Math · Interactive demo

How does a seat become a view?

Move a seat around a fictional stage. See how position, camera angle and perspective create a different view without a new photograph.

Created by ExplainerTools.

About this explainer

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ExplainerTools
Format
Interactive demo
Subject
Math
Where it runs
Plays here
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  • perspective
  • geometry
  • camera angles
  • 3D graphics

How the model works

1 See

A seat map gives you a location. A camera model turns that location into a view. Move around the stage and watch the same performer change size.

Model · fictional scene, not a venue
Model notes and sources

What is confirmed. Ryan Sael’s Best Seat in the House describes a fictional arena and modeled seat views, not a booking system. This does not establish that the demo infers angles from real photographs.

Our explanation, not his source code. This original tool shows one standard way to make seat views. It is not a reconstruction or audit of Ryan’s implementation, and does not establish his prompts, model internals or exact algorithm.

Coordinates. With distance d and azimuth a, eye = (d sin a, h, d cos a). The camera looks at stage target (0,2,0). Its horizontal turn from the forward direction is −a; pitch = atan2(2−h,d). A 1.8 m performer stands on the 2 m stage. Angular height = atan2(3.8−h,d) − atan2(2−h,d).

Perspective. Build unit forward/right/up vectors from eye and target. Dot each point minus eye into that basis. Screen x = f x/z and screen y = f y/z, with f = image height / (2 tan(60°/2)). Points behind the eye are omitted. This is the pinhole-camera model: see OpenCV camera model documentation and Three.js PerspectiveCamera.

Limits. Invented dimensions, a simplified stage, fixed vertical field of view, no crowd occlusion, lenses, screens, acoustics or real-venue calibration. This does not infer geometry from pictures or predict a purchased seat’s actual view. Inferring a real scene from images would require additional evidence and calibration.

An ExplainerTools Original. Concept inspired by Ryan Sael’s Best Seat in the House. Source is linked, not copied.

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