3D space: following the direction that an object is pointing towards, using the mouse pointer

Question

Given the 3D vector of the direction that the camera is facing and the orientation/direction vector of a 3D object in the 3D space, how can I calculate the 2-dimensional slope that the mouse pointer must follow on the screen in order to visually be moving along the direction of said object?

Basically I'd like to be able to click on an arrow and make it move back and forth by dragging it, but only if the mouse pointer drags (roughly) along the length of the arrow, i.e. in the direction that it's pointing to.

thank you

Answer 1

I'm not sure I 100% understand your question. Would you mind posting a diagram?

You might find these of interest. I answered previous questions to calculate a local X Y Z axis given a camera direction (look at) vector, and also a question to translate an object in a plane parallel to the camera.

Both of these examples use Vector dot product, Vector cross product to compute the required vectors. In your example the vector dot product can be also used to output the angle between two vectors once you have found them.

Answer 2

It depends to an extent on the transformation that you are using to convert your 3d real world coordinates to 2d screen coordinates, e.g. perspective, isometric, etc... You will typically have a forward (3d -> 2d) and backward (2d -> 3d) transformation in play, where the backward transformation loses information. (i.e. going forward each 3d point will map to a unique 2d point, but going back from the point may not yield the same 3d point). You can often project the mouse point onto the object to get the missing dimension.

For mouse dragging, you typically get the user to specify an operation (translation on the plane of projection, zooming in or out, or rotating about an anchor point). Your input is the mouse coordinate at the start and end of the drag, which you transform into your 3d coordinate system to get two 3d coordinates, which will give you dx, dy, dz for dragging / translation etc...