Plane.h

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// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)
// SPDX-FileCopyrightText: 2021 Jorrit Rouwe
// SPDX-License-Identifier: MIT
 
#pragma once
 
JPH_NAMESPACE_BEGIN
 
class [[nodiscard]] Plane
{
public:
    JPH_OVERRIDE_NEW_DELETE
 
                    Plane() = default;
    explicit        Plane(Vec4Arg inNormalAndConstant)                                      : mNormalAndConstant(inNormalAndConstant) { }
                    Plane(Vec3Arg inNormal, float inConstant)                               : mNormalAndConstant(inNormal, inConstant) { }
 
    static Plane    sFromPointAndNormal(Vec3Arg inPoint, Vec3Arg inNormal)                  { return Plane(Vec4(inNormal, -inNormal.Dot(inPoint))); }
 
    static Plane    sFromPointAndNormal(DVec3Arg inPoint, Vec3Arg inNormal)                 { return Plane(Vec4(inNormal, -float(DVec3(inNormal).Dot(inPoint)))); }
 
    static Plane    sFromPointsCCW(Vec3Arg inV1, Vec3Arg inV2, Vec3Arg inV3)                { return sFromPointAndNormal(inV1, (inV2 - inV1).Cross(inV3 - inV1).Normalized()); }
 
    // Properties
    Vec3            GetNormal() const                                                       { return Vec3(mNormalAndConstant); }
    void            SetNormal(Vec3Arg inNormal)                                             { mNormalAndConstant = Vec4(inNormal, mNormalAndConstant.GetW()); }
    float           GetConstant() const                                                     { return mNormalAndConstant.GetW(); }
    void            SetConstant(float inConstant)                                           { mNormalAndConstant.SetW(inConstant); }
 
    Plane           Offset(float inDistance) const                                          { return Plane(mNormalAndConstant - Vec4(Vec3::sZero(), inDistance)); }
 
    inline Plane    GetTransformed(Mat44Arg inTransform) const
    {
        Vec3 transformed_normal = inTransform.Multiply3x3(GetNormal());
        return Plane(transformed_normal, GetConstant() - inTransform.GetTranslation().Dot(transformed_normal));
    }
 
    float           SignedDistance(Vec3Arg inPoint) const                                   { return inPoint.Dot(GetNormal()) + GetConstant(); }
 
    static bool     sIntersectPlanes(const Plane &inP1, const Plane &inP2, const Plane &inP3, Vec3 &outPoint)
    {
        // We solve the equation:
        // |ax, ay, az, aw|   | x |   | 0 |
        // |bx, by, bz, bw| * | y | = | 0 |
        // |cx, cy, cz, cw|   | z |   | 0 |
        // | 0,  0,  0,  1|   | 1 |   | 1 |
        // Where normal of plane 1 = (ax, ay, az), plane constant of 1 = aw, normal of plane 2 = (bx, by, bz) etc.
        // This involves inverting the matrix and multiplying it with [0, 0, 0, 1]
 
        // Fetch the normals and plane constants for the three planes
        Vec4 a = inP1.mNormalAndConstant;
        Vec4 b = inP2.mNormalAndConstant;
        Vec4 c = inP3.mNormalAndConstant;
 
        // Result is a vector that we have to divide by:
        float denominator = Vec3(a).Dot(Vec3(b).Cross(Vec3(c)));
        if (denominator == 0.0f)
            return false;
 
        // The numerator is:
        // [aw*(bz*cy-by*cz)+ay*(bw*cz-bz*cw)+az*(by*cw-bw*cy)]
        // [aw*(bx*cz-bz*cx)+ax*(bz*cw-bw*cz)+az*(bw*cx-bx*cw)]
        // [aw*(by*cx-bx*cy)+ax*(bw*cy-by*cw)+ay*(bx*cw-bw*cx)]
        Vec4 numerator =
            a.SplatW() * (b.Swizzle<SWIZZLE_Z, SWIZZLE_X, SWIZZLE_Y, SWIZZLE_UNUSED>() * c.Swizzle<SWIZZLE_Y, SWIZZLE_Z, SWIZZLE_X, SWIZZLE_UNUSED>() - b.Swizzle<SWIZZLE_Y, SWIZZLE_Z, SWIZZLE_X, SWIZZLE_UNUSED>() * c.Swizzle<SWIZZLE_Z, SWIZZLE_X, SWIZZLE_Y, SWIZZLE_UNUSED>())
            + a.Swizzle<SWIZZLE_Y, SWIZZLE_X, SWIZZLE_X, SWIZZLE_UNUSED>() * (b.Swizzle<SWIZZLE_W, SWIZZLE_Z, SWIZZLE_W, SWIZZLE_UNUSED>() * c.Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_Y, SWIZZLE_UNUSED>() - b.Swizzle<SWIZZLE_Z, SWIZZLE_W, SWIZZLE_Y, SWIZZLE_UNUSED>() * c.Swizzle<SWIZZLE_W, SWIZZLE_Z, SWIZZLE_W, SWIZZLE_UNUSED>())
            + a.Swizzle<SWIZZLE_Z, SWIZZLE_Z, SWIZZLE_Y, SWIZZLE_UNUSED>() * (b.Swizzle<SWIZZLE_Y, SWIZZLE_W, SWIZZLE_X, SWIZZLE_UNUSED>() * c.Swizzle<SWIZZLE_W, SWIZZLE_X, SWIZZLE_W, SWIZZLE_UNUSED>() - b.Swizzle<SWIZZLE_W, SWIZZLE_X, SWIZZLE_W, SWIZZLE_UNUSED>() * c.Swizzle<SWIZZLE_Y, SWIZZLE_W, SWIZZLE_X, SWIZZLE_UNUSED>());
 
        outPoint = Vec3(numerator) / denominator;
        return true;
    }
 
private:
    Vec4            mNormalAndConstant;                                                 
};
 
JPH_NAMESPACE_END