虚幻引擎（数学方面未整理）

一、平面的描述使用Ax+By+Cz=W的形式。因此在手动计算时要注意不要使用现成的结论：Ax+By+Cz+D=0的形式：

/**
 * Structure for three dimensional planes.
 *
 * Stores the coeffecients as Xx+Yy+Zz=W.
 * Note that this is different from many other Plane classes that use Xx+Yy+Zz+W=0.
 */
MS_ALIGN(16) struct FPlane
	: public FVector
{
public:

	/** The w-component. */
	float W;

二从观察点和朝向定义View矩阵

void FViewMatrices::UpdateViewMatrix(const FVector& ViewLocation, const FRotator& ViewRotation)
{
	ViewOrigin = ViewLocation;

	FMatrix ViewPlanesMatrix = FMatrix(
		FPlane(0, 0, 1, 0), //X平面
		FPlane(1, 0, 0, 0), //Y平面
		FPlane(0, 1, 0, 0), //Z平面
		FPlane(0, 0, 0, 1)); //W平面，这个其实就是单纯的满足矩阵的要求，表示是一个点。

	ViewMatrix = FTranslationMatrix(-ViewLocation);
	ViewMatrix = ViewMatrix * FInverseRotationMatrix(ViewRotation);
　　　　　//世界坐标到观察坐标的变换：V=World的逆变换 = （旋转矩阵*平移矩阵）的逆变换=平移的逆变换*旋转的逆变换

	ViewMatrix = ViewMatrix * ViewPlanesMatrix;

	InvViewMatrix = FTranslationMatrix(-ViewMatrix.GetOrigin()) * ViewMatrix.RemoveTranslation().GetTransposed();

	// Duplicate HMD rotation matrix with roll removed
	FRotator HMDViewRotation = ViewRotation;
	HMDViewRotation.Roll = 0.f;
	HMDViewMatrixNoRoll = FInverseRotationMatrix(HMDViewRotation) * ViewPlanesMatrix;

	PreViewTranslation = -ViewOrigin;
	//using mathematical equality rule for matrix inverse: (A*B)^-1 == B^-1 * A^-1
	OverriddenTranslatedViewMatrix = TranslatedViewMatrix = FTranslationMatrix(-PreViewTranslation) * ViewMatrix;
	OverriddenInvTranslatedViewMatrix = InvTranslatedViewMatrix = InvViewMatrix * FTranslationMatrix(PreViewTranslation);

	// Compute a transform from view origin centered world-space to clip space.
	TranslatedViewProjectionMatrix = GetTranslatedViewMatrix() * GetProjectionMatrix();
	InvTranslatedViewProjectionMatrix = GetInvProjectionMatrix() * GetInvTranslatedViewMatrix();

	ViewProjectionMatrix = GetViewMatrix() * GetProjectionMatrix();
	InvViewProjectionMatrix = GetInvProjectionMatrix() * GetInvViewMatrix();
}