3D controller, perspective correct interpolation

[theagentd]

Hello. I want to add a 3D position controller like the red, green and blue arrows in this Maya:


The problem is handling mouse input. The movement has to snap to the axes of the controller. I therefore thought that the best way of doing this is to project the axis to the screen (multiply it by the view and projection matrices) so I simply have a 2D line on the screen. I then find the closest point lying on this line from the mouse. Finally I un-project this point back to world space, and I'll know exactly where the controller has been moved in 3D space.

The problem is that I don't know how to correctly interpolate the depth of the point based on the two end points. I'm pretty sure the solution is perspective correct interpolation which I've glimpsed over for texture mapping, but I only have a line, not a triangle! Given two 3D points on the screen (normalized device coordinates) how do I correctly interpolate the depth value for any point on the line between the two given points? (Linear interpolation does not give the right value due to the 3D perspective.)

[Danny02]

let say you figured out how to start dragging your object and now you know the line you want the object to move one (m) and the position of the mouse on screen(Pm).

Now you un-project the mouse position to a line in 3D space(l) (near&far clipping plane).

the next thing is to find the nearest point on (m) to (l), this is the new position of you object.
(to lazy to type hier an example how to do it ask if you have any questions)

Also beware to check if the movement vector has a very smal angle to the mouse vector or even parallel, because will cause problems.

[theagentd]

let say you figured out how to start dragging your object and now you know the line you want the object to move one (m) and the position of the mouse on screen(Pm).

Now you un-project the mouse position to a line in 3D space(l) (near&far clipping plane).

the next thing is to find the nearest point on (m) to (l), this is the new position of you object.
(to lazy to type hier an example how to do it ask if you have any questions)

Also beware to check if the movement vector has a very smal angle to the mouse vector or even parallel, because will cause problems.

That's exactly what I want to do, but don't I have to correctly interpolate the depth of the point in a specific way? =S

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[Danny02]

nah I propose to do everything in 3D not in 2D as you explained, also I don't think that you have to snap to the axis

ps:

Finally I un-project this point back to world space, and I'll know exactly where the controller has been moved in 3D space.

you can not unproject a 2D point to a 3D point, you can only get a line in 3D space out of a 2D point. To get the correct Position in worldspace you have to check where the two lines(unprojected & movment axis) are intersecting.
If you want to do it your way. I think what I did is perhaps cleaner cause you aren'T doing that much conversation between spaces.

[Riven]

how do I correctly interpolate the depth value for any point on the line between the two given points? (Linear interpolation does not give the right value due to the 3D perspective.)

Interpolate linearly in model space, not in screen space.

[theagentd]

I hate them.

Coding like I'm on fire at the moment, gimme a second to test this crap... >___<