Thanks for watching! If you want, you can join my discord (click my channel and you can find the links at the top). A link to my full game called "Step By Step" is also there if you're looking for a fun but difficult platforming challenge!
@@trippraineyokay but it's not really every shape though, in 3d software most people prefer their objects to be made out of quads, and while yes, it displays with triangles, it's still quads in the actual file
@@trippraineyI actually think that the squares and rectangles aren't made of triangles (because that would take more processing power), therefore some shapes (like a +) wouldn't have triangles in them, or some (like an arrow) would be made half made of triangles and half of rectangles. (Sorry if my english is bad I'm still learning c:)
@@stysan the gpu is optimised to render triangles, so generally quads get converted to triangles. Quads are only used for ease of modeling, but get converted to tris later
a circle is an infinite number of points equidistant from its center. so in theory, if you were to overlap a shit ton of triangles (or any shape as thats how apothems work) you could make a circle.
Makes me a lil confused 2 triangles make up a square right Which makes sense since a square has 360 degrees You can fit 3 triangles in a pentagon which makes up 420 degrees And so on But this means a shape that looks really similar to a circle, say hectogon with 100 sides has 17640 degrees While a circle is 360 Or does a circle have an infinite amount of degrees?
@@neeevirus Computers imitate circles using shapes with a definitive amount of sides that are very very close to a circle. But no, a circle is the 360 degrees itself, you cant have any amount of degrees between the sides because theres no definite side on a circle.
@@Destrixio Vector graphics are defined using math, on any given screen it can be converted to pixels but you can zoom infinitely into the image without blurriness or pixelation. For circles I think it does not use vertices, when converting a vector graphic image to pixels it just checks the distance of a pixel from the center.
"All these squares make a circle..." "All these squares make a circle..." "All these squares make a circle..." Edit: HOW IS THIS STILL GETTING SO MUCH ATTENTION IT HAS BEEN ONE MONTH-
@@trippraineyhello, i like your content, and i think alot of people want to support you, i suggest you make a ko fi account so people can support you or buy certain things like early access of games you make or even teaching people code if you want using memberships😁.
Thats how it wirks in a 3d dimensional polygonic space, how ever a 2 dimensional circle is actually just a series of puxels plotted along the edge abd with the circle function so its actually made of squares
Nyope, that's how a circle is calculated in a vector space, in a rendering space it's still made up of polygons. Because doing vector calculations is incredibly more resource intense than just doing a simple polygon render. Even in early video games you see this same principle at work
@birbopikle6431 Wth are you talking about?? 1st vector graphics ARE made out of "mathematical shapes", raster is made out of pixels 2nd what is "render space"? 3rd vector graphics still aren't made out of triangles(only triangles are triangles). It is just list of shapes with their properties. 4th vector graphics aren't faster in most cases. (Sorry for my bad English)
The shit is made from pixels, but a pixel is a square so two triangles makes up each pixel etc etc etc. computers still use triangles when making shapes though, not pixels.
A computer runs the image for a 2D circle off of a formula with no bases on polygons or straight lines. If, in the graphing program you where using to show polygons here, you used a circle formula it would generate a circle with no sides. No matter how far you zoom in, the computer will continue to generate curviturr forever. The only way you can say it has sides is by talking about pixels and screen resolution.
@@MINTGREENYT369 if it has sides, then it isn't a circle, it's just a polygon with a lot of sides, and the fill also can't be made of triangles if the shapes along the edges are cones, using the arcs of the edge. And a circle can't be in 3D, that's called a sphere. This video was talking about a 2 dimensional circle.
Shader based circles are a thing as well in which case the circle is composed of individual pixels, in theory it's still not a perfect circle due to displays generally use some sort of pixel grid; That said with circular & spherical objects there will always come a point where if the camera/view is close enough to them it'll look flat, see the people claiming the Earth isn't a globe as an example
@@borsukk Even Godot/Unity have real spheres with sphere colliders. And they are far more performant than any polygonal approximation, since a sphere is defined by a much simpler equation thus easier to calculate. This is just a content from first peak of Danning-Kruger, where a creator just found out about triangulation and approximations. Also, I believe, some mod capabilities in some games may allow only polygons, so this may be true, it just depends a lot.
you actually can:3 with a fragment shader you can discard every pixel thats further than X from a quad center, effectively giving you a circle, and since fragment shaders run in screen-space-pixels - it would let you zoom in infinitely, while also being two triangles for the quad.
@@5omebody yeah, but then you can't zoom in infinitely. unless you do it as an SDF sprite + a shader for that, but thats almost literally the same technique as shader-only render, just with distances pre-computed and stored on a texture.
@@everr.not.a.catgirl.y3t yeah - just noting sprites as another way to avoid triangles. of course, sprites do have their usecases too, like if you dont need to zoom to absurd levels it will probably be easier to get an artist to draw a sprite than write a sdf, and if you're going for a pixel art aesthetic then zooming in isn't really a problem
@@paulbunyangonewild7596not really, unless you are using a 3d space to make 2d games that's Is not always the case, see triangles are just the most effective way to make 3d, since no mater were you put the points, it will always look like a triangle, that is needed since a lot of transformations happen that is needed Now it's a different ballpark for pure 2d games, they just need to show you an image, a exact image at a point in the grid, they can just detect when a image changes place and then render that frame.
I can literally see the square pixels that make up all of your triangles. Also, you could use SVG to make your circles and then you can have those infinite points you were talking about.
No you dont, modern computer may generate some absurb number of "point" to make up that circle (may even increase when you zoom) but it can not make infinite point, which is how perfect circle is made
@@vuanhuc3582 Which is why the first part of their message mentions the square pixels. If you assume imperfect triangles made of imperfect square pixels are triangles, then an svg circle made of imperfect point/pixels/triangles, with enough of those, can be considered a circle. If it cannot, then you cannot make a triangle either. I assume this is what they meant
@@aencya yes, I was referring to the pixels, but the part about SVG (scalable vector graphics) specifically was that they are made of components that aren't rendered exclusively by drawing point to point to point. They are rendered with mathematical formula. I believe the circle component has an origin and a radius (at least, I think it has an aspect and rotation too, but that's irrelevant), and it uses those values alone to determine which pixels to set. As you zoom in to the canvas and the view refreshes, the radius increases, and the origin shifts, but you're not "adding more points", the pixels are still determined using the same fomula
@@Sirenhound You're absolutely right ! I had completely forgotten about that and I work in computer science. I guess sleeping properly is important I hope that clarified things for everyone either way !
"HOW DO ALL THESE SQUARES MAKE A CIRCLE I JUS-" "no no its fine its fine it doesnt bother me it bothers me bothers bothers me alot" "AND THAT ONE IS STILL GREEN"
@@mariovelez578 ofc it's less computationally intensive, but you're not actually doing the circle work in the vertices, but rather in a fragment shader, and here we're more talking about how to recreate circles with geometrical shapes. although i agree that using a shader is much faster, it doesn't always work for all cases (especially 3d modeling software, where a fragment shader won't really work).
@@batteraquette5843this is the funniest thing I have ever read. “Cheating” is just good programming. Avoiding the problem and skipping most of the work is good programming.
It's funny because the triangles are also ultimately an illusion, once finally being rendered everything becomes lots of little squares to be shown using pixels
Small bonus information, only using a single triangle and some shader, you can calculate the distance of every pixel in this triangle from the center of the triangle and hide them if they are too far, making a perfect circle no mater how far you zoom in
That’s not how you make circles, you can draw them as perfectly as possible (limited by pixels) just by doing (x-x1)^2+(y-y1)^2 for each pixel and colouring it if it is less than r^2. This way you can do it without using infinitely many triangles.
The potential for launching lightspeed railgun tnt minecarts in any direction needs to be acknowledged here. With your discoveries of particle acceleration and diagonal minecart and the ability to easily change the direction a minecart travels towards different launchpoints, that means with ocadirectional areas of attack or transportation, with a little more development, you can become the pioneer of minecart trolling and pranking, along with changing travel itself forever
Actually, the triangle approach IS the one used by libraries like OpenGL and Vulkan, just because it's the most efficient one for most use cases. You can make a renderer that renders with only squares, circles...
You can do a perfect circle, in fact you can even do it with a quad mesh. You just discard fragment in the fragment shader outside the radius of the circle. after rasterization of the mesh. and that's it :D
Technically the "real" circle is made up of pixels which are square shaped meaning each of the pixels can be made up of two triangles meaning a circle can be made if triangles of it's on a computer
If you do not include the pixels, it is actually possible to create a circle out of triangles in computer graphics, but you would just use a different rendering technique for shapes. For example, you can render a circle that is infinitely smooth pretty easily using an SDF in a shader language.
Btw you can fill any shape with triangles. Just becaude a shape has 5 sides doesn't necessarily mean that you can only fit 5 triangles. Theres a very simple way to know how many triangles can fit in a shape with any amount of sides. Just take the amount of sides and subtract them by 2 for example a sqaure with *4* sides can fit *2* triangles, a pentagon with *5* sides can fit *3* triangles, a hexagon with *6* sides can fit *4* triangles.
i don't know if this applies here, but looong time ago i saw a short of someone describing the same issue, he was able to make a PERFECT circle with just one triangle, if i remember correctly, he put some equation to remove the edges of the triangle and make it into a circle
Thanks for watching! If you want, you can join my discord (click my channel and you can find the links at the top). A link to my full game called "Step By Step" is also there if you're looking for a fun but difficult platforming challenge!
W Content
Erm actually 🤓☝️
How did you get the website that you used to increase the sides
What are the triangles made of?
@@Birdegypt That Was What I Was Asking!
Or every pixel is made from 2 triangles, and those 2 triangles make each pixel for the circle
yes I just didn't say that because it was unnecessary
Also, your display shows pixels which are squares, but the computer still calculates things internally using triangles
@@trippraineyokay but it's not really every shape though, in 3d software most people prefer their objects to be made out of quads, and while yes, it displays with triangles, it's still quads in the actual file
@@trippraineyI actually think that the squares and rectangles aren't made of triangles (because that would take more processing power), therefore some shapes (like a +) wouldn't have triangles in them, or some (like an arrow) would be made half made of triangles and half of rectangles.
(Sorry if my english is bad I'm still learning c:)
@@stysan the gpu is optimised to render triangles, so generally quads get converted to triangles. Quads are only used for ease of modeling, but get converted to tris later
Easy
1. Draw a head
2. Erase some of the more detailed features
3. Erase some more
123 and there you have it, a perfect circle.
A PERFECT CIRCLE? DO IT AGAIN
But then your eyes are made out of pixels
Nah it isint still perfect
SpongeBob reference.
@@misc.shortsikr
a circle is an infinite number of points equidistant from its center. so in theory, if you were to overlap a shit ton of triangles (or any shape as thats how apothems work) you could make a circle.
It's not a shit ton. It's an INFINITE amount of triangles.
@@whkn sounds like a lot
@@whkn so a shit ton?
Makes me a lil confused
2 triangles make up a square right
Which makes sense since a square has 360 degrees
You can fit 3 triangles in a pentagon which makes up 420 degrees
And so on
But this means a shape that looks really similar to a circle, say hectogon with 100 sides has 17640 degrees
While a circle is 360
Or does a circle have an infinite amount of degrees?
@@neeevirus Computers imitate circles using shapes with a definitive amount of sides that are very very close to a circle. But no, a circle is the 360 degrees itself, you cant have any amount of degrees between the sides because theres no definite side on a circle.
Wanna know where this circle goes? Thats right, the square hole!
Lol
*S Q U A R E H O L E*
YES
legendary meme
WHAAAAAAAAAA-
Using shaders it is possible to make circle made from an equation instead of set points.
Exactly. And it's actually a lot simpler for physics calculations
And a triangle-circle is much harder to compute than a center-distance circle
Or just use a texture
Still rendered with triangles tho.
@@dany5ful no its not, if it is done with a shader it is mathematically a circle and that is turned to pixels. No triangles
In vector graphics, you can make a true circle with no true vertices
How
@@Destrixio Vector graphics are defined using math, on any given screen it can be converted to pixels but you can zoom infinitely into the image without blurriness or pixelation. For circles I think it does not use vertices, when converting a vector graphic image to pixels it just checks the distance of a pixel from the center.
The rendering still uses triangles though right
@@dusty_giraffe2111 As far as I know, no. I believe it just calculates pixel by pixel. This is 2D graphics though, not 3D.
Isn't a Bézier circle just an approximation?
"I can't add an invinite amount of points" tell that to the banban devs
btw the drone remote has more polys than the entirety of super mario 64
*snickers*
@@ilfoxyy wha-
WHAT IS THAT REMOTE MADE OF
HOW MANY POINTS IT HAS?
Just played gob punchrush
@@Muho_is_meMore Than A Quarter Million
"All these squares make a circle..."
"All these squares make a circle..."
"All these squares make a circle..."
Edit: HOW IS THIS STILL GETTING SO MUCH ATTENTION IT HAS BEEN ONE MONTH-
'So I'm a hair's breath from perfection, and then Triclops shows up and decides 'I'm just gonna turn triangles into fucking squares!'"
Kami you need to tell me I can leave the observatory whenever I want
@@ogulcankaraer9627 you can leave the lookout whenever you want
AND THAT ONE'S STILL GREEN!
@@ogulcankaraer9627 mr popo you can leave the lookout-
Zooming into the blurry-ass edge of an already rasterized circle is a terrible way to drive this point home.
LMAO
Pizzas that are triangle yet makes Circles: WHAT THE FUCK AM I A JOKE TO YOU?!
vector graphics ftw!
@@quinnoconnor4929 YES
Bro just went from game programmer to geometry teacher 💀💀💀
My stocks going 📈📉
@@trippraineyhello, i like your content, and i think alot of people want to support you, i suggest you make a ko fi account so people can support you or buy certain things like early access of games you make or even teaching people code if you want using memberships😁.
@@trippraineynah they keep rising this shit is cool
A circle is a triangle because if you cut it into a upside down Y you will see the circle has three triangles
same thing really, game dev has a bunch of math and this is some of the simplest stuff
Instructions unclear, I am now fighting the king of curses using a wacky ball
I mean being able to clap 50 time 1 minutes is a really helpful ability
bro is really fighting sukuna
"How many vertices does a circle have?"
"At least 79"
I means infinity
Thats how it wirks in a 3d dimensional polygonic space, how ever a 2 dimensional circle is actually just a series of puxels plotted along the edge abd with the circle function so its actually made of squares
Nyope, that's how a circle is calculated in a vector space, in a rendering space it's still made up of polygons. Because doing vector calculations is incredibly more resource intense than just doing a simple polygon render. Even in early video games you see this same principle at work
@birbopikle6431 Wth are you talking about??
1st vector graphics ARE made out of "mathematical shapes", raster is made out of pixels
2nd what is "render space"?
3rd vector graphics still aren't made out of triangles(only triangles are triangles). It is just list of shapes with their properties.
4th vector graphics aren't faster in most cases.
(Sorry for my bad English)
@@regestriryisa1687the computer still calculates the shapes using triangles, not in pixels.
The shit is made from pixels, but a pixel is a square so two triangles makes up each pixel etc etc etc. computers still use triangles when making shapes though, not pixels.
Yeah, this video makes no sense.
"All these triangles make a circle. All these triangles make a circle."
Found the comment.
Fuck, I had typed this and looked to see if someone did first
???
@@NikTehWafel watch Dragon Ball Z Abridged, more specifically Mr. Popo clips
Me: *Laughs with a compass in my hand while not using a computer so its possible for a perfectly round circle to exist*
A computer runs the image for a 2D circle off of a formula with no bases on polygons or straight lines. If, in the graphing program you where using to show polygons here, you used a circle formula it would generate a circle with no sides. No matter how far you zoom in, the computer will continue to generate curviturr forever. The only way you can say it has sides is by talking about pixels and screen resolution.
Exactly, this short is totally wrong
That's a vector using curvature, the type of vector he used isn't with any curves, and he doesn't mean the outline, he means the fill
And in terms of 3D, a sphere is entirely polygons, which is 3d triangles
@@MINTGREENYT369 if it has sides, then it isn't a circle, it's just a polygon with a lot of sides, and the fill also can't be made of triangles if the shapes along the edges are cones, using the arcs of the edge. And a circle can't be in 3D, that's called a sphere. This video was talking about a 2 dimensional circle.
Shader based circles are a thing as well in which case the circle is composed of individual pixels, in theory it's still not a perfect circle due to displays generally use some sort of pixel grid; That said with circular & spherical objects there will always come a point where if the camera/view is close enough to them it'll look flat, see the people claiming the Earth isn't a globe as an example
You can define and render a circle implicitly without triangles my man
what do you expect from unity/godot "dev"
@@borsukk
Even Godot/Unity have real spheres with sphere colliders. And they are far more performant than any polygonal approximation, since a sphere is defined by a much simpler equation thus easier to calculate.
This is just a content from first peak of Danning-Kruger, where a creator just found out about triangulation and approximations.
Also, I believe, some mod capabilities in some games may allow only polygons, so this may be true, it just depends a lot.
@@borsukk you dont have to use the built in renderer so you can write your own that doesnt use tris
you didnt even get the point of the video lol
should we tell him
Circle that’s 99,9999999999% Triangles….“Damn it, gotta fake it till u make it, nobody will know Ross!“
you actually can:3 with a fragment shader you can discard every pixel thats further than X from a quad center, effectively giving you a circle, and since fragment shaders run in screen-space-pixels - it would let you zoom in infinitely, while also being two triangles for the quad.
Yup
or you can just draw a sprite from a spritesheet
@@5omebody yeah, but then you can't zoom in infinitely. unless you do it as an SDF sprite + a shader for that, but thats almost literally the same technique as shader-only render, just with distances pre-computed and stored on a texture.
@@everr.not.a.catgirl.y3t yeah - just noting sprites as another way to avoid triangles.
of course, sprites do have their usecases too, like if you dont need to zoom to absurd levels it will probably be easier to get an artist to draw a sprite than write a sdf, and if you're going for a pixel art aesthetic then zooming in isn't really a problem
@@everr.not.a.catgirl.y3tan SDF sprite would still have aliasing problems with finite resolution
in 3d, shapes are made from triangles, in 2d
shapes are made with images and colliders with triangles (or circles)
Those images are displayed using triangles, weather it's just a plain square or a fancy cut-out, it's still using triangles.
@@paulbunyangonewild7596 pixels are squares...
2d is not made out of triangles that would be unnecessary
@@paulbunyangonewild7596not really, unless you are using a 3d space to make 2d games that's Is not always the case, see triangles are just the most effective way to make 3d, since no mater were you put the points, it will always look like a triangle, that is needed since a lot of transformations happen that is needed
Now it's a different ballpark for pure 2d games, they just need to show you an image, a exact image at a point in the grid, they can just detect when a image changes place and then render that frame.
png's are just a bunch of squares with a color, jpegs are just a bunch of sine waves
"in computers, all shapes are made of triangles!"
vector graphics:
SDFs:
When i see how a circle is made of triangles, i think of pizza
i thought of pie charts
Finally a comment that says pizza
I can literally see the square pixels that make up all of your triangles.
Also, you could use SVG to make your circles and then you can have those infinite points you were talking about.
No you dont, modern computer may generate some absurb number of "point" to make up that circle (may even increase when you zoom) but it can not make infinite point, which is how perfect circle is made
@@vuanhuc3582
Which is why the first part of their message mentions the square pixels.
If you assume imperfect triangles made of imperfect square pixels are triangles, then an svg circle made of imperfect point/pixels/triangles, with enough of those, can be considered a circle.
If it cannot, then you cannot make a triangle either.
I assume this is what they meant
@@aencyaif its made up of pixels, pixels are square which can be made with 2 triangles... checkmate 😁
@@aencya yes, I was referring to the pixels, but the part about SVG (scalable vector graphics) specifically was that they are made of components that aren't rendered exclusively by drawing point to point to point. They are rendered with mathematical formula. I believe the circle component has an origin and a radius (at least, I think it has an aspect and rotation too, but that's irrelevant), and it uses those values alone to determine which pixels to set. As you zoom in to the canvas and the view refreshes, the radius increases, and the origin shifts, but you're not "adding more points", the pixels are still determined using the same fomula
@@Sirenhound You're absolutely right !
I had completely forgotten about that and I work in computer science.
I guess sleeping properly is important
I hope that clarified things for everyone either way !
Man went from game dev to math professor
Actually, it only takes 6 triangles to make an octagon. It’s just the number of sides minus 2
Just like a pentagon only needs 3. Glad I've seen another comment point that one out.
Exactly points cannot meet
Yeah. Using the video's method is simple for demonstration purposes, but it's funny because it takes 3 triangles to draw a triangle.
Yeah but you can still build it with 8
@@alessandrocapasso2440 You can build it with any numbers of triangle as long as it's 6 or above.
Spin the triangle really really fast
Acttualy, the circle is made from rectangles, the pixels
vector images:
Computers still have pixels
@@blobanimatesb7466yeah but that’s the display not the actual data
Also pixels aren’t triangular, they’re in a rectangular grid
Vector still ain't perfectly round
@@thenarwhalmage rectangle= two long triangles
Even thiugh there's no music but only a beat of a solid surface, it still is popular and a very succesful music, how impressive
That circle is a bloody triangle! (*laughs*) (*dies*)
I read this in the Demoman voice
@@SpudChickenSaltedChips because it is "written in demoman"
“All these squares make a circle. All these squares make a circle.”
two triangles and a fragment shader can make a perfectly round circle (limited by the display resolution, of course)
You can use shaders to add curve to the edges and make it a perfect circle
A circle is a polygon whose number of sides approach infinity
No, a circle is not a polygon.
A poligon with w (omega) sides is still a polygon, not a circle
Actually, a circle is, in fact, a polygon with an infinite amount of sides. Look it up before you disagree.
The reason a circle is a polygon is because of calculus
@@WarrenTaylor-vg8zraren't circles curved though?
Am I the only one that can seize the imperfections at the edge bro?😂
All these triangles make a circle, all these triangles make a circle, all these triangles make a circle
DBZA reference?!?!
You took the words from my mind!
"HOW DO ALL THESE SQUARES MAKE A CIRCLE I JUS-"
"no no its fine its fine it doesnt bother me it bothers me bothers bothers me alot"
"AND THAT ONE IS STILL GREEN"
AND THAT ONES STILL GREEN!
My dumbass thought he was talking about the rectangle being made of many little triangles 💀
That’s where you’re wrong. A perfect circle can be made of 2 triangles and a shader with the distance formula
in reality, it's just a quad mesh with a fragment shader controlling the colour output, so it's kinda cheating ig?
@@batteraquette5843 No? I don't see a problem with it. It works perfectly and can be more efficient than a mesh with 100 triangles
@@mariovelez578 ofc it's less computationally intensive, but you're not actually doing the circle work in the vertices, but rather in a fragment shader, and here we're more talking about how to recreate circles with geometrical shapes. although i agree that using a shader is much faster, it doesn't always work for all cases (especially 3d modeling software, where a fragment shader won't really work).
@@batteraquette5843this is the funniest thing I have ever read. “Cheating” is just good programming. Avoiding the problem and skipping most of the work is good programming.
@@batteraquette5843 Pretty sure Blender allows custom fragment shaders. Also it's creating a circle using the geometric definition of a circle.
"That's right, it goes in the triangle hole."
It's funny because the triangles are also ultimately an illusion, once finally being rendered everything becomes lots of little squares to be shown using pixels
the triangle logic is only for 3d calculations. for 2d, it uses pixels.
Or vectors
3d also "uses pixels", traditionnal (non-raytracing) 3d rendering has a step which is called "rasterization".
@@magen6233 that is getting into the specifics of things
I mean even in 3D you can totally represent spheres parametrically instead of using triangles to approximate it. The video is wrong.
GD creator: let's make a circle with a bunch of squares.... Yeah xD
I love how computers think in triangles and lines then output a whole bunch of squares. It’s just really interesting to me idk why
You can also make a circle with rectangles, i introduce you to calculus.
triangles are made with squares
Wait...What if the square is made with mini triangles?
@@Kanichari What if those mini triangles are made of minini squares?
@@Whitehot724 and the minini squares are made with mininini triangels?
You can also cheat a little and remove a single point by taking the center point and shifting it to the edge.
there are non-triangle circles
instead of defining a polygon, the draw engine can have a function for a point and radius, and draw a circle from that
And then, the billions of triangles are turned into thousands of tiny squares
ALL THESE SQUARES MAKE A CIRCLE
This makes me think people forgot about pizza since pizza is a circle made of triangle slices (most pizzas at least)
Came here for this.
It’s not a triangle though, it’s a sector
When you took Highschool geometry and already know this
Exactly!
The circle made of pixels(squares) and not triangles: 👁️👄👁️
Small bonus information, only using a single triangle and some shader, you can calculate the distance of every pixel in this triangle from the center of the triangle and hide them if they are too far, making a perfect circle no mater how far you zoom in
That’s not how you make circles, you can draw them as perfectly as possible (limited by pixels) just by doing (x-x1)^2+(y-y1)^2 for each pixel and colouring it if it is less than r^2. This way you can do it without using infinitely many triangles.
Guys you cut pizza into triangles it starts a circle good job
Can you tell me the website you used? Thank you!
Fr idk
I thought we all learned this in math class
That's why I can say that a circle is made up of Triangles 🔺️
Also, curved triangles make circles, it’s called an arc
Hey is there a planet section or something for stages
If not can you add it
24:00 “I didn’t have another Notch apple”
*The 3 Notch apples in his hotbar*
JuSt MaKe It LiKe A pIzZa!!!
Pizza: am I a joke?
Humans dont have that much accuracy to make a perfect circle
Pizza, isn’t made from triangles…
I mean real life isn’t a computer, so it’s probably technically possible for something to be a circle
Pizza has triangles slices BUT the crust is curved
@@SnugBmwreally? I always thought even the crust was straight based from what I can remember anyways.
A circle has infinite angles, as I learned in geometry this year. Therefore, it has infinite angles.
thats why triangles are my favorite shapes
A perfect circle can be made of triangles as a circle has infinite sides so you just need infinite triangles
At least that would make sense
A pizza is a circle, but we make it into triangles. Makes sense.
Bro almost just explained calculus.
My dumb brain was about to say, “how do they cut pizzas then?”
There are these shapes called digons (2 sides) and monagons (1 side)
Nonagon shape: exists
Me whenever I hear the word Nonagon: IS THAT AN ANIMATIC BATTLE REFERENCE???!!!
"when can a circle be made of triangles? when it's not actually a circle"
The potential for launching lightspeed railgun tnt minecarts in any direction needs to be acknowledged here.
With your discoveries of particle acceleration and diagonal minecart and the ability to easily change the direction a minecart travels towards different launchpoints, that means with ocadirectional areas of attack or transportation, with a little more development, you can become the pioneer of minecart trolling and pranking, along with changing travel itself forever
... What?
@@hamzamotara4304 railguns
"This human is made of triangles" is a statement i got in trouble for.
An infinite slice of pizza, sounds delicious
I mean technically a perfectly round circle can be made up of an infinite amount of triangles
Actually, the triangle approach IS the one used by libraries like OpenGL and Vulkan, just because it's the most efficient one for most use cases. You can make a renderer that renders with only squares, circles...
As someone who's played with blender, this makes perfect sense to me
You can also save time and resources by just rendering a square with a circle texture on it.
Circles can be rasterized at dr^2 and in a lot of graphics libraries that’s exactly what they do. No triangles involved
A perfect circle is basically infinite triangles.
Me: auto clicks the add points for 1 week
You can do a perfect circle, in fact you can even do it with a quad mesh. You just discard fragment in the fragment shader outside the radius of the circle. after rasterization of the mesh. and that's it :D
You got a point, it's even mentioned in algebra
The concept that a circle can be made of triangles is the entire reason that sine cosine and tangent can be used in circles
Technically the "real" circle is made up of pixels which are square shaped meaning each of the pixels can be made up of two triangles meaning a circle can be made if triangles of it's on a computer
If you do not include the pixels, it is actually possible to create a circle out of triangles in computer graphics, but you would just use a different rendering technique for shapes. For example, you can render a circle that is infinitely smooth pretty easily using an SDF in a shader language.
Bro the deffinitly present sync is CRAZYY 😂
Tripprainey teaches his viewers basic geometry
Btw you can fill any shape with triangles. Just becaude a shape has 5 sides doesn't necessarily mean that you can only fit 5 triangles. Theres a very simple way to know how many triangles can fit in a shape with any amount of sides. Just take the amount of sides and subtract them by 2 for example a sqaure with *4* sides can fit *2* triangles, a pentagon with *5* sides can fit *3* triangles, a hexagon with *6* sides can fit *4* triangles.
Everyone else asking how circles can be made from triangles:
Me: PIZZAA!
It is because there is an infinite amount of triangles that even the lines dont fit anymore and make a perfect shape like a circle.
I learned in a geometry class that EVERYTHING is triangles
Nothing is safe from the triangles
"one pizza that circle"
"but cutten to trinagle"
"tf you are"
Bro scared me with the pentagon (bfdi fans will understand)
The answer is always to have more triangles than pixels.
AND THATS WHY TRIANGLES ARE MY FAVORITE 2D SHAPE
Triangle gang WTF IS A CIRCLE🔥🔥🔥🔥
i don't know if this applies here, but looong time ago i saw a short of someone describing the same issue, he was able to make a PERFECT circle with just one triangle, if i remember correctly, he put some equation to remove the edges of the triangle and make it into a circle
this is correct, making circles out of tons of triangles is extremely inefficient