Theme Catppuccin
Make yourself at homeCatppuccin

A softer light for long learning sessions.

Appearance

Loading your preference…

Dark palette

Choose a dark palette to try it.

Light uses Latte. Your choices stay in this browser.

A room full of integrals

SKETCHBOOK / 01 The Lantern Room · 2-week chapter

Page 1 of 3: The Lantern Room starts as a question

Radiance / measurement

The Lantern Room starts as a question

Build a small original room: a pale floor, one colored wall, a matte object, and eventually a visible emitter. Keep geometry simple enough that a surprising pixel can be traced on paper. The final project is your CPU light-transport renderer, not a downloaded scene or a checklist of materials.

Radiance is power per projected area per solid angle, measured radiometrically in W·m⁻²·sr⁻¹ after integrating over wavelength. A renderer’s linear RGB is a chosen color representation of that directional light; it is not automatically a calibrated physical measurement. A pixel is not a physical light measurement until the camera, exposure, and reconstruction choices are specified. Start by recording the ray and the linear RGB quantity you estimate; a display-ready byte is a later representation.

The supplied companion now connects sampling and sphere queries to a small runnable diffuse renderer: a bounded path loop, a constant environment, surface emission, a sample trace, and an image. You can study one complete ray before extending it. Over sixteen weeks you will build the original room, richer materials, direct-light sampling, and progressive presentation, preserving this small reference as a regression scene.

TRY IT IN YOUR STUDIO

Sketch the room, label one camera ray and one emitter, then list what your existing renderer actually measures or approximates.

From the page to your own work

Your studio assignment.

Define your Lantern Room and verify one scalar estimator before adding indirect light.

A finish line you can see

A scene sketch, a written estimator contract, and a fixed-seed integral experiment with several-seed evidence.

  1. Choose your own room composition and one controlled light.
  2. Write the measure and PDF next to the estimator.
  3. Compare against pi and record sample counts and seeds.
  4. State what the companion supplies and what you will implement.
Keep the evidence in your weekly notebook ↗
Explain it like an engineer

Try answering aloud before opening the review notes. Use your own implementation as evidence.

How can a smooth image still be systematically wrong?
  • Distinguish variance from bias.
  • Identify normalization, missing paths, and display transforms as separate causes.
  • Use an analytic or controlled reference to isolate one cause.

These prompts support practice; they are not an automatic assessment of your work.

A small creative variation ↗

Estimate a constant function over the same hemisphere and predict its integral before running.

Optional. Save it for later if this chapter already feels full.

Coming back after a break? ↩

Run the companion unchanged, then write one line naming the integral and its units.

Books & principles behind this study +

Original Parallax explanations and assignments, with these works for further reading.

YOUR MARGIN NOTES

Leave yourself a good question.

What changed your mind? What would you try next?

Notes are private to this browser and saved as you write.

A CHECKPOINT, NOT A SCORE

Can you explain the idea and try the exercise yourself?

Completion records your own assessment. It does not compile or test your C++.
Companion source 10 files