Name: Pixar: The math behind...
Uploaded: 2025-11-09T12:02:01.535Z
Description: So, I'm going to do something slightly terrifying and move to a live demo here. So, what I have is a four-point polygon here, and it's going to be my job to make a smooth curve out of this thing. And I'm going to do it just using the idea of midpoints. So, the first thing I'm going to do is an operation I'll call split,

Tim Sweeney

For the third generation Unreal Engine, we are building two versions of every model in our game. We are building a source model with several million polygons, between 2 and 6 million polygons. We use that model for all the lighting detail on the mesh. Then we go to the in-game version, which is usually about 10,000 polygons.

American Businessman

John Carmack

To the game code, the world is still just a tile map, but for rendering, each map was exported as a general-purpose 3D model, and the artists could then go through it and spend the polygons any way they liked, without the limits of line-of-constant-z software rasterization that we lived with on the mobile phones.

American Scientist

Hideo Kojima

Many people are taking 2D games and making them into 3D games by recreating the characters in polygons. But the gameplay's still the same, and that's not what they should be doing.

Japanese Designer

Trip Hawkins

With our next generation hardware, polygon rendering will probably be an area we'll get more heavily into.

Picture polygons as flat, straight-lined figures on paper, like hexagons or pentagons.

Visualizing Polygons

Remember that polygons need at least three sides. Two sides don't make a polygon.

Minimum Sides

Explore various types like regular, where all sides and angles are equal, and irregular polygons.

Polygon Varieties

In games and movies, objects are made up of polygons; more polygons create more detail.

Graphics Representation

Learn how polygon meshes form 3D models. Meshes are networks of polygons connected at vertices.

Models and Meshes

More polygons can mean slower rendering times in computing. Optimization is key.

Rendering Complexity

 So, I'm going to do something slightly terrifying and move to a live demo here. So, what I have is a four-point polygon here, and it's going to be my job to make a smooth curve out of this thing. And I'm going to do it just using the idea of midpoints. So, the first thing I'm going to do is an operation I'll call split,

Pixar: The math behind...

 I made a serif type, you can see it on the right, without curved serifs. I made them polygonal, out of straight line segments, chamfered brackets. And look, as economical in data as a sans serif. We call it Charter, on the right. So I went to the head of engineering with my numbers, and I said proudly,

Matthew Carter: My life...

 whether mathematics was discovered or invented. Did we create mathematical concepts to help us understand the universe around us, or is math the native language of the universe itself, existing whether we find its truths or not? Are numbers, polygons and equations truly real,

Is math discovered or...

 Now, this was made from a life cast of Brad. So, in fact, anatomically, it is correct. The eyes, the jaw, the everything is in perfect alignment with what the real guy has. We have these maquettes scanned into the computer at very high resolution -- enormous polygonal count.

Ed Ulbrich: How Benjamin...

 these polygons Tundra ponds are something unique to the High Arctic that formed over thousands of years and this was very close to their den site and so I thought today in a effort to kind of better introduce us all to the life of a wolf from here on out I'm going to show

Storytellers Summit Day...

 started writing blog posts that talked about my experiences and issues I had feasts within the community and to my surprise they went viral within our scene a well-known fighting game website picked up one of my posts and later on polygon a gaming site covered my future

Calling out misogyny in...

 And vertices minus edges plus faces still equals two. And in fact, you could do this any which way -- cover this thing with all kinds of polygons and triangles and mix them up. And you take vertices minus edges plus faces -- you'll get two. Here's a different shape.

The mathematician who...

 when you increase the number of sides of a polygon to a very large number. And of course, it turns into a circle. And by the way, she was also very insistent on being able to change the color, an important feature for this demonstration.

Conrad Wolfram: Teaching...

 Any polygon with an odd number of sides can be used to generate a curve of constant width using the same method we applied earlier, though there are many others that aren't made in this way.

Why are manhole covers...

 Importantly, it also works for some polygons with fewer sides, including heptagons, hexagons, and pentagons. That’s good news, because if you cut off the sharp corners of the blob triangle,

Polygon

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