UE4 MVP 坐标转换

局部的模型点从局部空间（相对空间）到世界空间以及到屏幕空间。

ViewProject

视图投影矩阵。

	ULocalPlayer* const LP = Player ? Player->GetLocalPlayer() : nullptr;
	if (LP && LP->ViewportClient)
	{
		// get the projection data
		FSceneViewProjectionData ProjectionData;
		if (LP->GetProjectionData(LP->ViewportClient->Viewport, eSSP_FULL, /*out*/ ProjectionData))
		{ 
			FMatrix const InvViewProjMatrix = ProjectionData.ComputeViewProjectionMatrix().InverseFast();
		}
	}

DeprojectScreenToWorld

屏幕空间到世界空间。

void FSceneView::DeprojectScreenToWorld(const FVector2D& ScreenPos, const FIntRect& ViewRect, const FMatrix& InvViewProjMatrix, FVector& out_WorldOrigin, FVector& out_WorldDirection)
{
	float PixelX = FMath::TruncToFloat(ScreenPos.X);
	float PixelY = FMath::TruncToFloat(ScreenPos.Y);

	// Get the eye position and direction of the mouse cursor in two stages (inverse transform projection, then inverse transform view).
	// This avoids the numerical instability that occurs when a view matrix with large translation is composed with a projection matrix

	// Get the pixel coordinates into 0..1 normalized coordinates within the constrained view rectangle
	const float NormalizedX = (PixelX - ViewRect.Min.X) / ((float)ViewRect.Width());
	const float NormalizedY = (PixelY - ViewRect.Min.Y) / ((float)ViewRect.Height());

	// Get the pixel coordinates into -1..1 projection space
	const float ScreenSpaceX = (NormalizedX - 0.5f) * 2.0f;
	const float ScreenSpaceY = ((1.0f - NormalizedY) - 0.5f) * 2.0f;

	// The start of the ray trace is defined to be at mousex,mousey,1 in projection space (z=1 is near, z=0 is far - this gives us better precision)
	// To get the direction of the ray trace we need to use any z between the near and the far plane, so let's use (mousex, mousey, 0.5)
	const FVector4 RayStartProjectionSpace = FVector4(ScreenSpaceX, ScreenSpaceY, 1.0f, 1.0f);
	const FVector4 RayEndProjectionSpace = FVector4(ScreenSpaceX, ScreenSpaceY, 0.5f, 1.0f);

	// Projection (changing the W coordinate) is not handled by the FMatrix transforms that work with vectors, so multiplications
	// by the projection matrix should use homogeneous coordinates (i.e. FPlane).
	const FVector4 HGRayStartWorldSpace = InvViewProjMatrix.TransformFVector4(RayStartProjectionSpace);
	const FVector4 HGRayEndWorldSpace = InvViewProjMatrix.TransformFVector4(RayEndProjectionSpace);
	FVector RayStartWorldSpace(HGRayStartWorldSpace.X, HGRayStartWorldSpace.Y, HGRayStartWorldSpace.Z);
	FVector RayEndWorldSpace(HGRayEndWorldSpace.X, HGRayEndWorldSpace.Y, HGRayEndWorldSpace.Z);
	// divide vectors by W to undo any projection and get the 3-space coordinate
	if (HGRayStartWorldSpace.W != 0.0f)
	{
		RayStartWorldSpace /= HGRayStartWorldSpace.W;
	}
	if (HGRayEndWorldSpace.W != 0.0f)
	{
		RayEndWorldSpace /= HGRayEndWorldSpace.W;
	}
	const FVector RayDirWorldSpace = (RayEndWorldSpace - RayStartWorldSpace).GetSafeNormal();

	// Finally, store the results in the outputs
	out_WorldOrigin = RayStartWorldSpace;
	out_WorldDirection = RayDirWorldSpace;
}

ProjectWorldToScreen

世界空间到屏幕空间。

通过ViewProjectionMatrix矩阵把点从世界位置转为视口下，然后再从视口点转为近剪裁面上的点

FPlane Result = ViewProjectionMatrix.TransformFVector4(FVector4(WorldPosition, 1.f));

通过投射除法映射到NDC空间[-1.1]

// the result of this will be x and y coords in -1..1 projection space
const float RHW = 1.0f / Result.W;
FPlane PosInScreenSpace = FPlane(Result.X * RHW, Result.Y * RHW, Result.Z * RHW, Result.W);

通过半兰伯特手法把[-1.1]映射到[0,1]

// Move from projection space to normalized 0..1 UI space
const float NormalizedX = ( PosInScreenSpace.X / 2.f ) + 0.5f;
const float NormalizedY = 1.f - ( PosInScreenSpace.Y / 2.f ) - 0.5f;

通过和屏幕宽高相乘获得屏幕的位置

FVector2D RayStartViewRectSpace(
			( NormalizedX * (float)ViewRect.Width() ),
			( NormalizedY * (float)ViewRect.Height() )
			);

bool FSceneView::ProjectWorldToScreen(const FVector& WorldPosition, const FIntRect& ViewRect, const FMatrix& ViewProjectionMatrix, FVector2D& out_ScreenPos)
{
	FPlane Result = ViewProjectionMatrix.TransformFVector4(FVector4(WorldPosition, 1.f));
	if ( Result.W > 0.0f )
	{
		// the result of this will be x and y coords in -1..1 projection space
		const float RHW = 1.0f / Result.W;
		FPlane PosInScreenSpace = FPlane(Result.X * RHW, Result.Y * RHW, Result.Z * RHW, Result.W);

		// Move from projection space to normalized 0..1 UI space
		const float NormalizedX = ( PosInScreenSpace.X / 2.f ) + 0.5f;
		const float NormalizedY = 1.f - ( PosInScreenSpace.Y / 2.f ) - 0.5f;

		FVector2D RayStartViewRectSpace(
			( NormalizedX * (float)ViewRect.Width() ),
			( NormalizedY * (float)ViewRect.Height() )
			);

		out_ScreenPos = RayStartViewRectSpace + FVector2D(static_cast<float>(ViewRect.Min.X), static_cast<float>(ViewRect.Min.Y));

		return true;
	}

	return false;
}