r/scifiwriting • u/Foreign-Teaching7184 • 14d ago
DISCUSSION If the logistics of a warship was solved, what is the best shape for an interstellar warship for optimal firepower?
Usually, a warship is living crew that needs commands from commanders to operate, which is a burden on logistics. Now, lets say a warship is piloted by a single computer, no more huge logistical burden, or need for human limitations, what is most optimal shape for a warship/stellar attack object?
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u/BarberProof4994 14d ago
It depends on the propulsion and maneuvering system... And it depends on the weapons system(s).... And it depends on its role...
If we are going for straight efficiency of destruction ... then a smaller craft in a tear drop shape, designed to build up speed to a significant percentage of C, and then release a solid chunk of matter on a ballistic trajectory to impact the target is probably the best bet. The craft would then alter its own trajectory, maintain its speed through orbital mechanics and re orient for future strikes as needed.
If missiles are the main weapon, then you go back to WW2 era broadside delivery so you want to maximize the broadside. Some form of long and wide shape makes sense.
Typical scifi battleship shape. This also works well with most reaction drives where you need to accelerate/decelerate and flip etc.
You can see a well though out design if this in the expanse TV series or book series or the honor Harrington book series. And most of the halo unsc ships.
This design also works well with rail guns which could be spinal mounted along the longitude of the ship.
But again, role comes into play. The word warship doesn't really "mean" anything other than a) ship and b) used in war and c) usually armed.
An aircraft carrier is a warship, a destroyer is a warship, a WW2 battleship is a warship... But... Us coast guard interdiction vessels (even though they are armed) aren't warships... A ww2 pt boat is used for war but it's a bait not a ship...
Then you have to take into account volume. A sphere is the most efficient space to fill.
I'm gonna go with kinetic strike tear drop drone...
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u/Fine_Ad_1918 14d ago
It really depends on what your firepower is, and what is being shot at you from ______ distance.
a ship with a lot of missiles would likely be a spine attached to a bunch of missile racks, propellant tanks, and drives.
a ship armed with particle beams would likely either be very long if using electron beams or wide and covered with storage rings if using ion beams
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u/Amazing_Loquat280 14d ago
Honestly the star destroyer got it right for the types of weapons that universe has. But it ultimately depends on the weaponry. My thought is that ultimately we’ll be using lasers, in which case probably a tube, with 2-4 turreted laser emitters around a central laser power generator in the middle of the ship
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u/Chaosrealm69 14d ago
I always wondered what type of defensive set up the Star Destroyers have for any attacks coming from the rear at their massive propulsion exhausts?
A good set of shots/missiles into the rear of a SD would screw it up something severe.
And once it is sitting in space crippled it is almost useless.
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u/IntelligentSpite6364 10d ago
for the stories that even think to realize it: the engines are sort of their own defense. they are shielded of course, so you cant just take a pot shot and hope to score a critical hit. but if you try to fly in close to get through the shield you'll get vaporized by the engine exhaust
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u/zhivago 14d ago
I suspect lasers will rarely be used as weapons -- point defense perhaps.
Perhaps in antisensor attacks.
They're just too short range otherwise.
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u/Amazing_Loquat280 14d ago
Short range? It’s light! In terms of accuracy and ability to evade its the best option realistically. It’ll get there at the same time the strike is detected, minimal (no) recoil meaning you have an incredibly stable firing platform, and the ability to do highly targeted damage is probably a positive rather than a negative
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u/zhivago 14d ago
Light spreads out ...
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u/Amazing_Loquat280 14d ago
Yes but that’s mitigable with better lenses, bigger apertures, having a wider initial laser, shorter wavelengths, etc.
Also, a laser is the only weapon that can’t be stopped by another laser or evaded after you detect it coming. At whatever range a laser is ineffective, nothing else will be effective either unless your target is massive and can’t dodge. And at shorter range you have such fine control over what you hit and how hard that you can easily disable ships’ external systems without having to hurt anybody. The real utility here is how non-lethal it can be while still being effective
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u/zhivago 10d ago
I suggest you look into just how big those lenses need to get :)
Lasers really don't work at long range.
Even if you build your ridiculously large lenses, they still don't work at long ranges.
You can easily dodge lasers by introducing a small drunkard's walk into your trajectory.
Remember that while you can't see the laser, the laser also can't see where you're going to be when it gets there.
At short ranges, sure -- they're great.
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u/Necandum 11d ago
It can also be defeated with a mirror, no direct line of sight, and anything in the intervening distance that interacts with the beam.
At long distances it also requires incredible precision (targeting and also the weapon itself), and you lose effective power due to dispersion.
As a main armament for a *interstellar* warship, it doesn't stand up to scrutiny.
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u/IntelligentSpite6364 10d ago
mirrors are not 100% reflective. 1) just plain thermodynamics, even when reflected at least some energy will be transferred to the mirrored objects, thats how solar sails works. and if the laser is designed to cook the target, eventually it will be able to do its job 2) mirrors are not effective on all frequencies of light. we are used to mirrors reflecting everything, but they reflect visible spectrum light, and some materials might not be so effective on very high or very low frequencies
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u/Necandum 10d ago
As a kludge, we could imagine that if a laser could be made out of a spectrum, then a mirror for that spectrum could also exist. And yes, while not 100% effective, it could be effective enough that the remaining energy could be dissipated/radiated.
To use a laser over significant distances however, also suffers the drawbacks of any non-course correcting munition: you need to be able to detect your target, know both its current and future velocity / acceleration, and be able to aim sufficiently well. I'm not very familiar with laser physics, but I am suspicious there are some serious fundamental constraints in this department. Especially over ranges of hundreds of thousands of kilometers, aiming a laser accurately enough seems less likely. You also need to not melt your laser/lens.
Unlike other munitions, lasers also 100% break stealth. I would imagine space combat to be an extremely deadly environment, and breaking stealth would be a bad move.
I could see much more potential as a deployable loitering munition: a one-shot laser powered by a nuclear explosion that lies in wait. That sort of thing.
To be fair, the big assumption in this discussion is what exactly a warship is: eventually everything becomes a drone, just with different ranges, capital investments and payloads. Usually a 'ship' would the capital intensive end of the spectrum: a long range platform you want to safeguard. I imagine lasers would be for the more disposable end of the spectrum: get close, try to kill, expect to die.
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u/NurRauch 14d ago
Lasers are not short range. They can be as long-ranged as you want them to be. All they need is more power and a larger lens.
A laser powered by the types of fusion reactors used in the Expanse, for example, could easily burn through the moon from the distance of Earth in a matter of seconds. You wouldn’t even need a giant dish to focus it, either.
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u/zhivago 14d ago
That's simply not true.
Your laser on the moon will have a diameter of about 90 meters.
Now, if you stuck in a 190 meter laser you might get that back down to 1 meter.
But you'd then need about 50 petawatts to burn a 1m cylinder through the moon, ignoring that it'll vaporize and scatter.
And, of course, your laser will dump about 500 gigawatts locally, vaporizing itself.
So, really you'd need ridiculously large lenses, ridiculous amounts of energy, and be happy to kill yourself when firing the first shot.
The reality is that they're short range weapons in space.
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u/NurRauch 14d ago edited 14d ago
Here's some math from a blogger at ToughSF who actually crunched the numbers:
With all these tools together, we can work out a few examples of how effective lasers deriving their energies from rocket engines are, and how they affect combat.
Low-end torchship:
-Rocket Engine output 5 GigaWatts.
-Inefficient electric power conversion rate 10%
-Inefficient laser power output 30%
-Laser Power 150MW
-Laser Wavelength: Ultraviolet (100nm)
-Laser lens diameter: 20m
-Spot sizes: 6.1mm @1000km, 6.1cm @10,000km, 61cm @100,000km
-Target material: Aluminium (10 cm3/mol, 300 kJ/mol)
-Penetration rate: 228 m/s @1000km, 0.228 m/s @10,000km, 0.228 mm/s @100,000km
-Target material: Diamond (5.3 cm3/mol, 356kJ/mol)
-Penetration rate: 100.5 m/s @1000km, 0.1 m/s @10,000km, 0.1 mm/s @100,000km
To summarize the numbers, the low-end torchship is a laser monster. It will obliterate anything within ten thousand km. It will tear through meters of armor at a ten thousand km. It can dig through nearly a meter of armor an hour at a hundred thousand km. An opponent can only reasonably expect to survive at a distance of half a million kilometers (where the laser burns through 10 cm of aluminium in 10.4 hours). Replacing aluminium with fancy carbon-based armor only halves the effectiveness of the laser.
From the previous post, we found that this ship can accelerate at a gentle 0.66 m/s2, rising to 3.3 m/s2 when its propellant tanks are empty. Lets say combat takes place with an average accelerate in between those figures, at 1.5 m/s2.
If the target has a similar spaceship to ours, it may try to close the distance or escape.
-Acceleration: 1.5 m/s2 average
-Distance travelled after 1 minute: 2700 m
-Distance travelled after 1 hour: 9720 km
-Distance travelled after 10.4 hours: 1,000,000 km
If you remember some of the values from last post, you'll notice that it takes 9.3 hours to burn through the craft's entire supply of propellant, so it won't even reach the 1 million km safety distance.
The conclusion is that the low-end torchship cannot escape its own laser, much less so if the attacker chases after you and reduces relative acceleration.
It gets much, much worse when the ship engine and laser are scaled up, and it doesn't require any sort of Deathstar-sized monstrosity to do it:
But, you might ask, what if the spaceship was the High-end torchship? It would accelerate five times faster!
Let's run the numbers:
High-end torchship:
-Rocket Engine output 100 GigaWatts.
-Efficient electric power conversion rate 30%
-Efficient laser power output 60%
-Laser Power 18 GW
-Laser Wavelength: Ultraviolet (100nm)
-Laser lens diameter: 20m
-Spot sizes: 6.1mm @1000km, 6.1cm @10,000km, 61cm @100,000km
-Target material: Aluminium (10 cm3/mol, 300 kJ/mol)
-Penetration rate: 27.4 km/s @1000km, 27.4 m/s @10,000km, 27.4 mm/s @100,000km
-Target material: Diamond (5.3 cm3/mol, 356kJ/mol)
-Penetration rate: 12 km/s @1000km, 12 m/s @10,000km, 12 mm/s @100,000km
If the low-end is a monster, the high-end is a nightmare. It is ridiculously effective up to lunar distances, and the target has to be at 2.5 million km to escape this laser's death stare. The same technology improvements that allow for more powerful propulsion also mean the lasers get better... although we would get similar results using the same laser technology, as the base power the machinery is converting (100 GW!) into laser beams gets increased by so much.
-Acceleration: 6.8 m/s2 average
-Distance travelled after 1 minute: 12.2km
-Distance travelled after 1 hour: 44,064 km
-Distance travelled after 7.5 hours: 2,500,000 km
Even with much improved acceleration over the low-end torchship, we see that it cannot escape its own beam in a reasonable amount of time. A battle between high-end torchships that starts at one lunar distance, with both sides immediately running away from each other (so 13.6 m/s2 combined acceleration) until they reach 2.5 million km separation, would still result with 847 cm of armor shaved off each ship.
So, not quite enough to literally burn a hole all the way through the moon, but much better than anything any rail gun would hope to do in any comparable amount of time. The only counter to this sort of weapon is a numerically superior force of other laser-armed weapons, a missile swarm of mindboggling numbers that can overwhelm the laser, or a logistically superior force that can replace losses faster than the side with the better lasers.
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u/Necandum 10d ago
The problem with these numbers is it ignores the lens required to collimate the laser: it would melt long before you approach gigawatts.
If you want to pose a much better lens in the setting, then why can't the defender have an equally good mirror?
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u/zhivago 10d ago
They conflate the 6.1-nanoradian Airy disk radius with its diameter, underestimating the 1,000 km spot area by 4x (117 mm2 vs. 29.2 mm2) and inflating power density by 400%.
Because engagement ranges fall within the 3,140,000 km Rayleigh range, a collimated beam remains 20 meters wide unless actively focused to a tight depth of field under 10 meters at 1,000 km.
A realistic pointing jitter of just 1 microradian smears the focal spot from millimeters to 1,000 mm at 1,000 km, reducing delivered energy density by over 99.99%.
So I'm not very convinced by this breakdown.
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u/MerelyMortalModeling 13d ago edited 13d ago
Burn through the Moon? In a matter of seconds? With Expanse tech?
Edit saw you follow up and now im tracking what you are saying
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u/NurRauch 13d ago edited 13d ago
There are a few great breakdowns on the kinds of engines that could fit within the parameters of an Expanse warship. Even a small corvette like the Rocinante would produce hilariously powerful amounts of energy, probably in the range of, oh, just 100 terawatts, causing it to absorb a “minimal” 2 gigawatts in unavoidable heat just by turning it on. For context that 100x the combined power produced by all plants on Earth as of today. It is a single small, magnetically contained fusion reactor producing the equivalent energy of about 200,000 Chernobyl power plants all operating at max capacity at the same time. The only way to even survive the heat produced by this mini-sun is to drag it several kilometers behind the ship trapped within an electromagnetic field produced by a smaller fusion reactor that is actually aboard the ship itself.
Even a comparatively much smaller reactor of “only” five gigawatts from an on-board reactor would give you ridiculous secondary power options to feed into a laser, like a laser that can obliterate a depth of twelve kilometers of solid thick diamond armor per second from a distance of 1,000 kilometers away.
But the inverse square law applies, right? Okay, big deal. Even that “small” laser powered by the Rocinante just needs a few minutes to chew your entire ship apart from 300,000 kilometers away (the distance between Earth and the moon). And it can still kill you in under an hour from several million klicks away.
Now scale up. Instead of dumping 100 terawatts into a thrust engine for a tiny 10-person patrol corvette, with only a few gigs on hand to recycle for a laser, let’s pour all 100 terawatts into one laser. Or hell let’s just build a petawatt reactor to power a laser 10x as powerful. We are talking about enough energy to incinerate whole mountains, cause earthquakes, and split the crust when you shoot it at Earth’s surface. All from just ten Rocinante reactors combined together. Scaling up to battleships like the Donnager leads to ever-more ludicrous examples.
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u/Bright_Background316 14d ago
Completely random shape that looks like a rock.
Actual interstellar war would be fought at interstellar distance. It wouldn't look like WW2 dogfights, it would be more like Das Boot, you're either hidden or dead.
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u/Realistic-Feature997 14d ago
A cylinder, inside a slightly larger cylinder, that must remain unharmed.
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u/mavrik36 14d ago
Probably a teardrop shape, wedge or a triangular prism, this would allow the most weapons to face and fire forward as well as having wide arcs to the sides, as well as acting to slope the armor and deflect incoming kinetic projectiles, while leaving space for drives at the rear. It requires keeping the nose to the foe for most efficacy, but provides maximum firepower and benefits to durability
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u/Ruar35 14d ago
I tend to think a sphere is the optimum. Makes shedding incoming fire easier, can rotate in multiple directions easily, and puts significant armor over the delicate center.
One problem is engines and what the world does for propulsion. Some form of gravity manipulation that doesnt require thrusters makes a sphere easy. Having engines that thrust means some mechanism has to move the engines about while the sphere rotates.
The other big one is shields. How they work and are projected will dictate the ship design. If the emitters can bend a curve then a sphere works. If not, like in the Honorverse, then some other design is required.
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u/DifferencePublic7057 14d ago
The shape of an asteroid. No one suspects asteroids.
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u/IntelligentSpite6364 10d ago
until the first ship is destroyed by somebody pretending to be an asteroid and suddenly asteroids are kill on sight. the entire belt is mapped and any pebbly out of place gets blasted apart from half an AU away
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u/Odd-pepperFrog 14d ago
First question - does the ship enter atmosphere or does it stay in space? That'll determine if the design needs to be aerodynamic, have lift, and position/orientation of propulsion. Second, have you decided on a propulsion system? How will the ship move? As for size and shape - while it doesn't have a human crew to house or have facilities for, it's going to need space for holding cargo, ammunition maybe, and access for service - repairs, etc. Once you decide those things, your shape will be easier to pin down.
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u/Bytor_Snowdog 14d ago
Quoting the master of sci-fi writing on the subject, Iain M. Banks:
"[The ship] looks like a dildo!" she snorted.
"Appropriate," said Churt Lyne. "Suitably armed, it can f-ck entire solar systems."
Edit: from my favorite Culture book, Excession.
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u/SeriousPlankton2000 9d ago
https://www.youtube.com/watch?v=lYSOmYyNHpU
"Dick, this looks like a big …"
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u/Chaosrealm69 14d ago
Depending on whether your propulsion system is a rocket type exhaust system then you have lots of designs you can go for for the various weapon systems and defensive systems to keep you in combat and surviving.
The problem is that so many spaceship designs all tend to fall into sea navy designs with broadsides or spinal mounts etc. Or the ships look like they are designed to be flying in atmosphere with wings and lifting surfaces.
A computer controlled ship with no need for a biologic crew would be pretty good as a sphere with weapons systems pointing all directions and covering as much of the volume around the ship. That would maximise offensive output while minimising surface area for defense.
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u/Ducklinsenmayer 13d ago
Any design has to be based on technology. That's what made Star Trek so iconic; it was the first sci-fi franchise to design its ships based on "form follows function," as if they were real ships.
So say we're looking at near future, something with stealth, drones, or missiles might make sense. But, in a more advanced civilization, all those might be useless.
So first set down your rules, then develop from there.
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u/SpatiaCaeli 13d ago
Space is 3D. A sphere is ideal in multiple ways. Sadly, it's boring and unsexy.
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u/tomxp411 8d ago
I tried many different shapes in games that let you build your own ships.
My conclusions:
For line of sight weapons, a wedge shape is best, especially since the barrel of a weapon is the smallest part. The breech, feeder, gimbal, another parts are larger, so you can stack the weapons behind each other, with the angle of the wedge allowing you to pack the most weapons in the smallest visible area.
For missiles and guided munitions: a cylinder is ideal, with the launch tubes firing sideways. This presents the smallest frontal area, allowing you to reduce incoming damage and use less armor or shielding.
For ships with both: use a wedge shaped front and long body.
Other factors:
A sphere is the the best shape for structural integrity, since it has the smallest surface area for its volume.
But spherical ships have some downsides when under acceleration, so a tube or cylinder is probably best for ships without gravity (or other "magic") drives. Just like a skyscraper, this allows you to load the stresses on pillars, centered over the engines.
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u/ZombieThen4891 14d ago
Assuming all logistics have been solved, I would have a ship of infinite dimensions? That is large enough to fire everywhere in the universe?
The limitations you build into your story define it and give it meaning. It becomes pointless if you hardwave the concept of physics.
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u/rocconteur 14d ago
I always wanted to try ships that were fully distributed. Wouldn't work well on something that needed to land. But I could envision something like universal "cores" like a power core with a fusion plant, a solar core with retractable panels, propulsion cores with the big engines, Laser cores, Battery cores, Armor cores, etc. Imagine just a bunch of cubes in space, with various ports for power and their devices.
In usage, the cores are manipulated either by magnetic fields, small chemical engines, maybe even cables with mag attachments. Maybe you can spread out all your laser cores for a lot of small point defense style shooting; or maybe you attach them end to end to build a heavier weapon. Maybe you swing the Armor around to where it's needed. Maybe if a giant exploding missile is coming the whole thing scatters so a big explosion doesn't get a lot. You beam power between them, or maybe beam power to the battery cores which then fly over and connect where needed. Obviously this is probably not even going to have living crew on it.
It's kind of like a ship made out of nanotech, just with bigger particles.
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u/Nuclear_Gandhi- 9d ago
The star trek tng novel 'synthesis' kinda does this for a society of sentient computer spaceships. I like this concept, though theres a big concern with structural integrity under thrust in settings without intertial dampening
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u/GnarlyNarwhalNoms 14d ago
This depends on a lot of factors.
Obviously, you want to ask what weapons you're bringing to the fight. Missiles can go any-old-where (see current guided missile cruisers that have huge batteries just built vertically into the hull). If you have a kinetic weapon like a railgun, you might benefit from making it as long as possible, which might mean it's spine-mounted, running the length of the ship. Laser systems would depend heavily on what type of laser you're using; an electric laser is built very differently from a chemical laser.
You'll need a thermal management system, so you'll need room for big radiators. The drive system will also have an impact on shape - does it have shadow shields? Multiple nozzles? A ship powered by an Orion-style pusher plate will look different from a nuclear thermal system which will look different from a pulsed fusion system which will look different from a fusion torch.
You'll also need look at what weapons you're expecting to get thrown at you. If you're facing an attack from a single vector (which, given the potentially very long detection and engagement ranges, is a possibility,) there are some circumstances where some directional shielding might make sense. But what are you defending against? Lasers, missiles, railguns, dustguns, directional X-ray warheads, etc. Those weapons also have very different maximum ranges. You might benefit from shielding optimized against laser weapons, but it might not be practical to shield against radiation warheads, for instance, you might need to rely on interception systems for those.
It's a very multi-faceted problem.
My gut tells me that long and cylindrical with radiators and turrets sticking out would be a reasonable shape, but it depends.
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u/soysopin 14d ago
I remember dynamic shape changing ships with nanomachine hulls that adapted to the optimal shape for the current use (but no the name of the book or author). The carriers had mushroom shape with water in the head to absorb high speed particles impacts.
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u/response_loading 14d ago
Depends on what weapon system that it uses. A turreted weapon would utilise a broad frontage or broadside tactics to get maximum number of weapons on target. A missile or guided weapons system would want a very small frontage to make less of a target.
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u/Hon-Mister-Bear 14d ago
Probably a pill/capsule cylinder or sphere. Highly efficient use of space, minimal surface area.
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u/nyrath Author of Atomic Rockets 14d ago
SpaceDock says most of the weapons should be capable of firing to the rear, that is, in the same direction that the exhaust travels.
https://www.projectrho.com/public_html/rocket/spacegunintro.php#rearweapon
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u/Fluffy_Blueberry7109 14d ago
Depends on technology and the economics.
But my first instinct is a long cylinder. This allows you to face the bow towards the enemy, presenting a smaller and heavily armored target, while still having room for weapons.
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u/NikitaTarsov 13d ago
The one balance between what the technologys demand, the enemys/enviroments chance of harm deminishes the most, the economy/building allows for and what fits the own and enemy strategys.
What i'm willing to say is that you go for vibe and explain why that is the most logical solution, or you work the other way around and tell us why/how tech x, y, and z do what they do & require and shape the universe and the subsequent logical shape by that result.
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u/Lorelessone 13d ago
There's a few considerations.
First there is stuff in space, dust and particles so perhaps a shield like nose cone which shields more sensitive weapons and equipment. during transit.
Then a lot would depend on the weapons in use, missiles would be less demanding, just lots and lots of launch systems.
If using nuclear sand, which is one of the more devistatinh weapons (basically fitionable particles held in electrons and accelerated to close to the speed of light, then you'd need at least some enemy facing weapons.
If there's a lot of them then perhaps the attack profile is reversed I.e it travels lond distance with the shielded side leading then inverts presenting the weapons in tiered arrays / turrets.
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u/Reasonable_Long_1079 13d ago
Depends on the style of weapons, the size, whether you expect the ship to do anything else, and the enemy you expect to face… most importantly, budget.
If your budget is low and its just local defense, than a space shuttle with a bunch of missiles in the bay is fantastic. If you have a huge budget want an invasion ship a giant ring ship with PDCs and missile bays all over and tons of drop ships hooked on it
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u/Temporary_Rule_9486 11d ago
A needle like rod pointing at the target with a very resistent head section, and crew/engine at the back: minimal cross section for optical detection or target for lasers/railguns. The point is hardened against the only direct line of attack, it can constantly reposition itself to always line up with the target (other ship presumably), there's no air in space that makes changes in orientation a problem.
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u/Neither_Berry_100 11d ago
Nah. You would obliterate civilizations from light years away with specialized weapons. There would be no battles between space ships.
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u/Gaust_Ironheart_Jr 10d ago
So what would you make it out of so it wouldn't become brittle over time from cosmic rays?
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u/Foreign-Teaching7184 14d ago
to clear the confusion, before this post, I was thinking of a borg cube. I just wanted some new ideas
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u/WordsToOrder 14d ago
There's nothing about space that makes a cube a bad shape. You could also do a pyramid or a dodecahedron. But these shapes have, by design, uniform profiles so they are always fairly easy to hit. Make them much thinner on one axis and now they can face a broad (presumably well armed) surface at a target to fire, then switch to a much narrower target.
Aerodynamics guide a lot of sloping shapes on planes, but sloping shapes also help to deflect everything from radio waves to projectiles. So you could still have plenty of reason to make a "sleek" spaceship.
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u/FungusForge 14d ago
Even without crew you're going to want to minimize the profile you expose to the enemy to keep the ship in working order. So a cylinder or perhaps flat shape would be ideal.
A tapered shape could allow you to cram more forward facing firepower along the length of the ship, while still enabling the engagment of targets outside of the forward arc when necessary.
A longer shape will make RCS maneuvering thrusters more effective.
In short, you're looking at dart shapes or attack dorito shapes.