# Ribbed Glass

Study 10 looks at *Tidal Oval* through a pane with 22 vertical ribs. Switch to Clear at the same angle and gap to isolate what the rib profile does to the rose stroke and blue rim. The original photograph supplies the painting texture inside the existing [Raking Room silhouette trace](../raking-room/room.js). [Original painting photo](../../assets/tidal-oval.jpg)

| Recorded view | Pane | Angle | Air gap |
| --- | --- | ---: | ---: |
| [Cover](./cover.png) | Fluted | +7° | 34 mm |
| [Clear control](./clear.png) | Flat | +7° | 34 mm |
| [Side step](./side-step.png) | Fluted | −22° | 48 mm |

The stills are 1080 × 660 exports of the same canvas renderer used by the controls.

## Optical model

The pane spans 264 × 356 mm. In horizontal cross-section each 12 mm rib is a cylindrical arc of radius 14 mm. The glass is 3 mm thick at the joins and 4.351 mm at the crowns. The flat control is 3 mm thick. The simulation uses an assumed glass index of 1.52 and air index of 1. These dimensions describe an idealized profile. [National Glass Association, Types of Decorative Glass](https://www.glass.org/sites/default/files/2022-01/FB73-22_Types_of_Decorative_Glass.pdf#page=3)

Depth `z` increases from eye to artwork. For lateral position `u` relative to the nearest rib crown, the front surface is `z = −3 + sqrt(14² − 6²) − sqrt(14² − u²)` and the rear is `z = 0`. Orthographic rays travel horizontally in the cross-section. The renderer finds the front intersection by bisection and applies Snell’s law, `n₁ sin θ₁ = n₂ sin θ₂`, against the local cylindrical normal. At the flat rear it applies the glass-to-air bend, then walks across the adjustable air gap to the painting plane. At a gap `g`, a ray leaving the rear at `xᵣ` and angle `θₑ` samples `xᵣ + g tan θₑ`. The front reflection and direct transmission weights use unpolarized Fresnel terms. [Pharr, Jakob and Humphreys, Specular Reflection and Transmission](https://www.pbr-book.org/4ed/Reflection_Models/Specular_Reflection_and_Transmission)

The study isolates horizontal refraction under parallel viewing rays. Surface roughness, dispersion, glass absorption, internal reflections, perspective and the pane’s finite side faces are outside the model. The reflected light source, plaster, mount and shadows are authored for the scene. The sharp joins give a stronger band transition than a pane with rounded seams. There is no measured glass profile or physical prototype.

## Checks

Run the numerical checks from the study directory with `node --test verify.mjs`. They cover straight-on and oblique flat-pane controls, rib periodicity and symmetry, gap scaling, and 64,680 sampled rays across the pane and full angle range. The isolated Chrome checks exercised keyboard radio and slider changes, mobile touch, both presets, distinct rendered frames, static fallback and horizontal fit at 1440 px and 360 px.