235 lines
11 KiB
C#
235 lines
11 KiB
C#
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using System;
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using System.Diagnostics;
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using System.Runtime.CompilerServices;
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using Unity.IL2CPP.CompilerServices;
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namespace Unity.Mathematics.Geometry
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{
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/// <summary>
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/// A plane represented by a normal vector and a distance along the normal from the origin.
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/// </summary>
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/// <remarks>
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/// A plane splits the 3D space in half. The normal vector points to the positive half and the other half is
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/// considered negative.
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/// </remarks>
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[DebuggerDisplay("{Normal}, {Distance}")]
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[Serializable]
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[Il2CppEagerStaticClassConstruction]
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internal struct Plane
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{
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/// <summary>
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/// A plane in the form Ax + By + Cz + Dw = 0.
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/// </summary>
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/// <remarks>
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/// Stores the plane coefficients A, B, C, D where (A, B, C) is a unit normal vector and D is the distance
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/// from the origin. A plane stored with a unit normal vector is called a normalized plane.
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/// </remarks>
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public float4 NormalAndDistance;
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/// <summary>
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/// Constructs a Plane from arbitrary coefficients A, B, C, D of the plane equation Ax + By + Cz + Dw = 0.
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/// </summary>
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/// <remarks>
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/// The constructed plane will be the normalized form of the plane specified by the given coefficients.
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/// </remarks>
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/// <param name="coefficientA">Coefficient A from plane equation.</param>
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/// <param name="coefficientB">Coefficient B from plane equation.</param>
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/// <param name="coefficientC">Coefficient C from plane equation.</param>
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/// <param name="coefficientD">Coefficient D from plane equation.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public Plane(float coefficientA, float coefficientB, float coefficientC, float coefficientD)
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{
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NormalAndDistance = Normalize(new float4(coefficientA, coefficientB, coefficientC, coefficientD));
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}
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/// <summary>
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/// Constructs a plane with a normal vector and distance from the origin.
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/// </summary>
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/// <remarks>
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/// The constructed plane will be the normalized form of the plane specified by the inputs.
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/// </remarks>
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/// <param name="normal">A non-zero vector that is perpendicular to the plane. It may be any length.</param>
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/// <param name="distance">Distance from the origin along the normal. A negative value moves the plane in the
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/// same direction as the normal while a positive value moves it in the opposite direction.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public Plane(float3 normal, float distance)
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{
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NormalAndDistance = Normalize(new float4(normal, distance));
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}
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/// <summary>
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/// Constructs a plane with a normal vector and a point that lies in the plane.
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/// </summary>
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/// <remarks>
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/// The constructed plane will be the normalized form of the plane specified by the inputs.
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/// </remarks>
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/// <param name="normal">A non-zero vector that is perpendicular to the plane. It may be any length.</param>
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/// <param name="pointInPlane">A point that lies in the plane.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public Plane(float3 normal, float3 pointInPlane)
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: this(normal, -math.dot(normal, pointInPlane))
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{
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}
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/// <summary>
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/// Constructs a plane with two vectors and a point that all lie in the plane.
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/// </summary>
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/// <remarks>
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/// The constructed plane will be the normalized form of the plane specified by the inputs.
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/// </remarks>
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/// <param name="vector1InPlane">A non-zero vector that lies in the plane. It may be any length.</param>
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/// <param name="vector2InPlane">A non-zero vector that lies in the plane. It may be any length and must not be a scalar multiple of <paramref name="vector1InPlane"/>.</param>
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/// <param name="pointInPlane">A point that lies in the plane.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public Plane(float3 vector1InPlane, float3 vector2InPlane, float3 pointInPlane)
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: this(math.cross(vector1InPlane, vector2InPlane), pointInPlane)
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{
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}
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/// <summary>
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/// Creates a normalized Plane directly without normalization cost.
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/// </summary>
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/// <remarks>
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/// If you have a unit length normal vector, you can create a Plane faster than using one of its constructors
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/// by calling this function.
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/// </remarks>
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/// <param name="unitNormal">A non-zero vector that is perpendicular to the plane. It must be unit length.</param>
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/// <param name="distance">Distance from the origin along the normal. A negative value moves the plane in the
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/// same direction as the normal while a positive value moves it in the opposite direction.</param>
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/// <returns>Normalized Plane constructed from given inputs.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static Plane CreateFromUnitNormalAndDistance(float3 unitNormal, float distance)
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{
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return new Plane { NormalAndDistance = new float4(unitNormal, distance) };
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}
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/// <summary>
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/// Creates a normalized Plane without normalization cost.
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/// </summary>
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/// <remarks>
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/// If you have a unit length normal vector, you can create a Plane faster than using one of its constructors
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/// by calling this function.
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/// </remarks>
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/// <param name="unitNormal">A non-zero vector that is perpendicular to the plane. It must be unit length.</param>
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/// <param name="pointInPlane">A point that lies in the plane.</param>
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/// <returns>Normalized Plane constructed from given inputs.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static Plane CreateFromUnitNormalAndPointInPlane(float3 unitNormal, float3 pointInPlane)
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{
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return new Plane { NormalAndDistance = new float4(unitNormal, -math.dot(unitNormal, pointInPlane)) };
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}
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/// <summary>
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/// Get/set the normal vector of the plane.
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/// </summary>
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/// <remarks>
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/// It is assumed that the normal is unit length. If you set a new plane such that Ax + By + Cz + Dw = 0 but
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/// (A, B, C) is not unit length, then you must normalize the plane by calling <see cref="Normalize(Plane)"/>.
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/// </remarks>
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public float3 Normal
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{
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get => NormalAndDistance.xyz;
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set => NormalAndDistance.xyz = value;
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}
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/// <summary>
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/// Get/set the distance of the plane from the origin. May be a negative value.
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/// </summary>
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/// <remarks>
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/// It is assumed that the normal is unit length. If you set a new plane such that Ax + By + Cz + Dw = 0 but
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/// (A, B, C) is not unit length, then you must normalize the plane by calling <see cref="Normalize(Plane)"/>.
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/// </remarks>
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public float Distance
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{
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get => NormalAndDistance.w;
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set => NormalAndDistance.w = value;
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}
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/// <summary>
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/// Normalizes the given Plane.
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/// </summary>
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/// <param name="plane">Plane to normalize.</param>
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/// <returns>Normalized Plane.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static Plane Normalize(Plane plane)
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{
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return new Plane { NormalAndDistance = Normalize(plane.NormalAndDistance) };
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}
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/// <summary>
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/// Normalizes the plane represented by the given plane coefficients.
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/// </summary>
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/// <remarks>
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/// The plane coefficients are A, B, C, D and stored in that order in the <see cref="float4"/>.
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/// </remarks>
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/// <param name="planeCoefficients">Plane coefficients A, B, C, D stored in x, y, z, w (respectively).</param>
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/// <returns>Normalized plane coefficients.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 Normalize(float4 planeCoefficients)
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{
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float recipLength = math.rsqrt(math.lengthsq(planeCoefficients.xyz));
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return new Plane { NormalAndDistance = planeCoefficients * recipLength };
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}
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/// <summary>
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/// Get the signed distance from the point to the plane.
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/// </summary>
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/// <remarks>
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/// Plane must be normalized prior to calling this function. Distance is positive if point is on side of the
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/// plane the normal points to, negative if on the opposite side and zero if the point lies in the plane.
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/// Avoid comparing equality with 0.0f when testing if a point lies exactly in the plane and use an approximate
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/// comparison instead.
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/// </remarks>
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/// <param name="point">Point to find the signed distance with.</param>
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/// <returns>Signed distance of the point from the plane.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public float SignedDistanceToPoint(float3 point)
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{
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CheckPlaneIsNormalized();
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return math.dot(NormalAndDistance, new float4(point, 1.0f));
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}
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/// <summary>
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/// Projects the given point onto the plane.
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/// </summary>
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/// <remarks>
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/// Plane must be normalized prior to calling this function. The result is the position closest to the point
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/// that still lies in the plane.
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/// </remarks>
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/// <param name="point">Point to project onto the plane.</param>
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/// <returns>Projected point that's inside the plane.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public float3 Projection(float3 point)
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{
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CheckPlaneIsNormalized();
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return point - Normal * SignedDistanceToPoint(point);
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}
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/// <summary>
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/// Flips the plane so the normal points in the opposite direction.
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/// </summary>
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public Plane Flipped => new Plane { NormalAndDistance = -NormalAndDistance };
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/// <summary>
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/// Implicitly converts a <see cref="Plane"/> to <see cref="float4"/>.
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/// </summary>
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/// <param name="plane">Plane to convert.</param>
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/// <returns>A <see cref="float4"/> representing the plane.</returns>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static implicit operator float4(Plane plane) => plane.NormalAndDistance;
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[Conditional("ENABLE_UNITY_COLLECTIONS_CHECKS")]
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void CheckPlaneIsNormalized()
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{
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float ll = math.lengthsq(Normal.xyz);
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const float lowerBound = 0.999f * 0.999f;
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const float upperBound = 1.001f * 1.001f;
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if (ll < lowerBound || ll > upperBound)
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{
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throw new System.ArgumentException("Plane must be normalized. Call Plane.Normalize() to normalize plane.");
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}
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}
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}
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}
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