Interstellar: inside the black hole and tesseract
My name is Andrei Kolokoltsev. By the nature of my work, I have long been interested in stories about how eminent directors, producers, and studios cope with the creation of various visual pictures. For my first publication, I chose a movie that became for me an audiovisual revelation and a real emotional attraction (this is when watching a movie on the IMAX screen, 2/3 of impressions are lost on the TV at home). You do not jump up in surprise, because you’ve already read everything in the title - this is Christopher Nolan’s movie “Interstellar”. Despite the fact that interest in him has long since died away, I would like to bring to your attention a free translation of the original article by Mike Seymour “Interstellar: inside the black art” dated November 18, 2014. This article tells about how the visualization of “Gargantua” and other scenes from the film was created - I think it will be interesting for readers even after 1.5 years.
Interstellar director Christopher Nolan explains to Matthew McConaughey thefundamentals of quantum physics
Employees of special effects and computer graphics often face the need to create a visualization of what no one has ever seen. To this is added the requirement of the modern film industry, so that it all looks real, even though no one really knows what it might look like. In Christopher Nolan's film Interstellar, special effects supervisor Paul Franklin and the Double Negative team were supposed to create a visualization of things not from our dimension, while being as close as possible not only to quantum physics and relativistic mechanics, but also to our common understanding quantum gravity.
')
It was fortunate that among the main team of Double Negative was Oliver James, the main researcher with the Oxford education in the field of optics and atomic physics, as well as a deep understanding of Einstein's relativistic laws. As well as Franklin, he worked with the main producer and scientific consultant Kip Thorne. Thorne had to calculate complex mathematical equations and send them to James for translation into high-quality renders. The requirements for the film set for James the task not only to visualize calculations explaining the arc trajectories of light, but also to visualize cross sections of rays of light that change their size and shape during the journey through the black hole.
The James Code was only part of the overall solution. Hand in hand, he worked with the artistic team leader, computer graphics effects supervisor Yevgeny von Tanzelman, who added an accretion disk, and also created a galaxy and a nebula, distorted as soon as the light from them passes by the black hole. No less difficult was the task of demonstrating how someone enters a four-dimensional tesseract, combined with the three-dimensional space of a little girl's room — all in the form so that the viewer can understand what is happening on the screen.
In this article we will tell you about some key frames created by Double Negative, as well as about the scientific research that precedes them. Please note that spoilers are possible in the sequel.
Perhaps one of the most significant merits in achieving the Nolanoff task of maximum realism is the portrayal of the black hole Gargantua. After receiving input from Thorn, the filmmakers made every effort to show the behavior of light in a black hole and a wormhole. For Double Negative, this task necessitated writing a completely new physical renderer.
View from the camera on a circular equatorial orbit of a black hole rotating at 0.999 of its maximum possible rotation speed. The camera is located at a distance of r = 6.03 GM / c ^ 2, where M is the black hole mass, G and c is the Newton constant and the speed of light, respectively. The black hole event horizon is at a distance of r = 1.045 GM / c ^ 2.
“Kip explained to me the relativistic distortions of the space around the black hole,” says Paul Franklin, “Gravity, twisted in time, deflects light from itself, creating a phenomenon called the Einstein lens, the gravitational lens around the black hole. And at that moment I was thinking how can we create such an image and are there any examples with a similar graphic effect that we could rely on. ”
“I looked at the most basic simulations created by the scientific community,” adds Franklin, “and I thought, ok, the movement of this thing is so complicated that we have to do our own version from scratch. Then Kip began to work very closely with Oliver James, our main research assistant, and his department. They used Kip's calculations to get all the light paths and ray tracing paths around the black hole. In addition, Oliver worked on pressing issues of how to implement all this with the help of our new renderer DnGR (Double Negative General Relativity). ”
For the new renderer, it was necessary to establish all the most important parameters for their digital black hole. “We could set the speed, mass and diameter,” explains Franklin. “In essence, these are the only three parameters that you can change in a black hole - that is, this is all that we have to measure it. We spent a tremendous amount of time working on how to calculate the paths of light beams around a black hole. All the work was quite intensive - for six months the guys wrote software. We had an early version of the black hole, just in time for the end of the film’s pre-production period. ”
The resting black hole accelerates to a rotational speed of 0.999 from possible; then the camera approaches a black hole from a radius of 10 GM / c ^ 2 to a radius of r = 2.60 GM / c ^ 2, continuing to move along a circular equatorial orbit. The huge shadow of a black hole is distorted into a rectangular shape due to the conversion of the camera's camera image to a flat display.
These early images were used in the form of huge paintings for the background outside the ship - so the actors had something to look at while shooting. That is, not a single green screen was used; later, the staff of Double Negative replaced the used early images with the final ones, correcting some star clusters. “Most of the shots are from the back of the astronauts you see in the rolling version of the film,” notes Franklin, “this is a real shot. We had a lot of shots that were not included in the general list of shots with visual effects, although a great job was done to create them. ”
These “direct” camera shots were made possible through the collaboration of Double Negative and Doctor of Physics Hoyte Van Hoytem. Spotlights were used to highlight the resulting background images, with an aggregate luminous flux of 40,000 lumens per scene. ”
The same simulation is just bigger. The structure of the light of the starry sky transmitted through a gravitational lens is clearly visible here. At the edge of a black hole, the horizon moves towards us at a speed of close to the speed of light.
“We needed to move and reconfigure spotlights based on the scene tasks,” Franklin continues. “In general, it would take a whole week to set things up correctly, but in some cases everything should have been ready in 15 minutes. The guys worked so hard, because the spotlights are huge, cumbersome engines - each weighed about 270 kilograms. We had two specially made cells, mounted on a large electric winch with the ability to move it along and across the pavilion, respectively, we could use it to place the spotlights. On the radio, I explained to the guys with the spotlights how to calibrate them, simultaneously talking with the person driving the forklifts, running above the tightly crowded platform. ”
In the film, Cooper (Matthew McConaughey), Amelia (Ann Hathaway), Doyle (Weight Bentley) and AI Robot CASE visit a completely water-covered planet, the waves on which, due to their very close proximity to Gargantua, reach extraordinary sizes. Spectators have already seen thirty-meter waves in other films, but according to history, this was not enough - according to the script, the waves should have been more than a kilometer in height. To give the viewer a feel for this height, Double Negative had to rethink the standard approach to creating water. “When you take objects of this scale,” explains Franklin, “all the characteristics you associate with waves, such as breakers and curls on top, simply disappear as they become invisible relative to such a mass of water - that is, the wave becomes more like on a moving mountain out of the water. That is why we spent a lot of time working on pre-visualization and wondering how we can use such scale waves and a small Ranger spaceship that they wash off. The highlight of the scene is when the wave hits the Ranger and raises it high above the surface. And you see how the ship moves upward on a wave, it gets smaller and suddenly gets lost on it altogether. It was a key moment for feeling the scale of what is happening. ”
Anne Hathaway as Amelia on the Water Planet
The artists of Double Negative controlled the waves by animating the deformers, effectively changing them into each keyframe. “It gave us a basic waveform,” says Franklin, “but to perceive this picture as real, we need to add foam on the surface, interactive splashes, water swirls and bursts. To do this, we used our internal development, called Squirt Ocean. Well and, of course, after there was a lot of extra work in Houdini. ”
Frames were created in high resolution IMAX. This requirement somewhat limited the amount of time allowed for all possible Double Negative iterations. “I watched the wave animation part, said“ well, let's add everything else, ”Franklin laughs,“ and then I had to wait about a month and a half for all this to come back to me again — such a long process was conditioned by the resolution of IMAX . As you understand, we could not waste time, because usually the whole process was divided into many iterations, and at that time we had a maximum of three. ”
Robot CASE rescuing Amelia from the tidal wave, and his twin TARS, in fact, were 80 kilogram metal dolls, controlled by Icelandic artist Bill Irwin. Christopher Nolan wanted the film to have as many real elements as possible, and instead of just drawing it as many as possible, Double Negative needed to remove the artist behind the robot.
When CASE reconfigures itself to pass through the water, and then rolls toward Amelia, grabs her and takes her away, two solutions are combined in the frame: practical and digital. “In this frame,” says Franklin, “there was a built small water drilling rig mounted on an ATV. That is, we could ride “through” the water and get wonderful interactive splashes and splashes. Also, on an ATV, we had a special lift with the hands of a robot, on which we could carry the twin, Anne Hathaway. That is, the whole structure went and “cut” the water, and we just had to remove it from the image and replace it with the digital version of the robot. ”
Double Negative tried to limit the number of moments with digital robots that do unusual things. Those moments were running through the water, landing a robot on a ship, running through a glacier and some moments with no gravity. “What we have noticed long ago is that you can make digital moments work only if you combine them with real ones,” says Franklin, “For example, in frames where a robot climbs into a ship, at the very end of the segment we are already seeing the real version of the robot, not the digital one. That is, the scene ends with frames with reality, and this helps to feel the scene as truly real. ”
In the film, someone “they” turns out to be “us”, only advanced enough to help Cooper connect with his daughter, who has been on Earth years before. Since in the universe of quantum and relativistic laws, time travel is impossible, history solves this issue in such a way that Cooper leaves our three-dimensional space and falls into a higher order hyperspace. If our universe is displayed as a 2D disk or membrane, then the hyperspace will be the box surrounding this membrane in three dimensions. The way to make sense of this is that each dimension requires one dimension less to display it. Thus, the three-dimensional space is drawn as a 2D disk, and the three-dimensional environment around this disk (as physicists call it a brane) is one dimension above the membrane.
Image drawn by Kip Thorne explaining what the bran and membrane are
In the film, Michael Kane's character, Professor Brand, is trying to unravel the gravitational anomalies. An attempt to solve the problem in 4th and 5th dimensions is clearly visible on the boards in the film. The film says that if the Brand can understand these anomalies, they can be used to change the gravity on Earth and raise the huge humanity-saving structure into space.
While the transition from three-dimensional space to four-dimensional does not solve the problem of time travel, in the film this allows Cooper to send gravitational waves back in time. He can see any time, but can only cause ripples in these time intervals — gravitational ripples, which Cooper’s daughter, Murphy, is trying to understand.
The work of the Double Negative team was to visually demonstrate the four-dimensional tesseract, which the future "we" provide to Cooper, so that he could cause gravitational waves. This would be easy to do if done symbolically or as a dream, but the Double Negative team decided to visualize the four-dimensional tesseract in a more expressive way, creating a concept that would, of course, be a hypothesis, but it could even be used for teaching . It was at that moment that Thorn reappeared.
Kip Thorn's formulas explaining gravity in four and five dimensions. Please note that here “our” brane is clamped as a sandwich between two alternative realities or other branes.
To understand the Double Negative solution, it is worthwhile to understand the nature of higher order measurements. If the object is at rest, for example, a ball — for two-dimensional space, it is a circle; for one-dimensional - line. If you look at this circle in three-dimensional space, then we will see a ball (sphere). But what will happen to him if you go to the four-dimensional space? One of the theories, which was the basis for our daily thinking, was to present the fourth space as time. Then it turns out that the same ball, but not resting, but bouncing, and in an infinitely small period of time is seen as the same ball. But throughout the journey, he creates a pipe-shaped figure with hemispherical edges. That is, in four-dimensional space, the ball is a pipe, and the sphere is a three-dimensional projection of this four-dimensional figure.
If a cube in three-dimensional space changes its shape over time, for example, grow, then it will be depicted in four-dimensional space as a box, which eventually grows into a large box, displaying all the states of a three-dimensional box throughout its existence. She can animate and reshape as shown in this video:
According to the logic of the film, if you fall into this tesseract, you can see the three-dimensional space at any time during its existence, for example, in the form of lines that go into the past and the future. Moreover, if we take into account the assumption that there are an infinite number of parallel realities, you will see all the lines of all possible parallel realities that go into an infinite number of directions. This is precisely the conceptual solution of the four-dimensional space with which the studio worked. The "threads" of time that Cooper sees look like strings, and touching them, he can cause gravitational vibrations, thus communicating with his daughter. This is really a brilliant piece of artistic scientific visualization!
The installation of Nolan, that when creating videos, the actors should interact with the environment and extended to tesseract. After hitting a black hole, Cooper finds himself in a four-dimensional space in which he can see any objects and their “thread” of time. “Chris said that despite the fact that this is a very abstract concept, he would very much like to build something that we could shoot in reality,” says Franklin, “He wanted to see Matthew physically interact with the“ threads ” time, in real space, and not dangling in front of the green screen. "
This prompted Franklin to ponder how to embody the tesseract visualization. “I spent a lot of time puzzling about how to implement all this in real space,” he says, “How to show all these temporary“ threads ”of all objects in one room, and to make this clear in a physical sense. After all, the danger was that the space would be so cluttered with “threads” that you would have to figure out how to select the right moments among them. Plus, it was extremely important that Cooper not only saw the “threads” of time, but also saw their backlash on the interaction, and at the same time could also interact with the objects in his daughter’s room. ”
The final view of the “open lattice structure” was inspired by the very concept of tesseract. “Tesseract - a three-dimensional projection of the four-dimensional hypercube. It has a beautiful lattice-like structure, so we roughly understood what we were going to do. For a long time, I looked at the sweep from long-shot photographs (slit-scan photography) and how this technique allows you to display the same point in space at all times. The photo itself transforms time into one of the dimensions of the final image. The combination of this imaging technique and the tesseract lattice structure allowed us to create these three-dimensional “threads” of time, as if arising from the object. Rooms are photographs, moments embedded in the trellised structure of the “threads” of time, among which Cooper can search for the right ones by moving them back and forth. ”
“We’ve finished building one section of this physical model with four repeating sections around,” says Franklin. “Then we reproduced these sections endlessly on the computer so that no matter where you look, they go to eternity. Also during the shooting we used a lot of real projections. We enclosed the active "threads" of time under the real section, using projectors. This gave us a feeling of trembling and febrile energy - all information flowed along these “threads” from section to section and back. But, of course, each image of the final version of the film, among other things, contains an insane amount of digital effects embedded in the scene. "
But some moments forced Double Negative to completely switch to digital visual effects - such a moment was, for example, the movement of Cooper through the tesseract tunnels. “We didn’t have enough tesseract sections to capture this movement, so we shot Matthew among the projection screens, on which a pre-final version of the visualization of this scene was displayed - so he had something to interact with,” says Franklin, “ The actors loved it all so much, because in contrast to making commercials or a movie on a green screen, they had something to watch. Later we replaced this version with a high-quality final one, leaving only the pre-final version in some moments, as it just turned out to be out of focus and was not visible. ”
Franklin also notes that quite a few digital effects, removal of cables, and a huge amount of rotoscope (roto, rotopaint) were required to complete these scenes. In the implementation of effects, made entirely with the help of computer graphics, there were also certain difficulties. For example, in the part where the tesseract closes and begins to collapse. “We took the tesseract computer geometry, and let it through the rotation of the hypercube. The guys worked on how to realize the transformation of the rotation of the hypercube and apply it directly to the geometry of the tesseract that we created. For me it was a special moment. When I saw the results, I realized that it was perfect, exactly what I wanted. ”
Another difficult part, according to Franklin, was when Cooper interacts with dust and draws binary code on the floor during a storm. “We had to work with Matthew’s movements in the tesseract volume and make them interact with something that really caused these forms to appear on the floor in the room in front of him.”
Thank! I hope you were interested, and we will meet with you next time on the story of what Christopher Nolan tried to avoid so much.
Interstellar director Christopher Nolan explains to Matthew McConaughey the
Employees of special effects and computer graphics often face the need to create a visualization of what no one has ever seen. To this is added the requirement of the modern film industry, so that it all looks real, even though no one really knows what it might look like. In Christopher Nolan's film Interstellar, special effects supervisor Paul Franklin and the Double Negative team were supposed to create a visualization of things not from our dimension, while being as close as possible not only to quantum physics and relativistic mechanics, but also to our common understanding quantum gravity.
')
It was fortunate that among the main team of Double Negative was Oliver James, the main researcher with the Oxford education in the field of optics and atomic physics, as well as a deep understanding of Einstein's relativistic laws. As well as Franklin, he worked with the main producer and scientific consultant Kip Thorne. Thorne had to calculate complex mathematical equations and send them to James for translation into high-quality renders. The requirements for the film set for James the task not only to visualize calculations explaining the arc trajectories of light, but also to visualize cross sections of rays of light that change their size and shape during the journey through the black hole.
The James Code was only part of the overall solution. Hand in hand, he worked with the artistic team leader, computer graphics effects supervisor Yevgeny von Tanzelman, who added an accretion disk, and also created a galaxy and a nebula, distorted as soon as the light from them passes by the black hole. No less difficult was the task of demonstrating how someone enters a four-dimensional tesseract, combined with the three-dimensional space of a little girl's room — all in the form so that the viewer can understand what is happening on the screen.
In this article we will tell you about some key frames created by Double Negative, as well as about the scientific research that precedes them. Please note that spoilers are possible in the sequel.
Making a black hole
Perhaps one of the most significant merits in achieving the Nolanoff task of maximum realism is the portrayal of the black hole Gargantua. After receiving input from Thorn, the filmmakers made every effort to show the behavior of light in a black hole and a wormhole. For Double Negative, this task necessitated writing a completely new physical renderer.
View from the camera on a circular equatorial orbit of a black hole rotating at 0.999 of its maximum possible rotation speed. The camera is located at a distance of r = 6.03 GM / c ^ 2, where M is the black hole mass, G and c is the Newton constant and the speed of light, respectively. The black hole event horizon is at a distance of r = 1.045 GM / c ^ 2.
“Kip explained to me the relativistic distortions of the space around the black hole,” says Paul Franklin, “Gravity, twisted in time, deflects light from itself, creating a phenomenon called the Einstein lens, the gravitational lens around the black hole. And at that moment I was thinking how can we create such an image and are there any examples with a similar graphic effect that we could rely on. ”
“I looked at the most basic simulations created by the scientific community,” adds Franklin, “and I thought, ok, the movement of this thing is so complicated that we have to do our own version from scratch. Then Kip began to work very closely with Oliver James, our main research assistant, and his department. They used Kip's calculations to get all the light paths and ray tracing paths around the black hole. In addition, Oliver worked on pressing issues of how to implement all this with the help of our new renderer DnGR (Double Negative General Relativity). ”
For the new renderer, it was necessary to establish all the most important parameters for their digital black hole. “We could set the speed, mass and diameter,” explains Franklin. “In essence, these are the only three parameters that you can change in a black hole - that is, this is all that we have to measure it. We spent a tremendous amount of time working on how to calculate the paths of light beams around a black hole. All the work was quite intensive - for six months the guys wrote software. We had an early version of the black hole, just in time for the end of the film’s pre-production period. ”
The resting black hole accelerates to a rotational speed of 0.999 from possible; then the camera approaches a black hole from a radius of 10 GM / c ^ 2 to a radius of r = 2.60 GM / c ^ 2, continuing to move along a circular equatorial orbit. The huge shadow of a black hole is distorted into a rectangular shape due to the conversion of the camera's camera image to a flat display.
These early images were used in the form of huge paintings for the background outside the ship - so the actors had something to look at while shooting. That is, not a single green screen was used; later, the staff of Double Negative replaced the used early images with the final ones, correcting some star clusters. “Most of the shots are from the back of the astronauts you see in the rolling version of the film,” notes Franklin, “this is a real shot. We had a lot of shots that were not included in the general list of shots with visual effects, although a great job was done to create them. ”
These “direct” camera shots were made possible through the collaboration of Double Negative and Doctor of Physics Hoyte Van Hoytem. Spotlights were used to highlight the resulting background images, with an aggregate luminous flux of 40,000 lumens per scene. ”
The same simulation is just bigger. The structure of the light of the starry sky transmitted through a gravitational lens is clearly visible here. At the edge of a black hole, the horizon moves towards us at a speed of close to the speed of light.
“We needed to move and reconfigure spotlights based on the scene tasks,” Franklin continues. “In general, it would take a whole week to set things up correctly, but in some cases everything should have been ready in 15 minutes. The guys worked so hard, because the spotlights are huge, cumbersome engines - each weighed about 270 kilograms. We had two specially made cells, mounted on a large electric winch with the ability to move it along and across the pavilion, respectively, we could use it to place the spotlights. On the radio, I explained to the guys with the spotlights how to calibrate them, simultaneously talking with the person driving the forklifts, running above the tightly crowded platform. ”
Making waves
In the film, Cooper (Matthew McConaughey), Amelia (Ann Hathaway), Doyle (Weight Bentley) and AI Robot CASE visit a completely water-covered planet, the waves on which, due to their very close proximity to Gargantua, reach extraordinary sizes. Spectators have already seen thirty-meter waves in other films, but according to history, this was not enough - according to the script, the waves should have been more than a kilometer in height. To give the viewer a feel for this height, Double Negative had to rethink the standard approach to creating water. “When you take objects of this scale,” explains Franklin, “all the characteristics you associate with waves, such as breakers and curls on top, simply disappear as they become invisible relative to such a mass of water - that is, the wave becomes more like on a moving mountain out of the water. That is why we spent a lot of time working on pre-visualization and wondering how we can use such scale waves and a small Ranger spaceship that they wash off. The highlight of the scene is when the wave hits the Ranger and raises it high above the surface. And you see how the ship moves upward on a wave, it gets smaller and suddenly gets lost on it altogether. It was a key moment for feeling the scale of what is happening. ”
Anne Hathaway as Amelia on the Water Planet
The artists of Double Negative controlled the waves by animating the deformers, effectively changing them into each keyframe. “It gave us a basic waveform,” says Franklin, “but to perceive this picture as real, we need to add foam on the surface, interactive splashes, water swirls and bursts. To do this, we used our internal development, called Squirt Ocean. Well and, of course, after there was a lot of extra work in Houdini. ”
Frames were created in high resolution IMAX. This requirement somewhat limited the amount of time allowed for all possible Double Negative iterations. “I watched the wave animation part, said“ well, let's add everything else, ”Franklin laughs,“ and then I had to wait about a month and a half for all this to come back to me again — such a long process was conditioned by the resolution of IMAX . As you understand, we could not waste time, because usually the whole process was divided into many iterations, and at that time we had a maximum of three. ”
Robot CASE rescuing Amelia from the tidal wave, and his twin TARS, in fact, were 80 kilogram metal dolls, controlled by Icelandic artist Bill Irwin. Christopher Nolan wanted the film to have as many real elements as possible, and instead of just drawing it as many as possible, Double Negative needed to remove the artist behind the robot.
When CASE reconfigures itself to pass through the water, and then rolls toward Amelia, grabs her and takes her away, two solutions are combined in the frame: practical and digital. “In this frame,” says Franklin, “there was a built small water drilling rig mounted on an ATV. That is, we could ride “through” the water and get wonderful interactive splashes and splashes. Also, on an ATV, we had a special lift with the hands of a robot, on which we could carry the twin, Anne Hathaway. That is, the whole structure went and “cut” the water, and we just had to remove it from the image and replace it with the digital version of the robot. ”
Double Negative tried to limit the number of moments with digital robots that do unusual things. Those moments were running through the water, landing a robot on a ship, running through a glacier and some moments with no gravity. “What we have noticed long ago is that you can make digital moments work only if you combine them with real ones,” says Franklin, “For example, in frames where a robot climbs into a ship, at the very end of the segment we are already seeing the real version of the robot, not the digital one. That is, the scene ends with frames with reality, and this helps to feel the scene as truly real. ”
Inside the tesseract
In the film, someone “they” turns out to be “us”, only advanced enough to help Cooper connect with his daughter, who has been on Earth years before. Since in the universe of quantum and relativistic laws, time travel is impossible, history solves this issue in such a way that Cooper leaves our three-dimensional space and falls into a higher order hyperspace. If our universe is displayed as a 2D disk or membrane, then the hyperspace will be the box surrounding this membrane in three dimensions. The way to make sense of this is that each dimension requires one dimension less to display it. Thus, the three-dimensional space is drawn as a 2D disk, and the three-dimensional environment around this disk (as physicists call it a brane) is one dimension above the membrane.
Image drawn by Kip Thorne explaining what the bran and membrane are
In the film, Michael Kane's character, Professor Brand, is trying to unravel the gravitational anomalies. An attempt to solve the problem in 4th and 5th dimensions is clearly visible on the boards in the film. The film says that if the Brand can understand these anomalies, they can be used to change the gravity on Earth and raise the huge humanity-saving structure into space.
While the transition from three-dimensional space to four-dimensional does not solve the problem of time travel, in the film this allows Cooper to send gravitational waves back in time. He can see any time, but can only cause ripples in these time intervals — gravitational ripples, which Cooper’s daughter, Murphy, is trying to understand.
The work of the Double Negative team was to visually demonstrate the four-dimensional tesseract, which the future "we" provide to Cooper, so that he could cause gravitational waves. This would be easy to do if done symbolically or as a dream, but the Double Negative team decided to visualize the four-dimensional tesseract in a more expressive way, creating a concept that would, of course, be a hypothesis, but it could even be used for teaching . It was at that moment that Thorn reappeared.
Kip Thorn's formulas explaining gravity in four and five dimensions. Please note that here “our” brane is clamped as a sandwich between two alternative realities or other branes.
To understand the Double Negative solution, it is worthwhile to understand the nature of higher order measurements. If the object is at rest, for example, a ball — for two-dimensional space, it is a circle; for one-dimensional - line. If you look at this circle in three-dimensional space, then we will see a ball (sphere). But what will happen to him if you go to the four-dimensional space? One of the theories, which was the basis for our daily thinking, was to present the fourth space as time. Then it turns out that the same ball, but not resting, but bouncing, and in an infinitely small period of time is seen as the same ball. But throughout the journey, he creates a pipe-shaped figure with hemispherical edges. That is, in four-dimensional space, the ball is a pipe, and the sphere is a three-dimensional projection of this four-dimensional figure.
If a cube in three-dimensional space changes its shape over time, for example, grow, then it will be depicted in four-dimensional space as a box, which eventually grows into a large box, displaying all the states of a three-dimensional box throughout its existence. She can animate and reshape as shown in this video:
According to the logic of the film, if you fall into this tesseract, you can see the three-dimensional space at any time during its existence, for example, in the form of lines that go into the past and the future. Moreover, if we take into account the assumption that there are an infinite number of parallel realities, you will see all the lines of all possible parallel realities that go into an infinite number of directions. This is precisely the conceptual solution of the four-dimensional space with which the studio worked. The "threads" of time that Cooper sees look like strings, and touching them, he can cause gravitational vibrations, thus communicating with his daughter. This is really a brilliant piece of artistic scientific visualization!
But how to shoot it?
The installation of Nolan, that when creating videos, the actors should interact with the environment and extended to tesseract. After hitting a black hole, Cooper finds himself in a four-dimensional space in which he can see any objects and their “thread” of time. “Chris said that despite the fact that this is a very abstract concept, he would very much like to build something that we could shoot in reality,” says Franklin, “He wanted to see Matthew physically interact with the“ threads ” time, in real space, and not dangling in front of the green screen. "
This prompted Franklin to ponder how to embody the tesseract visualization. “I spent a lot of time puzzling about how to implement all this in real space,” he says, “How to show all these temporary“ threads ”of all objects in one room, and to make this clear in a physical sense. After all, the danger was that the space would be so cluttered with “threads” that you would have to figure out how to select the right moments among them. Plus, it was extremely important that Cooper not only saw the “threads” of time, but also saw their backlash on the interaction, and at the same time could also interact with the objects in his daughter’s room. ”
The final view of the “open lattice structure” was inspired by the very concept of tesseract. “Tesseract - a three-dimensional projection of the four-dimensional hypercube. It has a beautiful lattice-like structure, so we roughly understood what we were going to do. For a long time, I looked at the sweep from long-shot photographs (slit-scan photography) and how this technique allows you to display the same point in space at all times. The photo itself transforms time into one of the dimensions of the final image. The combination of this imaging technique and the tesseract lattice structure allowed us to create these three-dimensional “threads” of time, as if arising from the object. Rooms are photographs, moments embedded in the trellised structure of the “threads” of time, among which Cooper can search for the right ones by moving them back and forth. ”
“We’ve finished building one section of this physical model with four repeating sections around,” says Franklin. “Then we reproduced these sections endlessly on the computer so that no matter where you look, they go to eternity. Also during the shooting we used a lot of real projections. We enclosed the active "threads" of time under the real section, using projectors. This gave us a feeling of trembling and febrile energy - all information flowed along these “threads” from section to section and back. But, of course, each image of the final version of the film, among other things, contains an insane amount of digital effects embedded in the scene. "
But some moments forced Double Negative to completely switch to digital visual effects - such a moment was, for example, the movement of Cooper through the tesseract tunnels. “We didn’t have enough tesseract sections to capture this movement, so we shot Matthew among the projection screens, on which a pre-final version of the visualization of this scene was displayed - so he had something to interact with,” says Franklin, “ The actors loved it all so much, because in contrast to making commercials or a movie on a green screen, they had something to watch. Later we replaced this version with a high-quality final one, leaving only the pre-final version in some moments, as it just turned out to be out of focus and was not visible. ”
Franklin also notes that quite a few digital effects, removal of cables, and a huge amount of rotoscope (roto, rotopaint) were required to complete these scenes. In the implementation of effects, made entirely with the help of computer graphics, there were also certain difficulties. For example, in the part where the tesseract closes and begins to collapse. “We took the tesseract computer geometry, and let it through the rotation of the hypercube. The guys worked on how to realize the transformation of the rotation of the hypercube and apply it directly to the geometry of the tesseract that we created. For me it was a special moment. When I saw the results, I realized that it was perfect, exactly what I wanted. ”
Another difficult part, according to Franklin, was when Cooper interacts with dust and draws binary code on the floor during a storm. “We had to work with Matthew’s movements in the tesseract volume and make them interact with something that really caused these forms to appear on the floor in the room in front of him.”
Thank! I hope you were interested, and we will meet with you next time on the story of what Christopher Nolan tried to avoid so much.
Source: https://habr.com/ru/post/391845/
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