Let me get this straight :

**Linear projection** are **orthographic** projections.

Rather, I would say that Orthographic projections are linear projections. That makes 'oblique is linear, but not orthographic' make sense easier.

Only, in the **Ninja Gaiden** screen, we're dealing with an oblique projection which is a **linear projection** but not an **orthographic** projection. Am I right so far?

dpixel's edit would be **oblique projection**:

While my original screen would be... **orthographic projection**?:

dpixel's edit is definitely oblique -- the shapes described by his lines are incompatible with orthographic projection of rectangular objects. If that was an orthographic drawing, it would describe instead a series of parallelograms.

Your original could be considered as either oblique or orthographic, since no angling is involved.

Ok, I think this is the definition I was looking for. I've saved both pictures to my hardrive by the way.

So this perspective:

...is equivalent to this one:

Yes.

While this one:

...is equivalent to this one:

No. Sorry, I don't know how to render oblique projection with blender. Those two views I rendered are *both orthographic*. The first view has the object planes aligned perfectly with the camera, the second has them differing by 22.5 degrees in one axis.

So basically, I have to choose either an oblique or orthographic projection and then stick with it, am I getting this right?

.. Up to a certain point. It's pretty common to cheat perspective for gameplay purposes -- eg

LOZ:LttP (TVTropes warning).

Oblique projection just basically says out of the gate 'There's no camera, just lies and other lies.' so it gives you an excuse for the other cheats

(or to put it another way: an orthographic view is a possible perspective projection from a lense with infinite distance from the scene and infinite focal distance. Oblique just isn't a possible perspective projection, it's not something you could actually see given the shapes that are implied -- it's "forced depth".)

This would be orthographic:

The image isn't orthographic (it's a photo taken with a real lense, meaning it is in perspective, probably with a degree of lense distortion involved as well)

Some objects in perspective shots may be 'close enough' to orthographic, though -- remember my comment about infinite distance? The further the camera is from the object, the closer the result is to an orthographic projection. But we are talking serious distances here generally, no less than 100m just to qualify as 'getting somewhat towards ortho'. The top plane of that roll is probably still subject to perspective distortion.

Regarding oblique, as far as I know, there are no apparatus capable of taking 'oblique photos', if that concept even makes complete sense.

My question is: based on my screen, just how much of the top should I see? What's the eye level here?

Okay, I'll stop you there, because : that's up to you. Projections are not viewpoints. there are a range of possible oblique views, there are a much larger range of possible orthographic views (on a given scene).

Oh, btw, eye level is not a thing that effects projection (except clipping the image) in orthographic or oblique projections. The horizon is technically present but infinitely distant. Moving around the centre of the camera is directly equivalent to panning through the projected 2d image -- no angles or lengths ever change as a result.

The only meaningful parameters for orthographic projection are rotation (the three angles specifying the camera plane's orientation in 3d space).

For Oblique, correct me if I'm wrong, it has only two parameters: angle on the 2d plane, and ratio aka 'depth'.

Ratio describes the length of projection for a hypothetical cube of space.

Looking at dpixel's edit, we can work out the approximate ratio in use:

* One cube of space appears to be 27x27 along the front face, based on the spacing of the divisions.

* The upper face has a length of about 6. (sqrt(3*3 + 5*5) = 5.83, or sqrt(3*3 + 6*6) = 6.7, according to where you think it's correct to measure to. I took the average which is 6.26)

* Therefore the ratio is 6/27, which is 0.222222; or more precisely 6.26 / 27, which is 0.231

However, the problem here is actually one of relative size.

You have indicated the size of a block in your existing work. What is a block's shape in 3d? Is it a cube? Is the toilet roll supposed to occupy the same amount of space as said cube, or a multiple of it (ie, be a cylinder with length equal to diameter)?

If so, the answer is simple: The ellipse that fits exactly into your existing top surface.

Here's my impression of that, with the existing colors which are rather lacking for this:

If this is the wrong scale, then just multiply the sizes of the top surface and re-fit the ellipse to that. That's all I can say for now, I need to get to bed.

EDIT:

So to rephrase that, you need to decide the dimensions of your base unit (assumably that platform block), and the dimensions of your toilet roll. Then you can calculate the ratios between those dimensions, and you will have the information necessary to scale the two visible faces of your block. These scaled faces will exactly indicate the space that the toilet roll occupies, including how much of the top is visible. You can then fit the necessary ellipse onto the scaled top face and extrude a cylinder from it (assuming you want the toilet roll to be axis-aligned with other objects).

EDIT2: cleaned up some stuff and improved my understanding of oblique projection.