JoltPhysics/Jolt/Geometry/Plane.h

// SPDX-FileCopyrightText: 2021 Jorrit Rouwe
// SPDX-License-Identifier: MIT

#pragma once

namespace JPH {

/// An infinite plane described by the formula X . Normal + Constant = 0.
class [[nodiscard]] Plane
{
public:
	/// Constructor
					Plane() = default;
	explicit		Plane(Vec4Arg inNormalAndConstant)										: mNormalAndConstant(inNormalAndConstant) { }
					Plane(Vec3Arg inNormal, float inConstant)								: mNormalAndConstant(inNormal, inConstant) { }

	/// Create from point and normal
	static Plane	sFromPointAndNormal(Vec3Arg inPoint, Vec3Arg inNormal)					{ return Plane(Vec4(inNormal, -inNormal.Dot(inPoint))); }

	/// Create from 3 counter clockwise points
	static Plane	sFromPointsCCW(Vec3Arg inV1, Vec3Arg inV2, Vec3Arg inV3)				{ return sFromPointAndNormal(inV1, (inV2 - inV1).Cross(inV3 - inV1).Normalized()); }

	// Properties
	const 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); }

	/// Offset the plane (positive value means move it in the direction of the plane normal)
	Plane			Offset(float inDistance) const											{ return Plane(mNormalAndConstant - Vec4(Vec3::sZero(), inDistance)); }

	/// Distance point to plane
	float			SignedDistance(Vec3Arg inPoint) const									{ return inPoint.Dot(GetNormal()) + GetConstant(); }

	/// Returns intersection point between 3 planes
	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;													///< XYZ = normal, W = constant, plane: x . normal + constant = 0
};

} // JPH