[Book 1, Chapter 4.2] Z axis orientation

[dimitry-ishenko]

From chapter 4.2 of book 1:

For simplicity we'll start with the camera center at (0,0,0). We'll also have the y-axis go up, the x-axis to the right, and the negative z-axis pointing in the viewing direction. (This is commonly referred to as right-handed coordinates.)

It is my understanding that arrows on axes indicate positive direction. So, the above paragraph states that negative Z points towards the viewport, but the image shows the opposite -- the arrow (aka positive Z) is pointing towards the viewport.

Did I miss something?

[rupsis]

The coordinates here just act as a reference. Typically we associate axis illustrations (pointing arrows) with positive direction, but that's not the case here. Not wrong, but potentially confusing.

I personally think we should always label the axes. @hollasch do you have any thoughts?

p.s, linking to Right hand rule might be helpful.

[dimitry-ishenko]

It definitely confused me. I try to write my own code and when I glanced at the illustration above to make sure I go my axis directions right, I ended up with inverted Z axis.

Something like this might be less confusing:

[dimitry-ishenko]

This is slightly OT, but why did you chose right-handed coordinates? From what I understand both OpenGL and DirectX both use left-handed one.

[armansito]

I agree that the diagram is confusing. I understand the arrows as demonstrating the camera's basis vectors (up, right, look) and not the coordinate axes but this distinction could be illustrated better. Somewhat relatedly, I'm currently working on a similar diagram for the ray generation chapter of the GPU book where I intend to illustrate this clearly.

This is slightly OT, but why did you chose right-handed coordinates? From what I understand both OpenGL and DirectX both use left-handed one.

I can't speak for the authors' original choice but I think this is a matter of preference. The convention varies between graphics APIs (IIRC OpenGL defines a right left handed NDC system, Direct3D and Metal are left-handed, Vulkan is right-handed but with the $+y$-axis pointing down s.t. the view direction is towards $+z$).

It's ultimately a matter of convention. An application that targets more than one of these APIs will typically pick its own convention and reconcile any mismatch when computing the transformations. FWIW, I picked a right-handed ($+y$-up) system for the GPU book as it is common to work in right-handed world and object-space coordinates.

[hollasch]

Arrows indicate vector direction, always positive. But these are not axes; they are three independent vectors used to construct scene rays. They are not orthonormal, and they are not even orthogonal. In practice, the scene ray will move from target pixel to target pixel (and around target pixels for sampling). These are not the $X$, $Y$, or $Z$ basis vectors.

[dimitry-ishenko]

Arrows indicate vector direction, always positive. But these are not axes;

@hollasch that's not what the paragraph above the picture says (see my original post). Quote from the paragraph: "We'll also have the y-axis go up, the x-axis to the right, and the negative z-axis pointing in the viewing direction."

Figure 3 just below it seems to visually show what was said in the paragraph, but positive z-axis is pointing in the viewing direction.

They are not orthonormal

Not sure what this has to do with anything. We are talking about axis directions and not basis vectors.

and they are not even orthogonal.

They are according to the paragraph above. Are they not?

If they aren't, then I am even more confused by that paragraph and picture... 😕

[ParthKohli]

I was also confused by the z-axis orientation: the code seems to directly disagree with the diagram. The following in 1.4.2 indicates that the viewport is in the negative direction:

auto viewport_upper_left = camera_center
                             - vec3(0, 0, focal_length) - viewport_u/2 - viewport_v/2;

But if right-handed coordinates were actually being followed, then applying the right-hand rule suggests that the viewport is in the positive z-direction.

The above code listing should be modified to the following throughout the code:

auto viewport_upper_left = camera_center
                             + vec3(0, 0, focal_length) - viewport_u/2 - viewport_v/2;