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

屏幕空间深度梯度计算

最新推荐文章于 2024-09-19 22:08:02 发布

aa20274270

最新推荐文章于 2024-09-19 22:08:02 发布

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分类专栏：光栅渲染器文章标签： 3D数学

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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.youkuaiyun.com/aa20274270/article/details/70159075

开始推导：