Interstellar: inside a black hole and a tesseract
My name is Andrey Kolokoltsev. By type of activity, I have long been interested in stories about how eminent directors, producers, and studios cope with the creation of certain visual pictures. For my first publication, I chose a movie, which became for me an audiovisual revelation and a real emotional attraction (when watching a movie on the IMAX screen, at home, 2/3 of my impressions are lost on the TV). You do not jump from surprise, as the title has already read everything - this is Christopher Nolan's film "Interstellar". Despite the fact that interest in him has faded away for a long time, 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 talks about how the visualization of “Gargantua” and other scenes from the film was created - I think it will be interesting to readers even after 1.5 years.
Interstellar director Christopher Nolan explains to Matthew McConaughey thebasics of quantum physics the essence of the scene
Workers in the special effects and computer graphics department are often faced with the need to create a visualization of something that no one has ever seen. To this is added the requirement of the modern film industry to make it all look real, even despite the fact that, in fact, no one really knows what it might look like. In Christopher Nolan’s Interstellar film, special effects supervisor Paul Franklin and the Double Negative team were supposed to create visualizations 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 Oliver James, a senior fellow with an Oxford degree in optics and atomic physics, and a deep understanding of Einstein's relativistic laws were among the Double Negative core team. Like Franklin, he worked with Kip Thorne, chief producer and research consultant. Thorne had to calculate complex mathematical equations and send them to James for translation into high-quality renders. The requirements for the film set the task for James not only to visualize the calculations explaining the arc trajectories of light, but also to visualize the cross sections of light rays changing their size and shape during the journey through a black hole.
James's code was just part of the overall solution. Hand in hand, he worked with the head of the art team, computer graphics effects supervisor Eugene von Tanzelman, who added an accretion disk and also created a galaxy and nebula, distorted as soon as the light from them passes a 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 - and all this in such a way that the viewer understands what is happening on the screen.
In this article, we will talk about some key personnel created by Double Negative, as well as about the research that precedes them. Please note that spoilers are possible in future material.
Perhaps one of the most significant achievements in achieving the Nolanovian goal of maximum realism is the image of the Gargantua black hole. Having received input from Thorne, the filmmakers did their best to show the behavior of light in a black hole and wormhole. For Double Negative, this task necessitated the writing of a completely new physical renderer.
View from the camera in a circular equatorial orbit of a black hole rotating with 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 mass of the black hole, G and c are Newton's constant and the speed of light, respectively. The black hole event horizon is located at a distance r = 1.045 GM / c ^ 2.
“Kip explained to me the relativistic curvatures 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 make our own version from scratch. Kip then began to work very closely with Oliver James, our principal research fellow, 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, how to bring it all to life with our new DnGR renderer (Double Negative General Relativity). ”
For the new renderer, it was required to set all the most important parameters for their digital black hole. “We could set the speed, mass and diameter,” Franklin explains. “In essence, these are the only three parameters that you can change in a black hole - that is, that’s all we have to measure it. We spent a huge amount of time working on how to calculate the paths of light beams around a black hole. All the work went quite intensively - for six months the guys wrote software. We had an early version of the black hole, just in time for the film’s preproduction period to end. ”
A resting black hole accelerates to a rotation speed of 0.999 from the 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 in a circular equatorial orbit. The huge shadow from the black hole is distorted into a rectangular shape due to the conversion of the verification image from the camera 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 watch during the shoot. That is, not a single green screen was used, just later Double Negative employees replaced the used early images with the final ones, correcting some star clusters. “Most of the shots are due to the astronaut’s shoulder that you see in the rental version of the film,” Franklin notes, “this is a real shot. "We had a lot of frames that were not included in the general list of frames with visual effects, although a tremendous work was done to create them.”
These “direct” camera shots were made possible thanks to the collaboration of Double Negative and Hoyte Van Hoytem, MD. To illuminate the obtained background images, searchlights were used, with a total luminous flux of 40,000 lumens per scene. ”
The same simulation is only larger. Here, the structure of the light of the starry sky passed through a gravitational lens is clearly visible. At the edge of a black hole, the horizon moves at us at a speed close to the speed of light.
“We needed to move and reconfigure the floodlights based on the tasks of the scene,” Franklin continues, “In general, it could take a whole week to set everything up correctly, but in some cases everything had to be ready in 15 minutes. The guys worked so hard, because the spotlights are huge clumsy colossus - each weighed about 270 kilograms. We had two specially made cages mounted on a large electric winch with the ability to move it along and across the pavilion, respectively, we could use it for arranging spotlights. Using the walkie-talkie, I explained to the guys with the spotlights how to calibrate them, simultaneously talking to the person managing the forklifts, rushing over the site densely packed with people. ”
In the film, Cooper (Matthew McConaughey), Amelia (Anne Hathaway), Doyle (Wes Bentley) and the AI robot CASE visit a planet completely covered with water, the waves on which due to their very close proximity to Gargantua reach extraordinary sizes. Viewers have already seen thirty-meter waves in other films, but according to history, this was not enough - according to the scenario, the waves should have been more than a kilometer in height. To give the viewer a sense of this height, Double Negative had to rethink the standard approach to creating water. “When you take objects of this magnitude,” Franklin explains, “all the characteristics that you associate with the waves, such as the breakers and curls at the top, simply disappear, as they become invisible relative to such a mass of water - that is, the wave becomes more similar on a moving mountain out of the water. That is why we spent a lot of time working on pre-visualization and pondering how we can use such a scale of waves and the small Ranger spaceship washed away by them. The most important moment of the scene is when the wave catches the Ranger and raises it high above the surface. And you see how the ship moves along the wave upward, becomes smaller and suddenly completely gets lost on it. It was a key moment to feel the scale of what was happening. ”
Anne Hathaway as Amelia on the water planet
Double Negative artists controlled the waves through an animation of the deformers, effectively changing them into each keyframe. “It gave us the basic waveform,” Franklin says, “but to make this picture look real, we need to add surface foam, interactive splashes, water swirls and splashes. To do this, we used our internal development called Squirt Ocean. And of course, after that there was a lot of extra work at Houdini. ”
Frames were created in high resolution IMAX. This requirement somewhat limited the amount of time allotted for all possible Double Negative iterations. “I watched the part with the wave animation, said“ excellent, let's add everything else, ”Franklin laughs,“ and then I had to wait about a month and a half for all of this to return to me again - such a lengthy process was due specifically to IMAX resolution . As you know, we could not waste time in vain, because usually the whole process was divided into many iterations, and at that time we had a maximum of three. ”
The CASE robot saving Amelia from the tidal wave, and its TARS counterpart, were actually 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, like so many, just draw it, Double Negative needed to remove the artist behind the robot.
When KEYS reconfigures itself to pass through the water, and then rolls to Amelia, grabs it and takes it away, two decisions are combined in the frame: practical and digital. “In this shot,” Franklin says, “there was a small water rig that was built, mounted on a quad bike. That is, we could ride “through” the water and get wonderful interactive splashes and splashes. Also on the ATV we had a special lift with robot arms on which we could transport Anne Hathaway's double. That is, this whole construction went and “cut” the water, and we only had to remove it from the image and replace it with a digital version of the robot. ”
Double Negative tried to limit the number of moments with digital robots doing unusual things. Such moments were running through the water, landing the robot in the ship, running along the glacier and some moments with no gravity. “What we noticed a long time ago is that you can make digital moments work only if you combine them with real ones,” says Franklin, “for example, in the frames where the robot gets into the ship, at the very end of the segment we already see the real version of the robot, not digital. That is, the scene ends with frames with reality, and this helps to feel the scene as really real. ”
In the film, someone “they” turn out to be “us,” only advanced enough to help Cooper get in touch with his daughter, who was on Earth years earlier. Since time travels are not possible in the universe of quantum and relativistic laws, history solves this issue so that Cooper leaves our three-dimensional space and enters a higher-order hyperspace. If our universe is displayed as a 2D disk or membrane, then hyperspace will be the box surrounding this membrane in three dimensions. The way to understand this is that each dimension requires 1 dimension less to display. Thus, the three-dimensional space is drawn as a 2D disk, and the three-dimensional environment around this disk (physicists call it brane) is one dimension higher than the membrane.
Image by Kip Thorne explaining what a brane and a membrane are
In the film, the character of Michael Kane, Professor Brand, is trying to unravel the gravitational anomalies. On the boards in the film, an attempt to solve the problem in 4 and 5 dimensions is clearly visible. The film says that if Brand can understand these anomalies, they can be used to change the gravity on Earth and lift the huge structure saving the humanity into space.
While the transition from three-dimensional to four-dimensional space does not solve the problem of time travel, in the film this allows Cooper to send gravitational waves back in time. He can see at any time, but can only cause ripples in these lengths of time - the gravitational ripple that Cooper's daughter, Murphy, is trying to understand.
The work of the Double Negative team was to visually demonstrate the four-dimensional tesseract that the future "we" provide to Cooper so that he can cause gravitational waves. This would be easily feasible if done in a symbolic sense or in the form of a dream, but the Double Negative team decided to visualize the four-dimensional tesseract in a more expressive form, creating a concept that would, of course, be a hypothesis, but it could even be used for training . It was at that moment that Thorne reappeared.
Kip Thorne formulas explaining gravity in four and five dimensions. Please note that here “our” brane is sandwiched between two alternative realities or other branes.
To understand the Double Negative solution, it’s worth understanding the nature of higher order dimensions. If an object is resting, say, a ball - for two-dimensional space - this is a circle; for one-dimensional - a 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 we go to four-dimensional space? One of the theories that 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 jumping, and in an infinitely small period of time is visible as the same ball. But throughout the journey he creates a figure in the form of a tube 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, grows, 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 entire existence. It can be animated and change shape as shown in this video:
According to the logic of the film, if you get into this tesseract, you can see three-dimensional space at any moment of its existence, for example, in the form of lines that go back to the past and future. Moreover, if you take into account the assumption that there is 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 to 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 truly a brilliant piece of artistic scientific visualization!
Nolan’s installation that when creating videos, actors should interact with the environment also extended to the tesseract. After falling into 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 although this is a very abstract concept, he would really like to build something that we could shoot in reality,” Franklin says. “He wanted to see Matthew physically interacting with the“ threads ” time in real space, not dangling in front of a green screen. ”
This prompted Franklin to consider how to implement the visualization of the tesseract. “I spent a lot of time racking my brains on how to realize all this in real space,” he says. “How to show all these temporary“ threads ”of all objects in one room, and to make it clear in the physical sense. After all, the danger was that the space would turn out so cluttered with "threads" that you would have to figure out how to highlight the necessary moments among them. Plus, it was extremely important that Cooper not only saw the “threads” of time, but also saw their reaction to interaction, and at the same time he could interact with objects in his daughter’s room. ”
The final appearance of the “open lattice structure” was inspired precisely by the concept of the tesseract. “Tesseract is a three-dimensional projection of a four-dimensional hypercube. It has a beautiful lattice-like structure, so we roughly understood what we would do. For a long time I considered sweeps from slit-scan photographs and how this technique allows you to display the same point in space at all times. Photography itself turns time into one dimension of the final image. The combination of this shooting technique and the lattice structure of the tesseract allowed us to create these three-dimensional "threads" of time, as if flowing from the object. Rooms are photographs, moments built into the lattice structure of the “threads” of time, among which Cooper can search for the right ones by moving them back and forth. ”
“We finished building one section of this physical model with four repeating sections around,” Franklin says, “Then on the computer we multiplied these sections to infinity in such a way that wherever you look, they go into eternity. Also, during the shooting, we used a lot of real projections. We put active “threads” of time under real sections, using projectors. This gave us a feeling of trembling and febrile energy - all the information flowed along these “threads” from section to section and vice versa. But, of course, each image of the final version of the film, among other things, contains an insane amount of digital effects built into the scene. ”
But some points forced Double Negative to switch completely to digital visual effects - such a moment, for example, was the movement of Cooper through the tesseract tunnels. “We didn’t have enough tesseract sections to shoot this movement, so we shot Matthew among the projection screens on which a pre-clean version of the visualization of this scene was displayed around him - so he had something to interact with,” says Franklin, “ The actors liked all this madly, because in contrast to the production of commercials or films on a green screen, they had something to look at. Later we replaced this version with a high-quality final one, only in some moments leaving the final one, as it simply turned out to be out of focus and was not visible. ”
Franklin also notes that a lot of digital effects, removal of crosses and a huge amount of rotoscooping (roto, rotopaint) were required to complete these scenes. In the implementation of effects made entirely using computer graphics, there were also certain difficulties. For example, in the part where the tesseract closes and begins to collapse. “We took the computer geometry of the tesseract, and passed it through the rotation of the hypercube. The guys worked on how to implement the transformation of the rotation of the hypercube and apply it directly to the geometry of the tesseract that we created. It was a special moment for me. When I saw the results, I realized that it was perfect, exactly what I wanted. ”
Another difficult part, according to Franklin, was the moment when Cooper interacts with the dust and draws binary code on the floor during a storm. “We had to work with Matthew’s movements on the site in a tesseract volume and make them interact with something that really made these forms appear on the floor in the room in front of him.”
Thanks! I hope you were interested, and we will meet with you next time on the story of what Christopher Nolan tried to avoid - keying.
Interstellar director Christopher Nolan explains to Matthew McConaughey the
Workers in the special effects and computer graphics department are often faced with the need to create a visualization of something that no one has ever seen. To this is added the requirement of the modern film industry to make it all look real, even despite the fact that, in fact, no one really knows what it might look like. In Christopher Nolan’s Interstellar film, special effects supervisor Paul Franklin and the Double Negative team were supposed to create visualizations 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 Oliver James, a senior fellow with an Oxford degree in optics and atomic physics, and a deep understanding of Einstein's relativistic laws were among the Double Negative core team. Like Franklin, he worked with Kip Thorne, chief producer and research consultant. Thorne had to calculate complex mathematical equations and send them to James for translation into high-quality renders. The requirements for the film set the task for James not only to visualize the calculations explaining the arc trajectories of light, but also to visualize the cross sections of light rays changing their size and shape during the journey through a black hole.
James's code was just part of the overall solution. Hand in hand, he worked with the head of the art team, computer graphics effects supervisor Eugene von Tanzelman, who added an accretion disk and also created a galaxy and nebula, distorted as soon as the light from them passes a 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 - and all this in such a way that the viewer understands what is happening on the screen.
In this article, we will talk about some key personnel created by Double Negative, as well as about the research that precedes them. Please note that spoilers are possible in future material.
Black hole making
Perhaps one of the most significant achievements in achieving the Nolanovian goal of maximum realism is the image of the Gargantua black hole. Having received input from Thorne, the filmmakers did their best to show the behavior of light in a black hole and wormhole. For Double Negative, this task necessitated the writing of a completely new physical renderer.
View from the camera in a circular equatorial orbit of a black hole rotating with 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 mass of the black hole, G and c are Newton's constant and the speed of light, respectively. The black hole event horizon is located at a distance r = 1.045 GM / c ^ 2.
“Kip explained to me the relativistic curvatures 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 make our own version from scratch. Kip then began to work very closely with Oliver James, our principal research fellow, 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, how to bring it all to life with our new DnGR renderer (Double Negative General Relativity). ”
For the new renderer, it was required to set all the most important parameters for their digital black hole. “We could set the speed, mass and diameter,” Franklin explains. “In essence, these are the only three parameters that you can change in a black hole - that is, that’s all we have to measure it. We spent a huge amount of time working on how to calculate the paths of light beams around a black hole. All the work went quite intensively - for six months the guys wrote software. We had an early version of the black hole, just in time for the film’s preproduction period to end. ”
A resting black hole accelerates to a rotation speed of 0.999 from the 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 in a circular equatorial orbit. The huge shadow from the black hole is distorted into a rectangular shape due to the conversion of the verification image from the camera 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 watch during the shoot. That is, not a single green screen was used, just later Double Negative employees replaced the used early images with the final ones, correcting some star clusters. “Most of the shots are due to the astronaut’s shoulder that you see in the rental version of the film,” Franklin notes, “this is a real shot. "We had a lot of frames that were not included in the general list of frames with visual effects, although a tremendous work was done to create them.”
These “direct” camera shots were made possible thanks to the collaboration of Double Negative and Hoyte Van Hoytem, MD. To illuminate the obtained background images, searchlights were used, with a total luminous flux of 40,000 lumens per scene. ”
The same simulation is only larger. Here, the structure of the light of the starry sky passed through a gravitational lens is clearly visible. At the edge of a black hole, the horizon moves at us at a speed close to the speed of light.
“We needed to move and reconfigure the floodlights based on the tasks of the scene,” Franklin continues, “In general, it could take a whole week to set everything up correctly, but in some cases everything had to be ready in 15 minutes. The guys worked so hard, because the spotlights are huge clumsy colossus - each weighed about 270 kilograms. We had two specially made cages mounted on a large electric winch with the ability to move it along and across the pavilion, respectively, we could use it for arranging spotlights. Using the walkie-talkie, I explained to the guys with the spotlights how to calibrate them, simultaneously talking to the person managing the forklifts, rushing over the site densely packed with people. ”
Making waves
In the film, Cooper (Matthew McConaughey), Amelia (Anne Hathaway), Doyle (Wes Bentley) and the AI robot CASE visit a planet completely covered with water, the waves on which due to their very close proximity to Gargantua reach extraordinary sizes. Viewers have already seen thirty-meter waves in other films, but according to history, this was not enough - according to the scenario, the waves should have been more than a kilometer in height. To give the viewer a sense of this height, Double Negative had to rethink the standard approach to creating water. “When you take objects of this magnitude,” Franklin explains, “all the characteristics that you associate with the waves, such as the breakers and curls at the top, simply disappear, as they become invisible relative to such a mass of water - that is, the wave becomes more similar on a moving mountain out of the water. That is why we spent a lot of time working on pre-visualization and pondering how we can use such a scale of waves and the small Ranger spaceship washed away by them. The most important moment of the scene is when the wave catches the Ranger and raises it high above the surface. And you see how the ship moves along the wave upward, becomes smaller and suddenly completely gets lost on it. It was a key moment to feel the scale of what was happening. ”
Anne Hathaway as Amelia on the water planet
Double Negative artists controlled the waves through an animation of the deformers, effectively changing them into each keyframe. “It gave us the basic waveform,” Franklin says, “but to make this picture look real, we need to add surface foam, interactive splashes, water swirls and splashes. To do this, we used our internal development called Squirt Ocean. And of course, after that there was a lot of extra work at Houdini. ”
Frames were created in high resolution IMAX. This requirement somewhat limited the amount of time allotted for all possible Double Negative iterations. “I watched the part with the wave animation, said“ excellent, let's add everything else, ”Franklin laughs,“ and then I had to wait about a month and a half for all of this to return to me again - such a lengthy process was due specifically to IMAX resolution . As you know, we could not waste time in vain, because usually the whole process was divided into many iterations, and at that time we had a maximum of three. ”
The CASE robot saving Amelia from the tidal wave, and its TARS counterpart, were actually 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, like so many, just draw it, Double Negative needed to remove the artist behind the robot.
When KEYS reconfigures itself to pass through the water, and then rolls to Amelia, grabs it and takes it away, two decisions are combined in the frame: practical and digital. “In this shot,” Franklin says, “there was a small water rig that was built, mounted on a quad bike. That is, we could ride “through” the water and get wonderful interactive splashes and splashes. Also on the ATV we had a special lift with robot arms on which we could transport Anne Hathaway's double. That is, this whole construction went and “cut” the water, and we only had to remove it from the image and replace it with a digital version of the robot. ”
Double Negative tried to limit the number of moments with digital robots doing unusual things. Such moments were running through the water, landing the robot in the ship, running along the glacier and some moments with no gravity. “What we noticed a long time ago is that you can make digital moments work only if you combine them with real ones,” says Franklin, “for example, in the frames where the robot gets into the ship, at the very end of the segment we already see the real version of the robot, not digital. That is, the scene ends with frames with reality, and this helps to feel the scene as really real. ”
Inside the tesseract
In the film, someone “they” turn out to be “us,” only advanced enough to help Cooper get in touch with his daughter, who was on Earth years earlier. Since time travels are not possible in the universe of quantum and relativistic laws, history solves this issue so that Cooper leaves our three-dimensional space and enters a higher-order hyperspace. If our universe is displayed as a 2D disk or membrane, then hyperspace will be the box surrounding this membrane in three dimensions. The way to understand this is that each dimension requires 1 dimension less to display. Thus, the three-dimensional space is drawn as a 2D disk, and the three-dimensional environment around this disk (physicists call it brane) is one dimension higher than the membrane.
Image by Kip Thorne explaining what a brane and a membrane are
In the film, the character of Michael Kane, Professor Brand, is trying to unravel the gravitational anomalies. On the boards in the film, an attempt to solve the problem in 4 and 5 dimensions is clearly visible. The film says that if Brand can understand these anomalies, they can be used to change the gravity on Earth and lift the huge structure saving the humanity into space.
While the transition from three-dimensional to four-dimensional space does not solve the problem of time travel, in the film this allows Cooper to send gravitational waves back in time. He can see at any time, but can only cause ripples in these lengths of time - the gravitational ripple that Cooper's daughter, Murphy, is trying to understand.
The work of the Double Negative team was to visually demonstrate the four-dimensional tesseract that the future "we" provide to Cooper so that he can cause gravitational waves. This would be easily feasible if done in a symbolic sense or in the form of a dream, but the Double Negative team decided to visualize the four-dimensional tesseract in a more expressive form, creating a concept that would, of course, be a hypothesis, but it could even be used for training . It was at that moment that Thorne reappeared.
Kip Thorne formulas explaining gravity in four and five dimensions. Please note that here “our” brane is sandwiched between two alternative realities or other branes.
To understand the Double Negative solution, it’s worth understanding the nature of higher order dimensions. If an object is resting, say, a ball - for two-dimensional space - this is a circle; for one-dimensional - a 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 we go to four-dimensional space? One of the theories that 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 jumping, and in an infinitely small period of time is visible as the same ball. But throughout the journey he creates a figure in the form of a tube 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, grows, 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 entire existence. It can be animated and change shape as shown in this video:
According to the logic of the film, if you get into this tesseract, you can see three-dimensional space at any moment of its existence, for example, in the form of lines that go back to the past and future. Moreover, if you take into account the assumption that there is 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 to 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 truly a brilliant piece of artistic scientific visualization!
But how to shoot it?
Nolan’s installation that when creating videos, actors should interact with the environment also extended to the tesseract. After falling into 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 although this is a very abstract concept, he would really like to build something that we could shoot in reality,” Franklin says. “He wanted to see Matthew physically interacting with the“ threads ” time in real space, not dangling in front of a green screen. ”
This prompted Franklin to consider how to implement the visualization of the tesseract. “I spent a lot of time racking my brains on how to realize all this in real space,” he says. “How to show all these temporary“ threads ”of all objects in one room, and to make it clear in the physical sense. After all, the danger was that the space would turn out so cluttered with "threads" that you would have to figure out how to highlight the necessary moments among them. Plus, it was extremely important that Cooper not only saw the “threads” of time, but also saw their reaction to interaction, and at the same time he could interact with objects in his daughter’s room. ”
The final appearance of the “open lattice structure” was inspired precisely by the concept of the tesseract. “Tesseract is a three-dimensional projection of a four-dimensional hypercube. It has a beautiful lattice-like structure, so we roughly understood what we would do. For a long time I considered sweeps from slit-scan photographs and how this technique allows you to display the same point in space at all times. Photography itself turns time into one dimension of the final image. The combination of this shooting technique and the lattice structure of the tesseract allowed us to create these three-dimensional "threads" of time, as if flowing from the object. Rooms are photographs, moments built into the lattice structure of the “threads” of time, among which Cooper can search for the right ones by moving them back and forth. ”
“We finished building one section of this physical model with four repeating sections around,” Franklin says, “Then on the computer we multiplied these sections to infinity in such a way that wherever you look, they go into eternity. Also, during the shooting, we used a lot of real projections. We put active “threads” of time under real sections, using projectors. This gave us a feeling of trembling and febrile energy - all the information flowed along these “threads” from section to section and vice versa. But, of course, each image of the final version of the film, among other things, contains an insane amount of digital effects built into the scene. ”
But some points forced Double Negative to switch completely to digital visual effects - such a moment, for example, was the movement of Cooper through the tesseract tunnels. “We didn’t have enough tesseract sections to shoot this movement, so we shot Matthew among the projection screens on which a pre-clean version of the visualization of this scene was displayed around him - so he had something to interact with,” says Franklin, “ The actors liked all this madly, because in contrast to the production of commercials or films on a green screen, they had something to look at. Later we replaced this version with a high-quality final one, only in some moments leaving the final one, as it simply turned out to be out of focus and was not visible. ”
Franklin also notes that a lot of digital effects, removal of crosses and a huge amount of rotoscooping (roto, rotopaint) were required to complete these scenes. In the implementation of effects made entirely using computer graphics, there were also certain difficulties. For example, in the part where the tesseract closes and begins to collapse. “We took the computer geometry of the tesseract, and passed it through the rotation of the hypercube. The guys worked on how to implement the transformation of the rotation of the hypercube and apply it directly to the geometry of the tesseract that we created. It was a special moment for me. When I saw the results, I realized that it was perfect, exactly what I wanted. ”
Another difficult part, according to Franklin, was the moment when Cooper interacts with the dust and draws binary code on the floor during a storm. “We had to work with Matthew’s movements on the site in a tesseract volume and make them interact with something that really made these forms appear on the floor in the room in front of him.”
Thanks! I hope you were interested, and we will meet with you next time on the story of what Christopher Nolan tried to avoid - keying.