BRDFSlices.DisplayForm.half_diff_coords_to_std_coords C# (CSharp) Method

        public static void half_diff_coords_to_std_coords( double _ThetaHalf, double _PhiHalf, double _ThetaDiff, double _PhiDiff,
													ref Vector3 _In, ref Vector3 _Out )
        {
            double	SinTheta_half = Math.Sin( _ThetaHalf );
            Half.Set( Math.Cos( _PhiHalf ) * SinTheta_half, Math.Sin( _PhiHalf ) * SinTheta_half, Math.Cos( _ThetaHalf ) );

            // Build the 2 vectors representing the frame in which we can use the diff angles
            Vector3	OrthoX;
            Half.Cross( ref Normal, out OrthoX );
            if ( OrthoX.LengthSq() < 1e-6 )
                OrthoX.Set( 1, 0, 0 );
            else
                OrthoX.Normalize();

            Vector3	OrthoY;
            Half.Cross( ref OrthoX, out OrthoY );

            // Rotate using diff angles to retrieve incoming direction
            Half.Rotate( ref OrthoX, -_ThetaDiff, out Temp );
            Temp.Rotate( ref Half, _PhiDiff, out _In );

            // ...or by mirroring in "Half tangent space"
            double	MirrorX = -_In.Dot( ref OrthoX );
            double	MirrorY = -_In.Dot( ref OrthoY );
            double	z = _In.Dot( ref Half );
            _Out.Set(
                MirrorX*OrthoX.x + MirrorY*OrthoY.x + z*Half.x,
                MirrorX*OrthoX.y + MirrorY*OrthoY.y + z*Half.y,
                MirrorX*OrthoX.z + MirrorY*OrthoY.z + z*Half.z
            );

            // 			if ( _In.z < -0.5 || _Out.z < -0.5 )
            // 				throw new Exception( "RHA MAIS MERDE!" );
        }

        protected override void OnPaint(PaintEventArgs e)
        {
            base.OnPaint(e);

            if (m_Slice != null)
            {
                e.Graphics.DrawImage(m_Slice, 0, 0, Width, Height);
            }

            if (ShowIsoLines)
            {
                PointF P0 = new PointF(), P1 = new PointF();

                double ThetaHalf, PhiHalf, ThetaDiff, PhiDiff;
                double ThetaHalfN, PhiHalfN, ThetaDiffN, PhiDiffN;
                for (int IsolineIndex = 0; IsolineIndex < 20; IsolineIndex++)
                {
                    double ThetaI = (1 + IsolineIndex) / 20.0 * 0.495 * Math.PI;
//					double	ThetaI = Math.Sqrt( (1+IsolineIndex) / 12.0 ) * 0.49 * Math.PI;

                    for (int i = 0; i < 20; i++)
                    {
                        ThetaI = (1.0 + IsolineIndex) / 20.0 * 0.495 * Math.PI;
                        double HalfPhi = 0.5 * i * Math.PI / 20;
                        DisplayForm.std_coords_to_half_diff_coords(ThetaI, HalfPhi, ThetaI, -HalfPhi, out ThetaHalf, out PhiHalf, out ThetaDiff, out PhiDiff);
//Convert( ThetaI, Phi, out ThetaHalf, out ThetaDiff );

                        // Change Phi_d
                        double TestThetaI, TestPhiI, TestThetaO, TestPhiO;
                        DisplayForm.half_diff_coords_to_std_coords(ThetaHalf, PhiHalf, ThetaDiff, PhiD, out TestThetaI, out TestPhiI, out TestThetaO, out TestPhiO);
                        DisplayForm.std_coords_to_half_diff_coords(TestThetaI, TestPhiI, TestThetaO, TestPhiO, out ThetaHalf, out PhiHalf, out ThetaDiff, out PhiDiff);


                        ThetaI  = (1.2 + IsolineIndex) / 20.0 * 0.495 * Math.PI;
                        HalfPhi = 0.5 * (i + 1) * Math.PI / 20;
                        DisplayForm.std_coords_to_half_diff_coords(ThetaI, HalfPhi, ThetaI, -HalfPhi, out ThetaHalfN, out PhiHalfN, out ThetaDiffN, out PhiDiffN);
//Convert( ThetaI, Phi, out ThetaHalfN, out ThetaDiffN );

                        // Change Phi_d
                        DisplayForm.half_diff_coords_to_std_coords(ThetaHalfN, PhiHalfN, ThetaDiffN, PhiD, out TestThetaI, out TestPhiI, out TestThetaO, out TestPhiO);
                        DisplayForm.std_coords_to_half_diff_coords(TestThetaI, TestPhiI, TestThetaO, TestPhiO, out ThetaHalfN, out PhiHalfN, out ThetaDiffN, out PhiDiffN);

                        P0.X = (float)(Width * ThetaHalf * 0.63661977236758134307553505349006);                                         // divided by PI/2
                        P0.Y = (float)(Height * (1.0f - ThetaDiff * 0.63661977236758134307553505349006));                               // divided by PI/2
                        P1.X = (float)(Width * ThetaHalfN * 0.63661977236758134307553505349006);                                        // divided by PI/2
                        P1.Y = (float)(Height * (1.0f - ThetaDiffN * 0.63661977236758134307553505349006));                              // divided by PI/2
                        e.Graphics.DrawLine(m_Pen, P0, P1);
                    }

//Convert( ThetaI, 0.8 * Math.PI, out ThetaHalf, out ThetaDiff );

                    {
                        double ThetaDH = Math.Acos(Math.Sqrt(Math.Cos(ThetaI)));
                        double PhiI    = 2.0 * Math.Atan(1.0 / Math.Cos(ThetaDH));
//						DisplayForm.std_coords_to_half_diff_coords( ThetaI, 0, ThetaI, PhiI, out ThetaHalf, out PhiHalf, out ThetaDiff, out PhiDiff );
                        Convert(ThetaI, PhiI, out ThetaHalf, out ThetaDiff);
                    }

                    P0.X = (float)(Width * ThetaHalf * 0.63661977236758134307553505349006) - 16.0f;                                     // divided by PI/2
                    P0.Y = (float)(Height * (1.0f - ThetaDiff * 0.63661977236758134307553505349006)) - 0 * 16.0f;                       // divided by PI/2
                    e.Graphics.DrawString("" + (int)(ThetaI * 180 / Math.PI) + "°", Font, Brushes.Black, P0);
                }
            }

            if (ShowIsoLines)
            {
                PointF P0 = new PointF(), P1 = new PointF();

                double ThetaHalf, PhiHalf, ThetaDiff, PhiDiff;
                double ThetaHalfN, PhiHalfN, ThetaDiffN, PhiDiffN;
                for (int IsolineIndex = 0; IsolineIndex < 19; IsolineIndex++)
                {
                    double Phi = (1.0 + IsolineIndex) / 20.0 * Math.PI;
//					double	Phi = Math.Sqrt( (0.5+IsolineIndex) / 12.0 ) * Math.PI;

                    for (int i = 0; i < 40; i++)
                    {
                        double Angle = i * 0.50 * Math.PI / 40;

                        DisplayForm.std_coords_to_half_diff_coords(Angle, 0, Angle, Phi, out ThetaHalf, out PhiHalf, out ThetaDiff, out PhiDiff);
                        Convert(Angle, Phi, out ThetaHalf, out ThetaDiff);

                        Angle = (i + 1) * 0.50 * Math.PI / 40;
                        DisplayForm.std_coords_to_half_diff_coords(Angle, 0, Angle, Phi, out ThetaHalfN, out PhiHalfN, out ThetaDiffN, out PhiDiffN);
                        Convert(Angle, Phi, out ThetaHalfN, out ThetaDiffN);

                        P0.X = (float)(Width * ThetaHalf * 0.63661977236758134307553505349006);                                         // divided by PI/2
                        P0.Y = (float)(Height * (1.0f - ThetaDiff * 0.63661977236758134307553505349006));                               // divided by PI/2
                        P1.X = (float)(Width * ThetaHalfN * 0.63661977236758134307553505349006);                                        // divided by PI/2
                        P1.Y = (float)(Height * (1.0f - ThetaDiffN * 0.63661977236758134307553505349006));                              // divided by PI/2
                        e.Graphics.DrawLine(m_Pen, P0, P1);
                    }

                    DisplayForm.std_coords_to_half_diff_coords(0.5 * Math.PI, 0, 0.5 * Math.PI, Phi, out ThetaHalf, out PhiHalf, out ThetaDiff, out PhiDiff);
                    P0.X = (float)(Width * ThetaHalf * 0.63661977236758134307553505349006) - 30.0f;                                             // divided by PI/2
                    P0.Y = (float)(Height * (1.0f - ThetaDiff * 0.63661977236758134307553505349006)) + 2.0f;                                    // divided by PI/2
                    e.Graphics.DrawString("" + (int)(Phi * 180 / Math.PI) + "°", Font, Brushes.Black, P0);
                }
            }
        }