Martínez already knew Sam Shepherd – the musician behind Floating Points – before the idea for the video came about.
After introducing Shephard to Barquin's work, the Spanish directors formed a team that also included Anna Diaz Ortuño and Nathan Grimes to produce visuals for the track Silhouettes.
"We wanted to do a video with a technical achievement, but with an abstract story and a really artistic touch," Martínez told Dezeen.
Combining Shepard's music, Martínez's design style and Barquin's inventions, the group decided to create the visuals using light painting. The technique uses long exposure photography to capture the path of a moving light source as a trail.
"I was playing around with my first light-painting machine prototype and I thought it was a great opportunity to take the technical idea further and do an entire video with it," Barquin said.
Their references included the work of abstract animator Oskar Fischinger, particularly from Disney's 1940 film Fantasia.
"Sam's music is really cinematic and soulful, we wanted to catch the feeling of this by doing it all photographic and colourful, as well as making the light to paint the melodies of the track," said Martínez.
The video starts with landscape imagery chosen to look like the surface of Mars, filmed at the Rio Tinto valley in southwestern Spain for its arid conditions and distinctive red colouring.
Moving light paths begin to appear as basic abstract shapes, which flicker and bounce around the scenery.
"It's a mysterious light from the sky, that arrives in a desert landscape and oscillates in order to find its accurate form and harmony," Martínez said.
As the video progresses, the light shapes become more complicated – based on oscilloscope compositions and mathematical formulae.
To create the effects, the team developed and built a three-axis computer numerically controlled machine from scratch.
"The machine is capable of reproducing, in light, any form designed in 3D animation software," explained Barquin. "It is controlled by a bespoke plugin, into which we introduce 3D animation files that can be translated by the machine into physical space."
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"The LED traces the path of the animation and reproduces the movement frame by frame," he continued. "The same software that controls the machine also controls the camera and external elements such as lights, motion-control systems and remote cameras."
Although some scenes were shot on location, others were captured at the Hamill Industries studio in Barcelona.
Towards the end of the video, the camera pans out to shows viewers what it looked like behind the scenes.
It reveals a miniature landscape populated with soil and plants, created on a table top – one of three artificial sets built to look like Rio Tinto for filming.
"At the end we wanted to show a peek of Pablo's studio with Nathan and Anna working as well, just to get people curious," said Martínez.
"In the video, story and the technique are indivisible so it was almost imperative to us, to do a small revelation at the end," added Diaz Ortuño.
The team spent a total of two and a half months shooting the video for Silhouettes, which is taken from Floating Points' forthcoming album Elaenia, due for release 6 November 2015.