Raytracing

Light rays in this module can be parameterized in terms of either the emission inclination (${\theta }_s$), or the Mino time ($\mathrm{\Delta }\tau$). Parameterization in terms of emission inclination allows for images to be divided into sub images which are ray traced individually.

Raytracing conical surfaces

Surfaces of constant ${\theta }_s$ define spin axis centered cones whose apex lie at the origin of the Boyer-Lindquist coordinate system.

n=0 and n=1 images of emission coordinates originating from conical surfaces.

Raytracing with rays parameterized by Mino time

Mino time, $\tau$, is a parameter monotonic in affine parameter, ${\tau }^{\prime }$, defined by

$$d\tau =\mathrm{\Sigma }(r,\theta )d{\tau }^{\prime },$$

where

$$\mathrm{\Sigma }(r,\theta )=r^2+a^2{\cos }^2\theta .$$

Coordinate evolution with Mino time.

Cameras

Cameras cache pre-computed information that is constant for a given camera location. There are currently two types of cameras which can be used for either 'slow light' or 'fast light' raytracing.

• IntensityCamera : Pre-computes geodesic information necessary to solve the 'fast light' raytracing problem.

• SlowLightIntensityCamera : Pre-computes geodesic information necessary to solve the 'slow light' raytracing problem.

The GPU arrays can be passed to the cameras on construction to raytrace enforce raytracing on the GPU. A sketch of how to do this with a CUDA array is:

using CUDA
 
store = CUDA.fill(0.0, sze, sze)
camera = Krang.SlowLightIntensityCamera(metric, θo, -ρmax, ρmax, -ρmax, ρmax, sze, A=CuArray)
Krang.render!(store, camera, scene)