Spherical World Building with Josh Pierce

Art and technology often exist in a state of creative tension. While developing Satori, his immersive experience for SUBMERGE Project at ARTECHOUSE DC, digital artist Josh Pierce encountered a fundamental spatial layout challenge: capturing the energy forms of a meditator and an ancient digital tree within a constrained volumetric canvas without breaking geometric alignment.

The Orthographic Projection Barrier

In early production stages, Pierce utilized a standard 4-wall orthographic projection approach. While commonplace in immersive installations, this setup introduced severe perspective distortion and visual occlusions.

When aligning a virtual camera directly above the water’s surface at a perpendicular 90-degree angle (a Nadir orientation), planar projection math fails to resolve vertical parallax. Because standard planar perspective projections rely on rectilinear view frustums, objects parallel to or co-planar with the focal axis compress along the viewing vector. Consequently, the key focal elements—the elevated energy geometries of the tree and meditator—collapsed along the z-axis and completely disappeared from the rendered view frustum.

The Equirectangular Solution

To maintain spatial continuity and visual clarity, Pierce transitioned from planar frustum capture to spherical Equirectangular mapping.

In an equirectangular projection (also known as a plate carrée projection), latitude and longitude coordinates map directly to standard Cartesian x and y pixels across a 2:1 aspect ratio grid (360∘×180∘). The mathematical transformation maps spherical polar coordinates (θ,ϕ) into 2D raster coordinates (u,v):

u=2πθ/π​, v=π2π​/ϕ​

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Try It Out! Equirectangular Mapping

In this free browser tool, manipulate the world map to understand the principles of distortion through equirectangular mapping.

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This mapping ensures a uniform sampling of the surrounding virtual environment from a single, omnidirectional nodal point. In its raw 2D state, equirectangular mapping exhibits severe polar distortion, stretching objects near the top (ϕ=90∘) and bottom (ϕ=−90∘) poles across the entire horizontal resolution—analogous to how a Mercator map distorts landmasses at high latitudes.

However, when mapped back onto a non-planar physical display system—such as ARTECHOUSE DC’s curved 270-degree Immersion Gallery canvas—custom spatial calibration shaders re-project the distorted pixels onto the curved geometry. By matching the mathematical inverse of the physical screen curvature, the distortion resolves completely. Correct directional vectors and foreshortening restore true perspective, creating a seamless, proportioned visual environment for the viewer.

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Feeling calmer just looking at these images on your phone? Imagine stepping inside them.

Experience Satori as it was meant to be seen: surrounding you across ARTECHOUSE DC’s 270-degree Immersion Gallery.