how to translate 3d mesh, given a view direction and a change in cursor position

Question

My question is similar to 3D Scene Panning in perspective projection (OpenGL) except I don't know how to compute the direction in which to move the mesh.

I have a program in which various meshes can be selected. Once a mesh is selected I want it to translate when click-dragging the cursor. When the cursor moves up, I want the mesh to move up, and so on for the appropriate direction. In other words, I want the mesh to translate in directions along the plane that is perpendicular to the viewing direction.

I have the Vector2 for the Delta (x,y) in cursor postion, and I have the Vector3 viewDirection of the camera and the center of the mesh. How can I figure out which way to translate the mesh in 3d space with the Delta and viewDirection? Will I need other information in order to to this calculation (such as the up, or eye)?

It doesn't matter if if the scale of the translation is off, I'm just trying to figure out the direction right now.

EDIT: for some reason I had a confusion about getting the up direction. Clearly it can be calculated by applying the camera rotation to the specified perspective up vector.

Answer 1

You'll need an additional vector, upDirection, which is the unit vector pointing "up" from your camera. You can now cross-product viewDirection and upDirection to get rightDirection, the vector pointing "right" from your camera.

You want to map y deltas to motion along upDirection (or -upDirection) and x deltas to motion in rightDirection. These vectors are in world-space.

You may want to scale the translation speed to match the mouse speed. If you are using perspective projection you'll want to scale the translation speed with your model's depth with respect to your camera (The further the object is from your camera, the faster you will need to move it if you want it to match the mouse.)