Misaki.HighPerformance/Misaki.HighPerformance.Mathematics/Geometry/Plane.cs

using System.Diagnostics;
using System.Runtime.CompilerServices;

namespace Misaki.HighPerformance.Mathematics.Geometry;

/// <summary>
/// A plane represented by a normal vector and a distance along the normal from the origin.
/// </summary>
/// <remarks>
/// A plane splits the 3D space in half.  The normal vector points to the positive half and the other half is
/// considered negative.
/// </remarks>
public struct Plane
{
    /// <summary>
    /// A plane in the form Ax + By + Cz + Dw = 0.
    /// </summary>
    /// <remarks>
    /// Stores the plane coefficients A, B, C, D where (A, B, C) is a unit normal vector and D is the distance
    /// from the origin.  A plane stored with a unit normal vector is called a normalized plane.
    /// </remarks>
    public float4 normalAndDistance;

    /// <summary>
    /// Constructs a Plane from arbitrary coefficients A, B, C, D of the plane equation Ax + By + Cz + Dw = 0.
    /// </summary>
    /// <remarks>
    /// The constructed plane will be the normalized form of the plane specified by the given coefficients.
    /// </remarks>
    /// <param name="coefficientA">Coefficient A from plane equation.</param>
    /// <param name="coefficientB">Coefficient B from plane equation.</param>
    /// <param name="coefficientC">Coefficient C from plane equation.</param>
    /// <param name="coefficientD">Coefficient D from plane equation.</param>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public Plane(float coefficientA, float coefficientB, float coefficientC, float coefficientD)
    {
        normalAndDistance = Normalize(new float4(coefficientA, coefficientB, coefficientC, coefficientD));
    }

    /// <summary>
    /// Constructs a plane with a normal vector and distance from the origin.
    /// </summary>
    /// <remarks>
    /// The constructed plane will be the normalized form of the plane specified by the inputs.
    /// </remarks>
    /// <param name="normal">A non-zero vector that is perpendicular to the plane.  It may be any length.</param>
    /// <param name="distance">Distance from the origin along the normal.  A negative value moves the plane in the
    /// same direction as the normal while a positive value moves it in the opposite direction.</param>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public Plane(float3 normal, float distance)
    {
        normalAndDistance = Normalize(new float4(normal, distance));
    }

    /// <summary>
    /// Constructs a plane with a normal vector and a point that lies in the plane.
    /// </summary>
    /// <remarks>
    /// The constructed plane will be the normalized form of the plane specified by the inputs.
    /// </remarks>
    /// <param name="normal">A non-zero vector that is perpendicular to the plane.  It may be any length.</param>
    /// <param name="pointInPlane">A point that lies in the plane.</param>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public Plane(float3 normal, float3 pointInPlane)
    : this(normal, -math.dot(normal, pointInPlane))
    {
    }

    /// <summary>
    /// Constructs a plane with two vectors and a point that all lie in the plane.
    /// </summary>
    /// <remarks>
    /// The constructed plane will be the normalized form of the plane specified by the inputs.
    /// </remarks>
    /// <param name="vector1InPlane">A non-zero vector that lies in the plane.  It may be any length.</param>
    /// <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>
    /// <param name="pointInPlane">A point that lies in the plane.</param>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public Plane(float3 vector1InPlane, float3 vector2InPlane, float3 pointInPlane)
    : this(math.cross(vector1InPlane, vector2InPlane), pointInPlane)
    {
    }

    /// <summary>
    /// Creates a normalized Plane directly without normalization cost.
    /// </summary>
    /// <remarks>
    /// If you have a unit length normal vector, you can create a Plane faster than using one of its constructors
    /// by calling this function.
    /// </remarks>
    /// <param name="unitNormal">A non-zero vector that is perpendicular to the plane.  It must be unit length.</param>
    /// <param name="distance">Distance from the origin along the normal.  A negative value moves the plane in the
    /// same direction as the normal while a positive value moves it in the opposite direction.</param>
    /// <returns>Normalized Plane constructed from given inputs.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static Plane CreateFromUnitNormalAndDistance(float3 unitNormal, float distance)
    {
        return new Plane { normalAndDistance = new float4(unitNormal, distance) };
    }

    /// <summary>
    /// Creates a normalized Plane without normalization cost.
    /// </summary>
    /// <remarks>
    /// If you have a unit length normal vector, you can create a Plane faster than using one of its constructors
    /// by calling this function.
    /// </remarks>
    /// <param name="unitNormal">A non-zero vector that is perpendicular to the plane.  It must be unit length.</param>
    /// <param name="pointInPlane">A point that lies in the plane.</param>
    /// <returns>Normalized Plane constructed from given inputs.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static Plane CreateFromUnitNormalAndPointInPlane(float3 unitNormal, float3 pointInPlane)
    {
        return new Plane { normalAndDistance = new float4(unitNormal, -math.dot(unitNormal, pointInPlane)) };
    }

    /// <summary>
    /// Get/set the normal vector of the plane.
    /// </summary>
    /// <remarks>
    /// It is assumed that the normal is unit length.  If you set a new plane such that Ax + By + Cz + Dw = 0 but
    /// (A, B, C) is not unit length, then you must normalize the plane by calling <see cref="Normalize(Plane)"/>.
    /// </remarks>
    public float3 Normal
    {
        get => normalAndDistance.xyz;
        set => normalAndDistance.xyz = value;
    }

    /// <summary>
    /// Get/set the distance of the plane from the origin.  May be a negative value.
    /// </summary>
    /// <remarks>
    /// It is assumed that the normal is unit length.  If you set a new plane such that Ax + By + Cz + Dw = 0 but
    /// (A, B, C) is not unit length, then you must normalize the plane by calling <see cref="Normalize(Plane)"/>.
    /// </remarks>
    public float Distance
    {
        get => normalAndDistance.w;
        set => normalAndDistance.w = value;
    }

    /// <summary>
    /// Normalizes the given Plane.
    /// </summary>
    /// <param name="plane">Plane to normalize.</param>
    /// <returns>Normalized Plane.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static Plane Normalize(Plane plane)
    {
        return new Plane { normalAndDistance = Normalize(plane.normalAndDistance) };
    }

    /// <summary>
    /// Normalizes the plane represented by the given plane coefficients.
    /// </summary>
    /// <remarks>
    /// The plane coefficients are A, B, C, D and stored in that order in the <see cref="float4"/>.
    /// </remarks>
    /// <param name="planeCoefficients">Plane coefficients A, B, C, D stored in x, y, z, w (respectively).</param>
    /// <returns>Normalized plane coefficients.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static float4 Normalize(float4 planeCoefficients)
    {
        var recipLength = math.rsqrt(math.lengthsq(planeCoefficients.xyz));
        return new Plane { normalAndDistance = planeCoefficients * recipLength };
    }

    /// <summary>
    /// Get the signed distance from the point to the plane.
    /// </summary>
    /// <remarks>
    /// Plane must be normalized prior to calling this function.  Distance is positive if point is on side of the
    /// plane the normal points to, negative if on the opposite side and zero if the point lies in the plane.
    /// Avoid comparing equality with 0.0f when testing if a point lies exactly in the plane and use an approximate
    /// comparison instead.
    /// </remarks>
    /// <param name="point">Point to find the signed distance with.</param>
    /// <returns>Signed distance of the point from the plane.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public float SignedDistanceToPoint(float3 point)
    {
        CheckPlaneIsNormalized();
        return math.dot(normalAndDistance, new float4(point, 1.0f));
    }

    /// <summary>
    /// Projects the given point onto the plane.
    /// </summary>
    /// <remarks>
    /// Plane must be normalized prior to calling this function.  The result is the position closest to the point
    /// that still lies in the plane.
    /// </remarks>
    /// <param name="point">Point to project onto the plane.</param>
    /// <returns>Projected point that's inside the plane.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public float3 Projection(float3 point)
    {
        CheckPlaneIsNormalized();
        return point - Normal * SignedDistanceToPoint(point);
    }

    /// <summary>
    /// Flips the plane so the normal points in the opposite direction.
    /// </summary>
    public Plane Flipped => new Plane { normalAndDistance = -normalAndDistance };

    /// <summary>
    /// Implicitly converts a <see cref="Plane"/> to <see cref="float4"/>.
    /// </summary>
    /// <param name="plane">Plane to convert.</param>
    /// <returns>A <see cref="float4"/> representing the plane.</returns>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator float4(Plane plane) => plane.normalAndDistance;

    [Conditional("ENABLE_COLLECTIONS_CHECKS")]
    private void CheckPlaneIsNormalized()
    {
        var ll = math.lengthsq(Normal.xyz);
        const float lowerBound = 0.999f * 0.999f;
        const float upperBound = 1.001f * 1.001f;

        if (ll < lowerBound || ll > upperBound)
        {
            throw new System.ArgumentException("Plane must be normalized. Call Plane.Normalize() to normalize plane.");
        }
    }
}