GPU-Accelerated Rendering of Unbounded Nonlinear Iterated Function System Fixed Points

Table 1

Compression and decompression functions, and corresponding GPU per-pixel performance. erfc, atan, and rsqrt are evaluated independently along each axis; stereo is a 2D vector function. erfc is not built into GLSL, though it exists in CUDA.

Name	Description	Plane-to-texture function	Texture-to-plane function	Timing
erfc	Gaussian error function	𝑇(𝑝)=erfc(𝑝)/2	𝑃(𝑡)=erfc^−1(2𝑡)	0.40 ns
atan	Trigonometric tangent	𝑇(𝑝)=arctan(𝑝)/𝜋+(1/2)	𝑃(𝑡)=tan(𝜋𝑡−(𝜋/2))	0.16 ns
rsqrt	Reciprocal square root	𝑇(𝑝)=𝑝/(2√1+𝑝^2)+(1/2)	𝑢=2𝑡−1; 𝑃(𝑡)=𝑢/√1−𝑢^2	0.08 ns
stereo	Polar stereographic	𝑇(𝑝)⃗=𝑝/⃗(2√1+𝑝⃗⋅𝑝)⃗+(1/2)	𝑢⃗=2𝑡⃗−1; 𝑃(𝑡)⃗=𝑢/⃗√1−𝑢⃗⋅𝑢⃗	0.08 ns