Signed Distance Functions & Ray-Marching

[@MusicEngineeer]

Thank you. This may be very helpful for writing graphics rendering code.

[@sumandproduct]

I hope it will! When actually coding this, there are dozens of edge cases and practical problems to solve. But I hope that at least the mathematical foundation was made clear in the video.

[@jurgenrichter-gebert]

WOW. Very smooth....Next Level! Literally!

[@sumandproduct]

Thank you very much! 😄

[@Roxor128]

Ray-marching for collision-detection? Sounds useful. How to handle the different shapes of the objects involved, though? Could be a topic for a new video.

[@sumandproduct]

I've only used it for simple physics simulations where the objects moving around are small circles. But it's probably worth looking into more...

[@Roxor128]

@@sumandproduct Yeah, I can see how you'd do sphere-anything collision. Subtract the sphere's radius from the SDF of whatever it might hit and then ray-march the same as if you're rendering the scene. Basically, making a rounded box and doing sphere-box collision would be the same process. The real headscratcher is how to handle other shapes and the potential rotation that would be introduced when they collide.

[@sumandproduct]

@@Roxor128 From what I learned during the research for this video, I wouldn't be surprised if checking for collision of two arbitrary SDFs is just not possible.

[@bigfloppa9220]

@@sumandproduct it is actually possible, but it requires gradient descent on the sdfs, and likely only works on true sdfs, not ones created using the unions of the shapes. it boils down to reducing the problem to the same one as colliding sphere sdfs, but by solving the system of equations formed by the two sdfs you are colliding. very possible, but time consuming and not very performant, as opposed to using bounding volumes to perform collision detection. There are several papers on it from Nvidia/other graphics researchers, and I think it probably does have it's place in physics simulations

[@sumandproduct]

@@bigfloppa9220 Oh, that makes sense, yes. Thank you!

[@johnchessant3012]

Great video!

[@sumandproduct]

Thank you!

[@AnirudhMathur-qq9ch]

I have been searching for a channel like yours for so long. You just earned a sub 🫶

[@Asalraalaikum]

S tier video 👏 Thank you!

[@ryanjbuchanan]

Very well made video 😄

[@cadenmccorvey4153]

amazing video and extremely informative!

[@VRchitecture]

Lovely introduction! It’s nice you not only mentioned what SDFs are but also derived a couple of basics ones 👏🏻 P.S. Though ray marching usage is pretty rare, typically we render “pre-baked” 3D geometry (stored as a list of vertices and normals not its mathematical description) with some sort of ray tracing.

[@shadow15kryans23]

This is a good video 👏

[@CompanionCube]

This is a good comment 👏

[@freizagen]

you make video course on shaders and sdf. i will buy it

[@oncedidactic]

Very nice video! I learned a lot of new perspectives. As someone who works with spatial analysis tools on large datasets, I often wonder about how graphics approaches work versus the implementations of basic spatial relationship calculations. There is obviously much conceptual overlap, and I’m curious how many techniques are shared directly.

[@torikenyon]

I’m confused, is just a different way to write the dot product, or is it something different?

[@sumandproduct]

It is the dot product!

[@ValkyRiver]

How does ray marching work in spherical or hyperbolic geometries?

[@sumandproduct]

I imagine it works similarly whenever you have a metric.

[@starplatinum3305]

how to do collisions tho ? you have source for that ?

[@sumandproduct]

I have nothing on hand, as I don't use it much for physics. (Except sphere-vs-SDF, which is automatic.) But there's a new paper, which looks interesting: doi.org/10.1016/j.cagd.2024.102305 Haven't had time yet to read it, though.

[@alexandersedykh9280]

Why do we need to calculate the minimum distance to an object that is not located exactly in the direction of the ray?

[@sumandproduct]

Because in general, we don't know which objects lie in the direction we are looking. We can do a step before by looking at the "axes-aligned bounding box". This so-called AABB is the smallest box containing the object. We can intersect the ray with these boxes to check which objects are even candidates for a full intersection check. But in some way or another, we have to look at all objects.

[@thecritiquer9407]

finally a french competitor to 3blue1browm

[@jurgenrichter-gebert]

@@markusa.stokkenes2271 He IS German ;-)

[@notwithouttext]

@@w花b no they mean the COMPETITOR is french not the competitor's VIDEO

[@notwithouttext]

although, i think they're german, since the channel is in germany

[@ArnaudMEURET]

Doesn’t sound French at all. German. France produced Fabrice Bellard and that’s enough for a few centuries 😅

[@judef]

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