Видео

unbelievable...

I cannot believe this.

I see Inigo Quilez name everywhere... Now, I understand why. I must ask, which software you used for this 3d creations?

I wish I’d paid more attention in maths classes. this is god level. Bravo IQ sir! ❤

You're a genius.

I've just discovered this tuto, thanks IQ for doing all this 'magic' with maths!

Bjp is happy with TN results and DMK is happy with National results.. wonderful

please give noble prize for this one.. please

Cool!

i need you bro

I understand the Chinese subtitles as much as the words you are speaking. I feel so dumb.

you are my hero Inigo! Thanks for putting this beautiful and instructive video together and sharing your craft.

You sir have incredible talent and skill thank you for sharing!

Thanks!

This is misleading because that isn't what it is.

Amazing. So good.

У меня видеокарта отключается =)

hey buddy i want to reach out to you, smoothstep is your fault :) ❤ basically the entire graphics programming world is incapable of solving problems and making perceptive discernments because they aren't aware that higher order interpolation exists. can you please fix this? just yesterday i realised, that's why surface nets suck, because they try to fix them with gradient descent instead of just using 2nd order cubic interpolation which is only 3 mults and 4 samples!!! please fix this human species immediately!!!! :) people think perlin is ugly, it's just they've never seen correct interpolation!!!! :O

This is really cool. Would it be possible to have this natively on Linux without GUI?

Thanks!

wocao！niubi！

Hi im interested with your edits how do you show your math visualization?

This is magic.🪄

N= positive odd number. N changes to (3N+1)/2 (3N+1)/2 could be: 1- (3N+1)/2 = positive odd integer 2- (3N+1)/2 = positive even integer 1- assume (3N+1)/2 = positive odd integer. Since N = positive odd integer, it could be a value for (3N+1)/2 So, (3N+1)/2 = N 3N + 1 = 2N 3N - 2N = -1 N = -1, which contradicts with N = positive odd integer. So, the assumption (3N+1)/2 = positive odd integer is false. 2- assume (3N+1)/2 = positive even integer. Since N + 1 = positive even integer, it could be a value for (3N+1)/2 So, (3N+1)/2 = N + 1 3N + 1 = 2N + 2 3N - 2N = 2 - 1 N = 1, which does not contradict with N = positive odd integer. So, the assumption (3N+1)/2 = positive even integer is true, and (3N+1)/2 will change to smaller value (3N+1)/4 < N, getting toward the destination 1. If N = 1, (3N+1)/4 will equal 1, which is a term within the destination loop 1 → 2 → 1. So, N = positive odd integer, just changes to (3N+1)/2 = positive even integer, which changes to (3N+1)/4 < N, getting toward the destination 1. So, Collatz conjecture is true. Eng. Mahmoud Attalla. WhatsApp: +20 1112669096.

Hearing "Now look, because this is cool," in a video about math is something I wish I experienced more often.

What's the name of software u use?

Awesome

Are there extra useless abs function in sdCross()?

Inigo you're awesome! Thank you for this priceless lesson! Pricelesson!

If I ever have 1 year of time to spare - I'll try to understand all the math I just observed. Beautiful

Based on your video, I now understand why I always get so annoyed in Blender or Strata3D when I want to smooth the edges. I find the concept at around 26:00 in this Vid with the distances 1, 2 & 3 very problematic and basically poorly thought out. Basically it's a good approach with the distances but these individual lines in the X & Y direction have to be created in the Objcts inside not outside. Imagine my fit of rage when I create a text (as a only text first) in Blender and use Bevel (Strata) to drag it into the depth to make a 3D object out of it and then your theorem comes along: now I'm rounding the edges. What happens?! The individual letters of the text (maybe a company logo) fall into one another and the previously correct spacing is completely lost. This has something to do with typography that was completely forgotten in that concept. Or I take an image with a logo and load it into the 3D program, then I draw the edge, or I have a vector graphic of the company logo and load this into the 3D program and say make a 2D object out of it, then I drag it (again) into the depth to get a 3D object, all very simple standard processes up to this point. But if I now add a metallic texture to that Object, for example chrome or gold, wear are it is always most effective later as a moving object when the edges are minimal a bit rounded, the more curved the better the reflection effects, which is what creates the chrome or gold look for the human eye/brain. And now you might understand why I am appalled that you move P1/P2 and therefore P3 outwards instead of pulling them into the interior of the object. Even if I model something else, nobody wants to inflate the volume of this object outwards and then thus get collisions with other existing objects in the 3Dscene. A serious conceptual error!!! Apparently most 3D software engineers make exactly this mistake, which is a shame, as it creates massive extra work and causes tremendous stress when working with the programs. Can you please bring this Point somtimes up at Pixar & Blender Foundation etc. I know the people there will listen to you becuse you are a genius in betwin of time at this branch. All the rounding modifiers in Blender are obviously based on this wrong concept regarding the displacement/distance points. Maybe them can put too a switchbox in the GUI for "Inside or Outside" expanding "P1/P2 & P3" so that the old workflow is too posibly. Thanks in advance, with only the best wishes & greetings bennoH.🐹🙋 bennoH. love's ISF-Shaders for ResolumeArens + moo RealtimvideoSoft 💗 In respect and memory too the great 💗🙏💫 MojoVideoTech "DrMojo" hu switching shadertoys to ISF

"This is just high school mathematics" I went to the wrong highschool.

At 1:29:00 +/-, Inigo says about soft shadows... It's very great, few lines of code and super fast... And typing a cycle for 100 times calling global sdf function))) Good joke, Inigo, good joke!

I loved watching this video. A career dream of mine was to be doing similar things to this, bought all the (expensive) books. Unfortunately, life and the maths required meant it stayed a dream..

First I was surprised that 40 minutes had passed. Then I was surprised that I had watched the whole video again. Thank you so much for this. Late to the party, but this video needs all the attention it can get.

can you make blender 3d addon for can create smooth boolean transitions?)

So... was I watching a Marvel movie? The VFX blew my mind!

3:40:40 Sympathetic movements

Just beautiful.

*Abstract* This video demonstrates how to create a landscape painting using mathematical formulas instead of traditional paint and brushes. The process involves defining colors and shapes through formulas, which are then combined into one large formula to generate the final image. The video covers various aspects of the painting process, including creating the terrain, lighting, atmosphere, composition, and adding details like grass and clouds. *Summary* *Basic Polynomial Surface (Noise)* * *0:52**:* The terrain is initially created using a linear function of x and z coordinates. * *1:11**:* Increasing the degree of the polynomial adds undulations to the surface. * *1:37**:* To avoid computationally expensive high-degree polynomials, the terrain is divided into tiles, each with a unique low-degree polynomial. * *2:29**:* Coefficients for the polynomials are randomized to create a natural-looking terrain. * *3:53**:* The resulting undulating and random function is called "noise" and is commonly used in visual effects. *Fractal Surface (FBM)* * *4:13**:* The noise function is used to add finer details to the terrain by repeatedly compressing, squashing, rotating, and adding it back to the original surface. * *5:46**:* This process resembles a Fourier series or discrete cosine transform. *Key Lighting* * *6:30**:* Lighting is introduced by considering the sun as the key light. * *6:43**:* Derivatives of the terrain function are used to determine surface normals and identify areas facing the sun. * *7:18**:* The dot product between the surface normal and the sun direction determines illumination. * *8:09**:* Shadows are added by checking for intersections between the line of sight to the sun and the terrain. * *8:48**:* Soft shadows are created using a smooth transition zone between light and shadow. *Atmospheric Coloring* * *9:16**:* To create a sense of scale, atmospheric perspective is simulated by mixing gray into the surface color based on distance. * *10:42**:* Different attenuation factors for red, green, and blue channels create a blue tint in the atmosphere. *Composition and Cliffs* * *11:00**:* A specific section of the terrain is chosen and framed for the composition. * *11:55**:* Cliffs are sculpted by raising areas above a certain height. *Light Direction* * *12:33**:* The sun's position is adjusted to create dramatic lighting and shadows. * *13:03**:* Different sun directions are explored to find the optimal composition. *Sky* * *13:55**:* A blue background is added and adjusted to create a darker, more saturated sky at the top. * *14:18**:* Clouds are created by evaluating the terrain function on a horizontal plane and applying a smooth step. * *15:23**:* Cloud details are adjusted to achieve the desired look. *Fill Lighting* * *15:45**:* Overall contrast and saturation are adjusted. * *16:17**:* Areas not directly illuminated by the sun receive skylight based on their orientation. *Grass* * *17:43**:* Green is mixed into the terrain color based on the surface normal to create a grassy layer. *Tree Sculpting* * *18:32**:* Some terrain undulations are filtered out to create areas suitable for tree growth. * *19:22**:* Trees are created by tiling the space and evaluating a sphere's signed distance function within each tile. * *20:42**:* Randomness is introduced to vary the positions and sizes of the trees. * *21:13**:* Spheres are stretched vertically to resemble trees. * *22:11**:* Trees are positioned on the ground, leading to some appearing under the cliffs. * *22:43**:* The ground between trees is darkened to simulate reduced light penetration. *Tree Lighting and Coloring* * *24:55**:* Noise is used to distort the tree silhouettes and make them more organic. * *26:00**:* The lighting on the trees is adjusted to reveal the shape of the underlying terrain. * *26:56**:* Highlights are added to the trees, capturing the silhouettes of the hills. *Color Touchups* * *27:41**:* A rainforest color palette is chosen, and variations are added to the trees. * *32:04**:* The brightness and lighting of specific areas are adjusted. *Highlights* * *29:48**:* Highlights are added to the cliffs and trees using formulas that approximate real-world light behavior. *Clouds* * *34:45**:* More realistic clouds are sculpted using a solid block and adding noise. * *35:41**:* The plotting algorithm is changed to accumulate cloud density and color for a fluffy appearance. * *36:07**:* Fractal noise is used to create detailed cloud silhouettes. * *36:30**:* The cloud density gradient is filtered to soften the lighting. * *37:20**:* Cloud size and lighting are adjusted. * *38:14**:* Skylight is added to the clouds. *Cloud Shadows* * *39:26**:* Shadows cast by the clouds on the terrain are computed using the cloud density function. * *40:17**:* Shadow softness and size are adjusted. *Conclusion* * *40:35**:* The final painting is complete, demonstrating the use of mathematics to create a landscape image. i used gemini 1.5 pro to summarize the transcript Token count 11,153 / 1,048,576

As always fantastic video. I am sure making the video was 10 times harder than making the actual landscape, which makes it even more impressive and welcome.

Wow, this is amazing. Maths is beautiful 🤍

Hi from colombia: this is the start of holodek, im a star trek fan. i think the quantum computer can proces this or a virtual ray marching world in real time.

I kinda want to see how the negative side is different from the positive one now

if the edge is infinite doesnt that mean there is no anti solution to the conjecture?

**_**

Cool thx by bennoH.

Intresting & thats a way of thinking by do coding. So be creativ and teak the other way. Some of agiptical logic ar to impresiv and easy to in the end. Thanks foe teatching us by bennoH. & By the way, dit u have testing or doing coding in Vulkan SPIR-V Shaders and can you do a free online curs for us. Becus i think it's the next generation of schaders.

In which software I can try these formula?

Bob Ross of tech art. Thank you. Perfect material to enjoy a meal in between fighting with ShaderGraph and Unity memory management