360视频：分段球面投影SSP

分段球面投影（Segmented sphere projection，SSP）将球面分为3个部分：北极、南极、赤道。图1是SSP投影示意图，球面上三个部分的分界线是北纬45度和南纬45度。北极和南极投影后的面是圆，索引分别为0和1，赤道投影方式和ERP相同，赤道投影后被划分为4个相同的正方形面，索引为2到5。投影后面的两极圆的直径和赤道正方形边长相等，因为它们纬度都跨了90度。

图1 SSP投影

Frame Packing

SSP有两者frame packing方式，一种如图1所示，映射后按垂直方向展开。图2是真实图像垂直展开的示例。

图2 SSP垂直展开

SSP还可以按照水平方向展开，如图3所示。

图3 SSP水平展开

展开后各面的定义如表1。

表1 SSP各面的定义

投影变换

2D-3D变换，假设面的直径是A，则2D平面上的点(m,n)按下面方式转换为球面上的 $\begin{equation*} ( \phi ,\theta ) \end{equation*}{\color{DarkBlue} }$ ，

3D-2D变换，球面上的 $\begin{equation*} ( \phi ,\theta ) \end{equation*}{\color{DarkBlue} }$ 按下面方式转换为2D平面上的点(m,n)，

Void TSegmentedSphere::map2DTo3D(SPos& IPosIn, SPos *pSPosOut)
{POSType u, v,square = m_sVideoInfo.iFaceHeight,width = m_sVideoInfo.iFaceWidth,pitch, yaw;//u = IPosIn.x;u = IPosIn.x + (POSType)(0.5);v = IPosIn.y + (POSType)(0.5);#if SVIDEO_SSP_PADDING_FIX
#elseif ((u < 0 || u >= m_sVideoInfo.iFaceWidth) && (v >= 0 && v < m_sVideoInfo.iFaceHeight * 2 / 3)){u = u < 0 ? m_sVideoInfo.iFaceWidth + u : (u - m_sVideoInfo.iFaceWidth);}else if (v < 0){v = -v;u = u + (m_sVideoInfo.iFaceWidth >> 1);u = u >= m_sVideoInfo.iFaceWidth ? u - m_sVideoInfo.iFaceWidth : u;}else if (v >= m_sVideoInfo.iFaceHeight){v = (m_sVideoInfo.iFaceHeight * 2 / 3 << 1) - v;u = u + (m_sVideoInfo.iFaceWidth >> 1);u = u >= m_sVideoInfo.iFaceWidth ? u - m_sVideoInfo.iFaceWidth : u;}
#endifPOSType pole_x, pole_y, pole_d;if (IPosIn.faceIdx == 0){pole_x = u - width / 2;pole_y = v - square / 2;pole_d = ssqrt(pole_x*pole_x + pole_y*pole_y);yaw = (pole_d > 0) ? acos(pole_y / pole_d) : 0;yaw = (pole_x < 0) ? S_PI*2 - yaw : yaw;pitch = S_PI_2 - pole_d * S_PI_2 / square;}else if (IPosIn.faceIdx == 1){pole_x = u - width / 2;pole_y = v - square / 2;pole_d = ssqrt(pole_x*pole_x + pole_y*pole_y);yaw = (pole_d > 0) ? satan2(pole_y, pole_x) + S_PI_2 : 0;pitch = pole_d * S_PI_2 / square - S_PI_2;}else if (IPosIn.faceIdx == 2){yaw = (POSType)(u*S_PI_2 / m_sVideoInfo.iFaceWidth - S_PI);pitch = (POSType)(S_PI_2 - (v + square / 2)*S_PI / square / 2);}else if (IPosIn.faceIdx == 3){yaw = (POSType)((u + square)*S_PI_2 / m_sVideoInfo.iFaceWidth - S_PI);pitch = (POSType)(S_PI_2 - (v + square / 2)*S_PI / square / 2);}else if (IPosIn.faceIdx == 4){yaw = (POSType)((u + 2*square)*S_PI_2 / m_sVideoInfo.iFaceWidth - S_PI);pitch = (POSType)(S_PI_2 - (v + square / 2)*S_PI / square / 2);}else if (IPosIn.faceIdx == 5){yaw = (POSType)((u + 3*square)*S_PI_2 / m_sVideoInfo.iFaceWidth - S_PI);pitch = (POSType)(S_PI_2 - (v + square / 2)*S_PI / square / 2);}else{assert(!"Face index Error!\n");}pSPosOut->faceIdx = IPosIn.faceIdx;pSPosOut->x = (POSType)(scos(pitch)*scos(yaw));pSPosOut->y = (POSType)(ssin(pitch));pSPosOut->z = -(POSType)(scos(pitch)*ssin(yaw));
}Void TSegmentedSphere::map3DTo2D(SPos *pSPosIn, SPos *pSPosOut)
{POSType x = pSPosIn->x;POSType y = pSPosIn->y;POSType z = pSPosIn->z;POSType len = ssqrt(x*x + y*y + z*z);POSType square = m_sVideoInfo.iFaceHeight;POSType yaw = (POSType)(satan2(-z, x)),pitch = (POSType)(sasin(y / len));pSPosOut->z = 0;if (y > len*ssqrt(2) / 2){pSPosOut->faceIdx = 0;pSPosOut->x = square * ssin(yaw) * (S_PI_2 - pitch) / S_PI_2 +m_sVideoInfo.iFaceWidth / 2 - 0.5;pSPosOut->y = square / 2 * (1 + scos(yaw) * 2 * (S_PI_2 - pitch) / S_PI_2) - 0.5;}else if (y < -len*ssqrt(2) / 2){pSPosOut->faceIdx = 1;pSPosOut->x = square * ssin(yaw) * (S_PI_2 + pitch) / S_PI_2 +m_sVideoInfo.iFaceWidth / 2 - 0.5;pSPosOut->y = square / 2 * (1 - scos(yaw) * 2 * (S_PI_2 + pitch) / S_PI_2) - 0.5;}else if (z >= 0 && x < 0){pSPosOut->faceIdx = 2;pSPosOut->x = (S_PI + yaw)*m_sVideoInfo.iFaceWidth / S_PI_2 - 0.5;pSPosOut->y = (S_PI_2 - pitch) * square / S_PI_2 - square / 2 - 0.5;}else if (z > 0 && x >= 0){pSPosOut->faceIdx = 3;pSPosOut->x = (S_PI + yaw)*m_sVideoInfo.iFaceWidth / S_PI_2 - m_sVideoInfo.iFaceWidth - 0.5;pSPosOut->y = (S_PI_2 - pitch) * square / S_PI_2 - square / 2 - 0.5;}else if (z <= 0 && x > 0){pSPosOut->faceIdx = 4;pSPosOut->x = (S_PI + yaw)*m_sVideoInfo.iFaceWidth / S_PI_2 - 2 * m_sVideoInfo.iFaceWidth - 0.5;pSPosOut->y = (S_PI_2 - pitch) * square / S_PI_2 - square / 2 - 0.5;}else if (z < 0 && x <= 0){pSPosOut->faceIdx = 5;pSPosOut->x = (S_PI + yaw)*m_sVideoInfo.iFaceWidth / S_PI_2 - 3 * m_sVideoInfo.iFaceWidth - 0.5;pSPosOut->y = (S_PI_2 - pitch) * square / S_PI_2 - square / 2 - 0.5;}
}

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