# A weird question regarding isometric design

## choice

• ### 6

• Total voters
6

#### gstv87

##### Veteran
take a look at these pics and comment, to your eyes, which one makes the most sense or is most aesthetically pleasing.
there's a curious mathematical conundrum behind them I want to discuss, but I want an unbiased opinion from somebody totally oblivious to it.

for reference, the character dummies are about 1.8m tall or 6 ft

J-G

#### J-G

##### Veteran
I think 5 makes more sense to me

#### Kato-A

##### Artist and developer
I don't get the differences, between 1, 2, 5, and 3, 4, 6

#### Hyouryuu-Na

##### Sodium girl is on a break
@Kato-A You're not the only one ^^;
I guess there's slight changes in the angle but its so small that it doesn't really stand out that much.

Edit: After staring at the picture for quite some time, I think I like 1 (with accessory) and 3 (no accessory)

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#### JosephSeraph

##### White Mage
For me, 1 (slightly stretched vertically?)
I think I get what's going on, though. But the difference is too subtle to properly rationalize like that, especially since you did give us too many options and the difference between the accessory or no accessory is irrelevant for the math / angle problem.

When I do 3D like that (NOT isometric... Ortographic 1/2, isometric is something else entirely) I will usually have a camera at a 45 degree angle looking at the middle of the screen, and have a vertical stretch of 1.414. That'll make a box have both its top and it's bottom shape be perfect squares, or a square tile look, well, square, at the given camera angle and video stretch.

edit: that being said, my way of doing ortographic 1/2 is kinda weird. I should probably try to adapt these numbers for ortographic 3/4 at some point, having the camera point at a 3/4 angle and doing the vertical stretch so that a floor tile, or the sky-facing side of a cube = a square. welp, complicated. can't talk too much further about this without going into blender and cracking my head myself! XD

#### Kato-A

##### Artist and developer
Just a minimal change in perspective that is barely noticeable, this is image 2 over image 1

#### gstv87

##### Veteran
will usually have a camera at a 45 degree angle looking at the middle of the screen, and have a vertical stretch of 1.414. That'll make a box have both its top and it's bottom shape be perfect squares
.....annnnnnnd that's where the matter is going.... kinda.

here's what's going on:
I didn't made those models. They are at different scales. The monument is scaled ~50% down to fit 5 grid squares across.

it fits the camera always square, regardless of camera declination, which is 37 degrees.
you see how at 37 degrees it almost fits a perfect 5/4 area print, and almost a 1/1 silhouette when considering the height of the base?
that grid was made that size to fit the stride of the character.

yellow square is 48x64, blue is 32x64, so when standing still, the sprite fits within the 32px of Ace's grid.

*EVERYTHING* I threw at that grid, having those measurements in mind, gravitated towards 37 degrees being the most accurate, not 45.

picture 5 of that first set? 37 degrees.
everything else, is 40 degrees.
picture 1, is the set at 40 degrees, as it comes.... everything is centered to the grid.
picture 2, is the same set, but the statue is squashed a bit from the top, to fit a 2/1 ratio.
picture 3 and 4, same but with no halo on the statue, neat and squashed.
picture 5, 37 degrees, halo, neat, 3/2 ratio.
picture 6, 37 degrees, no halo, squashed.

you can count pixels right from that picture, and you'll see the math.

For me, 1 (slightly stretched vertically?)
see? it looks stretched, but it's actually the correct proportion!
the thing is, it's at 40, not 45, and it looks off.... but at 37, it looks correct!

there's something going on with the "vertical" when comparing that statue to the characters.

look at what happens with the same characters in another scene.

40 deg.

37 deg.

see how everything seems to have the "vertical" almost perfectly aligned between pillars and characters, and characters and back wall?

the problem is, the back wall is 1 and 3/4er grid squares, when it should be 2 grid squares, to work with autotiles.

when I make them 2 squares tall, the perspective looks off.

it is as if the back wall was angled respect to the "vertical", and parallel to the camera.

everything related to the props, checks out.... at 35, 37, 40, 45 and even 50 degrees.

the walls?
I can't prevent them from looking like that, at any angle.
every time I try to make them work 2x2, they look like that.
the only "correct" size, is not at all correct, at 1 and 3/4 grid squares, or 1 and 5/8ths, which I also considered.

with no walls?
the props look OK, even when the character is not aligned to the grid.
(which is something I also considered: pixel movement. But dropped it because it interferes with the battle system)

What The Maths, here?

(that house model, is from Oblivion. They come as interior and exterior models. When I aligned them and measured the wall thickness, they came out, at 37 degrees, at almost exactly half *my* grid size. And my grid size was based on another model completely unrelated. HOW does that proportion hold, at 37 degrees, but not 45, when that figure of 37 came out of a calculation I made with another model!?)

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#### JosephSeraph

##### White Mage
Hmm indeed that's super odd. I don't think I can help any further than showing an example map with my own numbers -- keep in mind this perspective is EXTREMELY fake, and it's only one of several possible approaches.

So here you have a camera that's at a perfect 45 degrees. At this number, and a vertical stretching of ~143%....

I do get everything to neatly fit into a square grid. But rotated objects WILL look pretty awful at this. This is one solution and it's not the best but it's the one I had worked at the time (this is a 5 year old map xD)

By playing around with other angles and vertical stretch ratios (i don't think you're trying vertical stretching) it's possible to align the square to the floor in different ways i think... but yeah, there are drawbacks to every form of trying to fit graphics into an ortographic grid-locked viewpoint.

hope this helps but it probably wont

#### gstv87

##### Veteran
but that's the thing: I don't want to stretch anything.

there must be a way to have a wall at reasonable height in 3D space, that also looks proportionally correct in 2D, when viewed at a perspective of around 37 degrees.
there's a lot more going on behind that, involving the battler animations on the battle scene, their sprite sizes, their file sizes, etc... things that I already have tuned out, that leave this loose end to tie up.
if I was to fit everything to this, it'd throw all that out of balance.

for indoor shots, this is manageable, because the background is almost always black.
but for outdoor walls, there has to be a way to render tall walls that can reach 3 or 4 times the height of the character, without looking "flat", and holding true when compared with other objects around the scene.
the games I've looked at avoid this by being either true isometric (45º x, 45º z) and blurring the effect across two planes, or by being Ace games made with parallax mapping and a ton of layering tiles dedicated to what could have been autotiles.
Factorio was the closest thing to orthographic AND autotiles I could find, and that's where I began, but I want to build something more detailed than that.
I can't use true isometric, and I don't like using parallax because the whole thing would be huge in megabytes.

(door frames and windows are a huge point to balance, because the character often stands in front of them, so their size and proportion is more evident. And, when it comes to doors, they must be one tile wide at most, because the tiles to either side can't be transparent, and can't be two tiles high, and can't be less than what the character sprite is tall, proportionally.)

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#### gstv87

##### Veteran
eureka? I guess?
¯\_(ツ)_/¯

the problem has always been getting the wall, the detailing, the pillars, the windows/doors, and height to match up, with the aim of creating a western european style with a small overhang of upper floors.

I think I'm settling with a small displacement of the whole thing towards the back, so it's the pillars that match up with the grid rather than the foot of the wall.
the indentation must exist, for some weird perceptive reason, so that the wall doesn't appear "flat" when considering the grid.

not ideal, not the most elegant solution, and I still can't shake the feeling that it looks flat when used on it's own.
on top of that, I've concluded that the whole thing will have to be made, lit, rendered with shadows, and the shadows baked into the final cut of the overlay tiles.
So the walls (bare) will be autotiles, they'll only be good for tiling horizontally, and anything that goes on top of that will have to add the shading through transparency on overlay tiles, such as furniture, windows, and anything that's supposed to be below any overhangs will have to have shadows and ambient occlusion baked in.

Fortunately, I've accounted for that in advance, so the calculations are still valid, but there's a lot of surface that'll go to rendering just shadows, which will make the cutting of the final product a LOT more complicated.

now excuse me while I go inside the closet to cry out in desperation.

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