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More on the system used for the Eyebrows. As shown before, a curve is projected on the face, and then the eyebrow mesh is wrapped onto the curve. Unlike before, there is now a second layer of projection that guarantees the eyebrow mesh stays above the surface of the... show more

aVersionOfReality

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The #geometrynodes Curve Normals Proxy Rig is almost ready! You place it on the face and adjust some controls to line things up, and it just works. The controls can be worked with in lots of different ways. You can attach it to an existing rig or animate it. Those bones are controlling a mesh which controls the curve points, so you can also make Shapekeys on the meshes instead and Drive them to match other expression keys! The forehead above the top curve blends to Radial Normals, and under the chin blends to the actual mesh Normals. I'm adding the rest of the controls to allow completely arbitrary Normals per curve point, and then its just cleanup and it can be released! (There's lots more that can be added to it like falloff and interpolation controls, but if I try to put everything into the first version it'll never release.)

The #geometrynodes Curve Normals Proxy Rig is almost ready! You place it on the face and adjust some controls to line things up, and it just works. The controls can be worked with in lots of different ways. You can attach it to an existing rig or animate it. Those bones are controlling a mesh which controls the curve points, so you can also make Shapekeys on the meshes instead and Drive them to match other expression keys! The forehead above the top curve blends to Radial Normals, and under the chin blends to the actual mesh Normals. I'm adding the rest of the controls to allow completely arbitrary Normals per curve point, and then its just cleanup and it can be released! (There's lots more that can be added to it like falloff and interpolation controls, but if I try to put everything into the first version it'll never release.)

aVersionOfReality

57,639 Aufrufe • vor 1 Jahr

This is how the eyes have been modelled! it has an eye white mesh, iris mesh, a mesh for shadow and then the eyelids. The eyelids can move separately for more emotion. And the eyes can look around through blendshapes but there is clipping because of curved surfaces.

This is how the eyes have been modelled! it has an eye white mesh, iris mesh, a mesh for shadow and then the eyelids. The eyelids can move separately for more emotion. And the eyes can look around through blendshapes but there is clipping because of curved surfaces.

Zel Kanis 🦾 3DVartist (@zelkanis.com 🦋)

38,346 Aufrufe • vor 8 Monaten

$Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.$

Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.

Cliff Pickover

30,895 Aufrufe • vor 7 Monaten

$Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.$

Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.

Cliff Pickover

14,464 Aufrufe • vor 10 Monaten

In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Mathelirium

23,254 Aufrufe • vor 2 Monaten

While hiking, these people come across a Ford Mustang 5.0 that had missed a curve and flipped over the guardrail above. There are marks on the car where the jaws of life were used along with a pair of shoes on the ground near the wreck. Why was this left there and not removed?

While hiking, these people come across a Ford Mustang 5.0 that had missed a curve and flipped over the guardrail above. There are marks on the car where the jaws of life were used along with a pair of shoes on the ground near the wreck. Why was this left there and not removed?

Blonde of War (JJ)

237,795 Aufrufe • vor 5 Monaten

I'm putting a lot of attention into getting a high quality transfer for the Face Proxy Mesh we're adding to the Fondant Custom Normals Blender addon. Even if the proxy has great Normals, it will not matter if the transfer is distorted. A basic world space Nearest Surface (aka Nearest Face Interpolated) transfer can get screwed up if there are gaps between the meshes. And if they are different shapes and poly counts, there will be! So the first big piece of the puzzle is getting a clean transfer. Before transferring Normals, a transfer space is made and a UV map is transferred from the proxy. Then any other data needed can be transferred in that UV space. As long as it is right, any other data will be clean! (Normals or anything else you might want.) And a UV map is easy to debug because you can put a grid texture on it. If the grid is evenly spaced, then distortion is minimal. This clip shows the differences in distortion between a basic World Space transfer and a better transfer space made by blending Sphere projection and a simple projection of the face forward onto the proxy (used down the center line.) Different faces will need slightly different configuration. Most of this is automatic, but the addon will have some simple controls to adjust it to different face shapes.

I'm putting a lot of attention into getting a high quality transfer for the Face Proxy Mesh we're adding to the Fondant Custom Normals Blender addon. Even if the proxy has great Normals, it will not matter if the transfer is distorted. A basic world space Nearest Surface (aka Nearest Face Interpolated) transfer can get screwed up if there are gaps between the meshes. And if they are different shapes and poly counts, there will be! So the first big piece of the puzzle is getting a clean transfer. Before transferring Normals, a transfer space is made and a UV map is transferred from the proxy. Then any other data needed can be transferred in that UV space. As long as it is right, any other data will be clean! (Normals or anything else you might want.) And a UV map is easy to debug because you can put a grid texture on it. If the grid is evenly spaced, then distortion is minimal. This clip shows the differences in distortion between a basic World Space transfer and a better transfer space made by blending Sphere projection and a simple projection of the face forward onto the proxy (used down the center line.) Different faces will need slightly different configuration. Most of this is automatic, but the addon will have some simple controls to adjust it to different face shapes.

aVersionOfReality

14,935 Aufrufe • vor 1 Jahr

Calculus of Variations is what happens when you stop optimizing values and start optimizing geometries. The unknown isn’t a single x...it’s a whole curve y(x). And the thing you’re minimizing usually isn’t a formula you can eyeball...it’s an integral that judges the entire shape. For our first lecture, we look at the famous Brachistochrone problem. Fix two points, switch on gravity, and ask a question that sounds too simple...which track gets a bead from A to B in the least time? Your intuition will betray you on the first try. It’s not the straight line. It’s not the drop hard then cruise sketch either. The winner is a cycloid...the curve traced by a point on a rolling circle. In the animation, the track is the moving character. We start with an imperfect curve, run gradient descent in curve-space, and watch the geometry reshape frame by frame as T[y] collapses until it locks into the brachistochrone. Pls see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Calculus of Variations is what happens when you stop optimizing values and start optimizing geometries. The unknown isn’t a single x...it’s a whole curve y(x). And the thing you’re minimizing usually isn’t a formula you can eyeball...it’s an integral that judges the entire shape. For our first lecture, we look at the famous Brachistochrone problem. Fix two points, switch on gravity, and ask a question that sounds too simple...which track gets a bead from A to B in the least time? Your intuition will betray you on the first try. It’s not the straight line. It’s not the drop hard then cruise sketch either. The winner is a cycloid...the curve traced by a point on a rolling circle. In the animation, the track is the moving character. We start with an imperfect curve, run gradient descent in curve-space, and watch the geometry reshape frame by frame as T[y] collapses until it locks into the brachistochrone. Pls see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Mathelirium

106,981 Aufrufe • vor 7 Monaten

Boop says there is a lot more pressure on Clix than on Veno right now "The comparison will be that Veno won FNCS with Curve but can he do that with Clix now, that will be the pressure on Clix"

Boop says there is a lot more pressure on Clix than on Veno right now "The comparison will be that Veno won FNCS with Curve but can he do that with Clix now, that will be the pressure on Clix"

Stack

50,887 Aufrufe • vor 1 Monat

Oil sold off the moment the Iran peace deal appeared. That part makes perfect sense. Nobody wants to be long crude into open supply routes and normalizing tanker flows. The fundamental value of oil is closer to 50 a barrel than 150. But here is where it gets interesting. If this were only supply normalizing, the curve would still hold its shape. Inventories are drained. Tankers are disrupted. Refineries are scrambling. As long as demand is firm, the curve should stay in strong backwardation. Backwardation means front-month crude trades above later contracts. It is the market telling you it wants barrels today. It is a sign of tightness. That backwardation is nearly gone. The prompt spread, the first two contracts, has narrowed to under a buck. The three-month spread has dropped to just over 2, after being 30 not long ago. The front is selling off far harder than the back. Some of that is supply normalizing. The good kind. But when the curve gets this close to contango this fast, it points to something more troubling. Contango is what a glut looks like in the futures market. Too much oil for the demand in front of it. The curve is not there yet. But it is moving that way. And that is the warning. You have to be careful about exactly why oil is plunging this far, this fast.

Oil sold off the moment the Iran peace deal appeared. That part makes perfect sense. Nobody wants to be long crude into open supply routes and normalizing tanker flows. The fundamental value of oil is closer to 50 a barrel than 150. But here is where it gets interesting. If this were only supply normalizing, the curve would still hold its shape. Inventories are drained. Tankers are disrupted. Refineries are scrambling. As long as demand is firm, the curve should stay in strong backwardation. Backwardation means front-month crude trades above later contracts. It is the market telling you it wants barrels today. It is a sign of tightness. That backwardation is nearly gone. The prompt spread, the first two contracts, has narrowed to under a buck. The three-month spread has dropped to just over 2, after being 30 not long ago. The front is selling off far harder than the back. Some of that is supply normalizing. The good kind. But when the curve gets this close to contango this fast, it points to something more troubling. Contango is what a glut looks like in the futures market. Too much oil for the demand in front of it. The curve is not there yet. But it is moving that way. And that is the warning. You have to be careful about exactly why oil is plunging this far, this fast.

Jeffrey P. Snider

49,942 Aufrufe • vor 1 Monat

There’s going to be a demolition of the Accra-Kumasi highway, which will commence soon. The demolition start-point will be at Ablekuma curve as seen on the video

There’s going to be a demolition of the Accra-Kumasi highway, which will commence soon. The demolition start-point will be at Ablekuma curve as seen on the video

𝔸𝕝 𝕍𝕒𝕣𝕠 𝕏

42,602 Aufrufe • vor 5 Monaten

A physical system, its phase-space state, and the energy function that governs the flow, all linked together. The point of the animation is that these are not three different objects. They are three views of the same dynamics. The pendulum on the left is the physical motion. The curve on the floor is the evolution of its state. The translucent surface shows the energy landscape that organizes that motion.

A physical system, its phase-space state, and the energy function that governs the flow, all linked together. The point of the animation is that these are not three different objects. They are three views of the same dynamics. The pendulum on the left is the physical motion. The curve on the floor is the evolution of its state. The translucent surface shows the energy landscape that organizes that motion.

Mathelirium

19,865 Aufrufe • vor 3 Monaten

Everyone was positioned for oil at 200 a barrel. Inventories were low. The trade made sense. Then the curve flattened. In two weeks. Almost overnight. A flat curve after a supply shock is not supposed to happen. Normal shortage logic says near term prices trade at a premium while the market waits on inventories to refill. Instead the front of the curve collapsed hardest. That is not a supply story. That is the market pricing in demand disappearing faster than constrained supply can even matter. Stack it next to the household employment numbers, the drop in labor force participation, falling real incomes. The oil curve is not an isolated signal. It is confirmation.

Everyone was positioned for oil at 200 a barrel. Inventories were low. The trade made sense. Then the curve flattened. In two weeks. Almost overnight. A flat curve after a supply shock is not supposed to happen. Normal shortage logic says near term prices trade at a premium while the market waits on inventories to refill. Instead the front of the curve collapsed hardest. That is not a supply story. That is the market pricing in demand disappearing faster than constrained supply can even matter. Stack it next to the household employment numbers, the drop in labor force participation, falling real incomes. The oil curve is not an isolated signal. It is confirmation.

Jeffrey P. Snider

57,605 Aufrufe • vor 22 Tagen

Here's what's coming next for the Fondant Custom Normals Addon: Adjustable 3D anime face proxy mesh! If you've tried the proxy method before, you know that it can be difficult to get good results as you need the right topology and shape for good Normals, and also for it to fit to the face properly for a clean transfer. The solution is to use two proxies: one for the shape, and one for the fitting. But that gets cumbersome! And it is still often unintuitive to get the correct shading shapes. The next major feature of the addon will be aiming to solve these problems by providing a convenient proxy mesh that you can fit to your character's face with some rig controls, and then handles the rest under the hood with Geometry Nodes. All the benefits of complexity without having to deal with it yourself! This clip shows the general idea, but is early stages. I'll be sharing more as I build it out.

Here's what's coming next for the Fondant Custom Normals Addon: Adjustable 3D anime face proxy mesh! If you've tried the proxy method before, you know that it can be difficult to get good results as you need the right topology and shape for good Normals, and also for it to fit to the face properly for a clean transfer. The solution is to use two proxies: one for the shape, and one for the fitting. But that gets cumbersome! And it is still often unintuitive to get the correct shading shapes. The next major feature of the addon will be aiming to solve these problems by providing a convenient proxy mesh that you can fit to your character's face with some rig controls, and then handles the rest under the hood with Geometry Nodes. All the benefits of complexity without having to deal with it yourself! This clip shows the general idea, but is early stages. I'll be sharing more as I build it out.

aVersionOfReality

106,964 Aufrufe • vor 1 Jahr

Slowly adding to my tool stack for Hallway . This is a spline patch making a mesh that is wrapped from UV space onto the model. There's also setups to unwrap meshes on the surface back to UV space. Working in UV space enables a lot of procedural workflows. #b3d

Slowly adding to my tool stack for Hallway . This is a spline patch making a mesh that is wrapped from UV space onto the model. There's also setups to unwrap meshes on the surface back to UV space. Working in UV space enables a lot of procedural workflows. #b3d

aVersionOfReality

81,464 Aufrufe • vor 3 Jahren

Women's hockey continues to grow, and ice hockey legend Hilary Knight thinks there is a lot of catching up to be done now. "We need to cut that curve of not having investment for as many years as we haven't had," Knight said during the TIME100 gala red carpet. One of the greatest players in the history of women's hockey, Knight is on the TIME100 list this year. Read more about her legacy here:

Women's hockey continues to grow, and ice hockey legend Hilary Knight thinks there is a lot of catching up to be done now. "We need to cut that curve of not having investment for as many years as we haven't had," Knight said during the TIME100 gala red carpet. One of the greatest players in the history of women's hockey, Knight is on the TIME100 list this year. Read more about her legacy here:

TIME

23,097 Aufrufe • vor 3 Monaten

The value of the work we're doing at Optimum is encapsulated quite well by the phrase "speed is money". In modern markets there are real economic advantages to latency reduction. This is nothing new. Wall Street firms have long been optimizing on latency, primarily through colocation and top of the line hardware. However, when it comes to decentralized systems, expensive hardware and geographic concentration are antithetical to their purpose. Therefore we should optimize decentralized network latency through software, which I'm thrilled about because it's exactly what I've spent the better part of the past 2 decades working on with Random Linear Network Coding. Now let’s talk about networking economics, the relationship between speed and money. First, it's important to note that users will only pay for low latency if it can be consistently guaranteed. Second, you can only make that latency guarantee for a certain number of users. This is a universal law of networking. We can model this relationship on a delay curve, shown below. The delay curve is determined by the utilization rate of the network, meaning how much traffic is flowing through the network divided by the network's throughput. As you approach a level of traffic equal to the available throughput, latency trends infinitely higher. On this delay curve we can impose some utility thresholds. These thresholds are the levels of latency which are important to different groups of users because of how that latency guarantee improves their economic outcomes. Finding the point on the curve where each threshold intersects will tell us what level of traffic we can guarantee that level of latency for. Essentially, there exists a finite supply of speed on a network and the highest utility users of that speed are willing to pay more for it. I like to think of this similarly to expedited shipping options on Amazon. This is why we say speed is money, and why we can create a Latency Marketplace. The only way to increase the supply of speed is to fundamentally increase network throughput. This is what we work on at Optimum by using Random Linear Network Coding. The same relationship between traffic and throughput still applies, but now the delay curve is shifted out further to the right. Now more traffic can be processed at the same latency, or the same traffic can be processed at a lower latency. More speed available to the network. More value unlocked for the network’s users. Crucially, that value is no longer only reserved for those who can afford to sit closest to the machine. Expanding the supply of speed widens who can reach each latency threshold, keeping the network's advantage decentralized rather than concentrated in the hands of a few. When nodes join Optimum and participate, they reap the benefits, but they also add to the capacity. Rather than vying against each other in a zero-sum game, nodes help themselves and others.

The value of the work we're doing at Optimum is encapsulated quite well by the phrase "speed is money". In modern markets there are real economic advantages to latency reduction. This is nothing new. Wall Street firms have long been optimizing on latency, primarily through colocation and top of the line hardware. However, when it comes to decentralized systems, expensive hardware and geographic concentration are antithetical to their purpose. Therefore we should optimize decentralized network latency through software, which I'm thrilled about because it's exactly what I've spent the better part of the past 2 decades working on with Random Linear Network Coding. Now let’s talk about networking economics, the relationship between speed and money. First, it's important to note that users will only pay for low latency if it can be consistently guaranteed. Second, you can only make that latency guarantee for a certain number of users. This is a universal law of networking. We can model this relationship on a delay curve, shown below. The delay curve is determined by the utilization rate of the network, meaning how much traffic is flowing through the network divided by the network's throughput. As you approach a level of traffic equal to the available throughput, latency trends infinitely higher. On this delay curve we can impose some utility thresholds. These thresholds are the levels of latency which are important to different groups of users because of how that latency guarantee improves their economic outcomes. Finding the point on the curve where each threshold intersects will tell us what level of traffic we can guarantee that level of latency for. Essentially, there exists a finite supply of speed on a network and the highest utility users of that speed are willing to pay more for it. I like to think of this similarly to expedited shipping options on Amazon. This is why we say speed is money, and why we can create a Latency Marketplace. The only way to increase the supply of speed is to fundamentally increase network throughput. This is what we work on at Optimum by using Random Linear Network Coding. The same relationship between traffic and throughput still applies, but now the delay curve is shifted out further to the right. Now more traffic can be processed at the same latency, or the same traffic can be processed at a lower latency. More speed available to the network. More value unlocked for the network’s users. Crucially, that value is no longer only reserved for those who can afford to sit closest to the machine. Expanding the supply of speed widens who can reach each latency threshold, keeping the network's advantage decentralized rather than concentrated in the hands of a few. When nodes join Optimum and participate, they reap the benefits, but they also add to the capacity. Rather than vying against each other in a zero-sum game, nodes help themselves and others.

Muriel Medard

43,142 Aufrufe • vor 27 Tagen

Elon Musk just said the AI community is misunderstanding the math of superintelligence by two orders of magnitude. Not slightly off. Not directionally wrong. A hundred times off. Musk: “Most people in the AI community don’t yet understand. The intelligence density potential is vastly greater than what we’re currently experiencing.” Everyone is focused on the hardware race. Bigger data centers. More GPUs. Nuclear power plants built to feed the compute. That’s half the equation. Musk: “I think we’re off by two orders of magnitude in terms of intelligence density per gigabyte. That’s just algorithmic improvement. Same computer.” Read that carefully. Not more hardware. Not more energy. Not more capital. The same machine. A hundred times smarter. Through software alone. That’s before the hardware improvements compound on top of it. Musk: “And the computers are getting better. That’s why I think it is a 10x improvement per year type thing. 1,000 percent.” A thousand percent compounding annual growth rate in raw intelligence. A system that becomes 10x more capable every twelve months doesn’t follow a linear curve. It doesn’t follow an exponential curve that human intuition can track. It follows a curve that human intuition cannot simulate at all. In year one it’s 10x smarter. In year two it’s 100x. In year three it’s 1,000x. At that point, the gap between that system and a human brain is wider than the gap between a human brain and a calculator. This is the math the public isn’t running. The models aren’t just getting better. They are compounding on themselves at a rate that makes every previous technology curve look flat. Musk: “The intelligence density potential is vastly greater than what we’re currently experiencing.” We aren’t approaching superintelligence on the timeline most people imagine. We are already inside the curve.

Elon Musk just said the AI community is misunderstanding the math of superintelligence by two orders of magnitude. Not slightly off. Not directionally wrong. A hundred times off. Musk: “Most people in the AI community don’t yet understand. The intelligence density potential is vastly greater than what we’re currently experiencing.” Everyone is focused on the hardware race. Bigger data centers. More GPUs. Nuclear power plants built to feed the compute. That’s half the equation. Musk: “I think we’re off by two orders of magnitude in terms of intelligence density per gigabyte. That’s just algorithmic improvement. Same computer.” Read that carefully. Not more hardware. Not more energy. Not more capital. The same machine. A hundred times smarter. Through software alone. That’s before the hardware improvements compound on top of it. Musk: “And the computers are getting better. That’s why I think it is a 10x improvement per year type thing. 1,000 percent.” A thousand percent compounding annual growth rate in raw intelligence. A system that becomes 10x more capable every twelve months doesn’t follow a linear curve. It doesn’t follow an exponential curve that human intuition can track. It follows a curve that human intuition cannot simulate at all. In year one it’s 10x smarter. In year two it’s 100x. In year three it’s 1,000x. At that point, the gap between that system and a human brain is wider than the gap between a human brain and a calculator. This is the math the public isn’t running. The models aren’t just getting better. They are compounding on themselves at a rate that makes every previous technology curve look flat. Musk: “The intelligence density potential is vastly greater than what we’re currently experiencing.” We aren’t approaching superintelligence on the timeline most people imagine. We are already inside the curve.

Dustin

1,553,639 Aufrufe • vor 5 Monaten

TFTC 633 w/ DETERMINISTIC OPTIMISM 🌞: "The uncomfortable truth is that base layer Bitcoin is not for everyone. There is not enough sats. The math doesn't add up." We discuss: ⚡️ Bitcoin self-custody ⚡️ AI is replacing the middle of the bell curve ⚡️ Why covenants matter for 1000-year vaults

TFTC 633 w/ DETERMINISTIC OPTIMISM 🌞: "The uncomfortable truth is that base layer Bitcoin is not for everyone. There is not enough sats. The math doesn't add up." We discuss: ⚡️ Bitcoin self-custody ⚡️ AI is replacing the middle of the bell curve ⚡️ Why covenants matter for 1000-year vaults

TFTC

17,410 Aufrufe • vor 1 Jahr