One photon sheet, three ways to evaluate it

Strategy 32 is not simply the rasterized photon hourglass. The methods differ first in how they construct the refracted family, then in how the camera evaluates it.

Strategy 20

Derive

An analytical sphere turns the swept refracted family into an axis-revolved hourglass. Camera rays solve crossings against that geometry and use its Jacobian.

Strategy 32

Reconstruct

Finite rays travel through triangle glass. Compatible neighboring histories become triangular sheets; camera rays intersect a sheet BVH and gather the crossings.

Fast preview

Project

Either family can be projected into a reduced-resolution image. Triangles are rasterized, filtered and enlarged instead of gathered independently by each camera ray.

Where the approximations enter

Method	What it gains	What remains approximate
Analytical 20	Exact continuous one-sphere sheet; sharp singular structure	Restricted geometry and path support; optional grazing guard can discard energy
Normal 32	Concavity, holes, varying mesh normals and chains of glass objects	Finite angular sampling, adaptive topology cuts and a grazing cutoff; more passes do not remove fixed tessellation error
Fast preview	Responsive viewfinder and fractional pixel coverage of narrow sheets	Screen resolution, interpolation, tangency clamp, blur, occlusion-edge leakage, and omitted camera-side specular sheet views

Why 32 handles harder geometry

It is the numerical light-side construction that matters. Strategy 20 knows the closed-form geometry of a sphere. Strategy 32 instead asks the scene where each refracted ray goes, so the same construction can follow a monkey, teapot, torus or several separate glass bodies. Its finite angular tessellation makes it approximate, but bias is not the source of its geometric reach.

20 derives the sheet. 32 reconstructs it numerically. Fast preview rasterizes either one.

The preview can look better sooner on thin folds and near singularities because fractional pixel coverage does not wait for a camera sample to land on a narrow feature, while its grazing floor and filter suppress extreme values. That is a useful visualization trade: it changes the limiting image. For measurements, use normal 32 and increase both pass count and angular resolution. For framing a caustic or inspecting a chain, enable Fast structure preview (biased).