Muli3D <6> Struct m3dtriangleinfo 的属性 fZDdx，fZDdy 的推导

记录一下：

根据 

struct m3dtriangleinfo { float32 fCommonGradient; ///< Gradient constant. const m3dvsoutput *pBaseVertex; ///< Base vertex for gradient computations. /// z partial derivatives with respect to the screen-space x- and y-coordinates. float32 fZDdx, fZDdy; /// w partial derivatives with respect to the screen-space x- and y-coordinates. float32 fWDdx, fWDdy; shaderreg ShaderOutputsDdx[c_iPixelShaderRegisters]; ///< Shader register partial derivatives with respect to the screen-space x-coordinate. shaderreg ShaderOutputsDdy[c_iPixelShaderRegisters]; ///< Shader register partial derivatives with respect to the screen-space y-coordinate. /// Integer-coordinates of current pixel; needed by pixel shader for computation of partial derivatives. uint32 iCurPixelX, iCurPixelY; float32 fCurPixelInvW; ///< 1.0f / w of the current pixel; needed by pixel shader for computation of partial derivatives. }; 知道了 fZDdx, fZDdy 其实就是 z partial derivatives with respect to the screen-space x- and y-coordinates.就是 ∂z/∂x, ∂z/∂y

那么 怎么计算 ∂z/∂x, ∂z/∂y， 在Muli3D给出来结果：

// v1.x - v0.x, v2.x - v0.x const float32 fDeltaX[2] = { i_pVSOutput1->vPosition.x - i_pVSOutput0->vPosition.x, i_pVSOutput2->vPosition.x - i_pVSOutput0->vPosition.x }; // v1.y - v0.y, v2.y - v0.y const float32 fDeltaY[2] = { i_pVSOutput1->vPosition.y - i_pVSOutput0->vPosition.y, i_pVSOutput2->vPosition.y - i_pVSOutput0->vPosition.y }; // value = 1.0f / (v1.x - v0.x) * (v2.y - v0.y) - (v2.x - v0.x) * (v1.y - v0.y) m_TriangleInfo.fCommonGradient = 1.0f / ( fDeltaX[0] * fDeltaY[1] - fDeltaX[1] * fDeltaY[0] ); // 设置pBaseVertex m_TriangleInfo.pBaseVertex = i_pVSOutput0; // The derivatives with respect to the y-coordinate are negated, because in screen-space the y-axis is reversed. // v1.z - v0.z , v2.z - v0.z const float32 fDeltaZ[2] = { i_pVSOutput1->vPosition.z - i_pVSOutput0->vPosition.z, i_pVSOutput2->vPosition.z - i_pVSOutput0->vPosition.z }; // ((v1.z - v0.z) * (v2.y - v0.y) - (v2.z - v0.z) * (v1.y - v0.y)) / (v1.x - v0.x) * (v2.y - v0.y) - (v2.x - v0.x) * (v1.y - v0.y) m_TriangleInfo.fZDdx = ( fDeltaZ[0] * fDeltaY[1] - fDeltaZ[1] * fDeltaY[0] ) * m_TriangleInfo.fCommonGradient; // -((v1.z - v0.z) * (v2.x - v0.x) - (v2.z - v0.z) * (v1.x - v0.x)) / (v1.x - v0.x) * (v2.y - v0.y) - (v2.x - v0.x) * (v1.y - v0.y) m_TriangleInfo.fZDdy = -( fDeltaZ[0] * fDeltaX[1] - fDeltaZ[1] * fDeltaX[0] ) * m_TriangleInfo.fCommonGradient; 那么问题来了，上面是怎么推导出来的：

主要参考 ： http://blog.csdn.net/aa20274270/article/details/70159075

开始推导：

这里就已经推导出来了，

对比代码的 m_TriangleInfo.fZDdx

((v1.z - v0.z) * (v2.y - v0.y) - (v2.z - v0.z) * (v1.y - v0.y)) / (v1.x - v0.x) * (v2.y - v0.y) - (v2.x - v0.x) * (v1.y - v0.y)

和   m_TriangleInfo.fZDdy

 -((v1.z - v0.z) * (v2.x - v0.x) - (v2.z - v0.z) * (v1.x - v0.x)) / (v1.x - v0.x) * (v2.y - v0.y) - (v2.x - v0.x) * (v1.y - v0.y)

完全一致。

接下来，对于 m3dtriangleinfo 的 属性 fWDdx, fWDdy; 方法也是一样的。