarks>
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/// <param name="center">Center of AABB.</param>
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/// <param name="extents">Full extents of AABB.</param>
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/// <returns>AABB created from inputs.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static MinMaxAABB CreateFromCenterAndExtents(float3 center, float3 extents)
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{
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return CreateFromCenterAndHalfExtents(center, extents * 0.5f);
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}
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/// <summary>
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/// Creates the AABB from a center and half extents.
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/// </summary>
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/// <remarks>
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/// This function takes half extents. It is half the distance between <see cref="Min"/> and <see cref="Max"/>.
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/// If you have full extents, you can call <see cref="CreateFromCenterAndExtents"/>.
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/// </remarks>
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/// <param name="center">Center of AABB.</param>
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/// <param name="halfExtents">Half extents of AABB.</param>
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/// <returns>AABB created from inputs.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static MinMaxAABB CreateFromCenterAndHalfExtents(float3 center, float3 halfExtents)
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{
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return new MinMaxAABB(center - halfExtents, center + halfExtents);
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}
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/// <summary>
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/// Computes the extents of the AABB.
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/// </summary>
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/// <remarks>
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/// Extents is the componentwise distance between min and max.
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/// </remarks>
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public float3 Extents => Max - Min;
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/// <summary>
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/// Computes the half extents of the AABB.
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/// </summary>
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/// <remarks>
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/// HalfExtents is half of the componentwise distance between min and max. Subtracting HalfExtents from Center
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/// gives Min and adding HalfExtents to Center gives Max.
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/// </remarks>
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public float3 HalfExtents => (Max - Min) * 0.5f;
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/// <summary>
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/// Computes the center of the AABB.
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/// </summary>
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public float3 Center => (Max + Min) * 0.5f;
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/// <summary>
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/// Check if the AABB is valid.
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/// </summary>
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/// <remarks>
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/// An AABB is considered valid if <see cref="Min"/> is componentwise less than or equal to <see cref="Max"/>.
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/// </remarks>
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/// <returns>True if <see cref="Min"/> is componentwise less than or equal to <see cref="Max"/>.</returns>
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public bool IsValid => math.all(Min <= Max);
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/// <summary>
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/// Computes the surface area for this axis aligned bounding box.
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/// </summary>
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public float SurfaceArea
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{
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get
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{
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float3 diff = Max - Min;
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return 2 * math.dot(diff, diff.yzx);
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}
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}
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/// <summary>
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/// Tests if the input point is contained by the AABB.
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/// </summary>
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/// <param name="point">Point to test.</param>
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/// <returns>True if AABB contains the input point.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public bool Contains(float3 point) => math.all(point >= Min & point <= Max);
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/// <summary>
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/// Tests if the input AABB is contained entirely by this AABB.
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/// </summary>
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/// <param name="aabb">AABB to test.</param>
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/// <returns>True if input AABB is contained entirely by this AABB.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public bool Contains(MinMaxAABB aabb) => math.all((Min <= aabb.Min) & (Max >= aabb.Max));
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/// <summary>
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/// Tests if the input AABB overlaps this AABB.
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/// </summary>
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/// <param name="aabb">AABB to test.</param>
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/// <returns>True if input AABB overlaps with this AABB.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public bool Overlaps(MinMaxAABB aabb)
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{
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return math.all(Max >= aabb.Min & Min <= aabb.Max);
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}
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/// <summary>
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/// Expands the AABB by the given signed distance.
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/// </summary>
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/// <remarks>
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/// Positive distance expands the AABB while negative distance shrinks the AABB.
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/// </remarks>
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/// <param name="signedDistance">Signed distance to expand the AABB with.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Expand(float signedDistance)
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{
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Min -= signedDistance;
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Max += signedDistance;
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}
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/// <summary>
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/// Encapsulates the given AABB.
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/// </summary>
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/// <remarks>
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/// Modifies this AABB so that it contains the given AABB. If the given AABB is already contained by this AABB,
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/// then this AABB doesn't change.
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/// </remarks>
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/// <seealso cref="Contains(Unity.Mathematics.Geometry.MinMaxAABB)"/>
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/// <param name="aabb">AABB to encapsulate.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Encapsulate(MinMaxAABB aabb)
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{
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Min = math.min(Min, aabb.Min);
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Max = math.max(Max, aabb.Max);
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}
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/// <summary>
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/// Encapsulate the given point.
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/// </summary>
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/// <remarks>
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/// Modifies this AABB so that it contains the given point. If the given point is already contained by this AABB,
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/// then this AABB doesn't change.
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/// </remarks>
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/// <seealso cref="Contains(Unity.Mathematics.float3)"/>
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/// <param name="point">Point to encapsulate.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Encapsulate(float3 point)
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{
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Min = math.min(Min, point);
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Max = math.max(Max, point);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public bool Equals(MinMaxAABB other)
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{
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return Min.Equals(other.Min) && Max.Equals(other.Max);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public override string ToString()
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{
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return string.Format("MinMaxAABB({0}, {1})", Min, Max);
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}
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}
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public static partial class Math
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{
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/// <summary>
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/// Transforms the AABB with the given transform.
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/// </summary>
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/// <remarks>
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/// The resulting AABB encapsulates the transformed AABB which may not be axis aligned after the transformation.
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/// </remarks>
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/// <param name="transform">Transform to apply to AABB.</param>
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/// <param name="aabb">AABB to be transformed.</param>
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/// <returns>Transformed AABB.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static MinMaxAABB Transform(RigidTransform transform, MinMaxAABB aabb)
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{
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float3 halfExtentsInA = aabb.HalfExtents;
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// Rotate each axis individually and find their new positions in the rotated space.
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float3 x = math.rotate(transform.rot, new float3(halfExtentsInA.x, 0, 0));
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float3 y = math.rotate(transform.rot, new float3(0, halfExtentsInA.y, 0));
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float3 z = math.rotate(transform.rot, new float3(0, 0, halfExtentsInA.z));
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// Find the new max corner by summing the rotated axes. Absolute value of each axis
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// since we are trying to find the max corner.
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float3 halfExtentsInB = math.abs(x) + math.abs(y) + math.abs(z);
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float3 centerInB = math.transform(transform, aabb.Center);
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return new MinMaxAABB(centerInB - halfExtentsInB, centerInB + halfExtentsInB);
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}
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/// <summary>
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/// Transforms the AABB with the given transform.
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/// </summary>
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/// <remarks>
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/// The resulting AABB encapsulates the transformed AABB which may not be axis aligned after the transformation.
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/// </remarks>
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/// <param name="transform">Transform to apply to AABB.</param>
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/// <param name="aabb">AABB to be transformed.</param>
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/// <returns>Transformed AABB.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static MinMaxAABB Transform(float4x4 transform, MinMaxAABB aabb)
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{
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var transformed = Transform(new float3x3(transform), aabb);
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transformed.Min += transform.c3.xyz;
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transformed.Max += transform.c3.xyz;
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return transformed;
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}
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/// <summary>
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/// Transforms the AABB with the given transform.
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/// </summary>
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/// <remarks>
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/// The resulting AABB encapsulates the transformed AABB which may not be axis aligned after the transformation.
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/// </remarks>
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/// <param name="transform">Transform to apply to AABB.</param>
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/// <param name="aabb">AABB to be transformed.</param>
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/// <returns>Transformed AABB.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static MinMaxAABB Transform(float3x3 transform, MinMaxAABB aabb)
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{
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// From Christer Ericson's Real-Time Collision Detection on page 86 and 87.
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// We want the transformed minimum and maximums of the AABB. Multiplying a 3x3 matrix on the left of a
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// column vector looks like so:
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//
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// [ c0.x c1.x c2.x ] [ x ] [ c0.x * x + c1.x * y + c2.x * z ]
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// [ c0.y c1.y c2.y ] [ y ] = [ c0.y * x + c1.y * y + c2.y * z ]
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// [ c0.z c1.z c2.z ] [ z ] [ c0.z * x + c1.z * y + c2.z * z ]
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//
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// The column vectors we will use are the input AABB's min and max. Simply multiplying those two vectors
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// with the transformation matrix won't guarantee we get the new min and max since those are only two
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// points out of eight in the AABB and one of the other six may set the new min or max.
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//
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// To ensure we get the correct min and max, we must transform all eight points. But it's not necessary
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// to actually perform eight matrix multiplies to get our final result. Instead, we can build the min and
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// max incrementally by computing each term in the above matrix multiply separately then summing the min
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// (or max). For instance, to find the new minimum contributed by the original min and max x component, we
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// compute this:
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//
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// newMin.x = min(c0.x * Min.x, c0.x * Max.x);
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// newMin.y = min(c0.y * Min.x, c0.y * Max.x);
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// newMin.z = min(c0.z * Min.x, c0.z * Max.x);
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//
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// Then we add minimum contributed by the original min and max y components:
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//
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// newMin.x += min(c1.x * Min.y, c1.x * Max.y);
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// newMin.y += min(c1.y * Min.y, c1.y * Max.y);
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// newMin.z += min(c1.z * Min.y, c1.z * Max.y);
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//
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// And so on. Translation can be handled by simply initializing the new min and max with the translation
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// amount since it does not affect the min and max bounds in local space.
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var t1 = transform.c0.xyz * aabb.Min.xxx;
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var t2 = transform.c0.xyz * aabb.Max.xxx;
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var minMask = t1 < t2;
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var transformed = new MinMaxAABB(select(t2, t1, minMask), select(t2, t1, !minMask));
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t1 = transform.c1.xyz * aabb.Min.yyy;
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t2 = transform.c1.xyz * aabb.Max.yyy;
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minMask = t1 < t2;
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transformed.Min += select(t2, t1, minMask);
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transformed.Max += select(t2, t1, !minMask);
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t1 = transform.c2.xyz * aabb.Min.zzz;
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t2 = transform.c2.xyz * aabb.Max.zzz;
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minMask = t1 < t2;
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transformed.Min += select(t2, t1, minMask);
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transformed.Max += select(t2, t1, !minMask);
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return transformed;
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}
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}
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}
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