计算3D坐标

Question

我最近一直在尝试从鼠标位置计算3D点。到目前为止，我有这个：

const D3DXMATRIX* pmatProj = g_Camera.GetProjMatrix();

POINT ptCursor;
GetCursorPos( &ptCursor );
ScreenToClient( DXUTGetHWND(), &ptCursor );

// Compute the vector of the pick ray in screen space
D3DXVECTOR3 v;
v.x = ( ( ( 2.0f * ptCursor.x ) / pd3dsdBackBuffer->Width ) - 1 ) / pmatProj->_11;
v.y = -( ( ( 2.0f * ptCursor.y ) / pd3dsdBackBuffer->Height ) - 1 ) / pmatProj->_22;
v.z = 1.0f;

// Get the inverse view matrix
const D3DXMATRIX matView = *g_Camera.GetViewMatrix();
const D3DXMATRIX matWorld = *g_Camera.GetWorldMatrix();
D3DXMATRIX mWorldView = matWorld * matView;
D3DXMATRIX m;
D3DXMatrixInverse( &m, NULL, &mWorldView );

// Transform the screen space pick ray into 3D space
vPickRayDir.x = v.x * m._11 + v.y * m._21 + v.z * m._31;
vPickRayDir.y = v.x * m._12 + v.y * m._22 + v.z * m._32;
vPickRayDir.z = v.x * m._13 + v.y * m._23 + v.z * m._33;
vPickRayOrig.x = m._41;
vPickRayOrig.y = m._42;
vPickRayOrig.z = m._43;

然而，由于我的数学技能乏善可陈，我不确定如何利用方向和原点来产生一个位置。我需要执行哪些计算/公式才能产生预期的结果？

Answer 1

就像a * x + b一样，除了三次。

来自d的任何距离vPickRayOrig（正面或负面）：

newPos.x = d * vPickRayDir.x + vPickRayOrig.x;
newPos.y = d * vPickRayDir.y + vPickRayOrig.y;
newPos.z = d * vPickRayDir.z + vPickRayOrig.z;