A Matter of Perspective...

[Ai]

You take the ruleset of the cabinet projection and construct an ellipse.
Make sure that you don't draw a circle. The ellipse is affected by the projection as well.

look at this - that's how a circle appears at a top-plane in cavalier projection:

I think it's worth noting, that for any given oblique projection, you can take the 'base circle' (circle as it would be plotted on front face), and turn it into a correct circle for one of the sides by scaling it and then skewing it:



Obviously you then need to clean it up, but it makes any such process pretty easy overall.

Strongly agree with your message that a projection is not necessarily a perspective, though perspective is a type of projection. This seems to be the central issue that Zizka is struggling with here, the fact that what we are dealing with is not a perspective.

[Zizka]

Alright, this is what I have so far:

Now, shadows nonwithstanding, does it look right to you guys?

Is this how things should look, especially "C" and "D"?

EDIT: Cyangmou: The images are hosted at noelshack and Im.gur. I don't know how long either will be in business, so there is no guarantee.

Can I post your spritorial at other places on the internet? The one about perspective? I'd mention it's from you of course.

[Cyangmou]

Can I post your spritorial at other places on the internet? The one about perspective? I'd mention it's from you of course.

It's not a "tutorial" in a tutorial sense, since a lot of the information also depends on the critique text.

As you see some further critique were given by Hawken and AI, which also build on it.
I am neither sure if everything I wrote down is 100% exact nor formulated in the clearest way possible.
I haven't planned it out as tutorial, I just put down thoughts based on what was already there and regarding your questions.

The best would therefore be, if you post to the whole thread or directly to the message (you can get a link by clicking on the message header)



However since there seems to be a generally huge confusion about the topic it might be best to turn everything in this thread and in hawken's thread
http://wayofthepixel.net/index.php?topic=17704.msg160136#msg160136
in a clearly formated and easily understandable infograph.
However currently I am busy with link directories for the good reads section, so this project, despite it would help, has to wait because of time reasons.

[Ai]

Is this how things should look, especially "C" and "D"?

Hmm. Well, this is close enough, I think. Except that it isn't using cavalier projection (it's using a general oblique projection with an angle of something like -33.6 degrees). Did you change your mind about that?

Some small issues I thought I'd better point out just in case:
* the vertical roll C is intersecting 2px with the wall (top plane of roll is 8px, top plane of blocks is 6px.) If the bright line is not actually part of the top face, then the difference is more severe (7 and 5).
* The small roll D has an elliptical (3:4) inner contour and an elliptical (7:6) outer contour. Given that the end of the roll is facing front, ideally these should both be as close to circular as possible.

I consider them small things because games often successfully get away with worse inconsistencies.

I presume you mean 'Imgur' (no dot).

[Pinux]

You could Look at Castle Crashers even though it isn't a pixel styled game

[Zizka]

@Ai:
Oh I haven't changed my mind, I'm just still experimenting. You're right in your observation.

@Pinux: Could be a good reference, thanks!

So we’ve talked about persepctive so far. I’m currently experimenting but I’m having some trouble still.
Let’s say I use an orthographic perspective and I want to rotate a cube in this perspective, how would I manage this?

So I took some time to really analyze this.

Suppose I want to rotate the rectangle on the “x” axis.

Would it look like this?


The second half of the animation looks right to me but not the first part, why is that?

Since there’s no vanishing point, it makes it more difficult to determine how the rectangle would rotate.

What if I wanted to rotate it on the y axis, how would that work?

[stevenblanc]

You need to add in one or two frames when the lighter portion reaches the bottom the angle would cause it to appear to shrink, as opposed to disappearing completely as it currently does. The same is true when it reappears on the top.

Technically with lighting though the light portion should be identically coloured when its in the center position as well.

Finally I think your proportions are a little off as the diminishing portion of the cube should never be taller than the cube at full front face. It should appear shorter.

[Ai]

So we’ve talked about persepctive so far. I’m currently experimenting but I’m having some trouble still.
Let’s say I use an orthographic perspective and I want to rotate a cube in this perspective, how would I manage this?

So I took some time to really analyze this.

Suppose I want to rotate the rectangle on the “x” axis.

Would it look like this?


The second half of the animation looks right to me but not the first part, why is that?

Not sure.. They're both incorrect in the way stevenblanc specified.

The more or less constant amount of movement per frame you have appears to be correct. However, you are reducing the object's volume during the rotation, which makes it seem like it's not a cube.

I'd suggest you study this, particularly how little the visible profile changes during rotation:


Here's a diagram showing the limits of the profile:



It indicates clearly that the profile never becomes smaller than the straight-on size of one face, and that the profile when straight on is 70% of the size when rotated by 45 degrees (the largest the profile can become). Because we are using an orthographic projection, the object does not become larger or smaller according to it's closeness to the camera.

Since there’s no vanishing point, it makes it more difficult to determine how the rectangle would rotate.

Since there is no vanishing point, you can take your square and rotate it by constant amounts. Then you can just measure the coverage of the two visible faces. My diagram above illustrates this: when rotated by 45 degrees,  the space occupied is 43px and half of this goes to the 'top' face, half to the 'bottom' face.

In orthographic, these ratios are also reversible: if you have a frame (22.5 degrees) where your top face has 13px and the bottom one has 28, then a later frame (67.5 degrees) will have your top face with 28px and the bottom with 13px. In this manner you can construct only 45 degrees of your rotation and get the other 45 degrees 'free'.


rotating y, that's mostly just a 2d transform:



And heck, it's easy enough to do, may as well do Z:


The same set of ratios apply to all of them AFAICS. I would suggest that drawing 3 accurate frames: 0 degrees, 22.5 degrees, and 45 degrees, is enough to extrapolate any further frames correctly.