如何使用 DirectXMath 将世界空间中的 3D position 转换为 2D position

Question

I want to take advantage of the SSE intrinsics (mostly for the speed advantage) that DirectXMath provides How would i do it? this is the current code im using

DirectX::XMFLOAT4 clipCoordinates;
DirectX::XMFLOAT4X4 WorldMatrix4x4;
DirectX::XMStoreFloat4x4(&WorldMatrix4x4, WorldMatrix);
    
clipCoordinates.x = pos.x * WorldMatrix4x4._11 + pos.y * WorldMatrix4x4._12 + pos.z * WorldMatrix4x4._13 + WorldMatrix4x4._14;
clipCoordinates.y = pos.x * WorldMatrix4x4._21 + pos.y * WorldMatrix4x4._22 + pos.z * WorldMatrix4x4._23 + WorldMatrix4x4._24;
clipCoordinates.z = pos.x * WorldMatrix4x4._31 + pos.y * WorldMatrix4x4._32 + pos.z * WorldMatrix4x4._33 + WorldMatrix4x4._34;
clipCoordinates.w = pos.x * WorldMatrix4x4._41 + pos.y * WorldMatrix4x4._42 + pos.z * WorldMatrix4x4._43 + WorldMatrix4x4._44;

Answer 1

If by 2D position you mean screenspace coordinates:

First transform from local space to world space:

XMVECTOR world_pos = XMVector4Transform(pos, world_matrix);

Then transform from world space to camera space:

XMVECTOR view_pos = XMVector4Transform(world_pos, view_matrix);

Then transform from camera space to clip space:

XMVECTOR clip_pos = XMVector4Transform(view_pos , proj_matrix);

Remember that you can concatenate all of these into one transform by multiplying the XMMATRIX matrix = world_matrix * view_matrix * proj_matrix; together and then transforming the point by matrix .

Now divide by w coordinate to get NDC:

XMVECTOR w_vector = XMVectorSplatW(clip_pos);
XMVECTOR ndc = XMVectorDivide(clip_pos, w_vector);

You can combine the transform and divide by using XMVECTOR ndc = XMVector3TransformCoord(clip_pos, matrix);

Your NDC x and y components are in interval [-1,1] . To transform them in [0,ScreenWidth] and [0,ScreenHeight] you use the following formulas:

float ndc_x = XMVectorGetX(ndc);
float ndc_y = XMVectorGetY(ndc);
float pixel_x = (1.0f + ndc_x) * 0.5 * ScreenWidth;
float pixel_y = (1.0f - ndc_y) * 0.5 * ScreenHeight;

And those are your screen coordinates.