tzyt's Blog

Derives peak, valley, average current, and average power for an LR electromagnet under steady PWM, with interactive frequency and duty-cycle charts.

Derives least squares from calculus and linear algebra, explaining squared-error minimization, normal equations, and the geometric interpretation.

GAMES101 notes on 3D rotations, coordinate transformations, projection, rasterization, interpolation, and related graphics mathematics.

Explains the graph-based solution to USACO Find and Replace, including cycle handling, special cases, minimum operations, and implementation details.

Notes on Stanford CS144 Lab 4, combining the TCP sender and receiver into a complete connection and handling state transitions and segments.

Notes on Stanford CS144 Labs 0–3, covering the byte stream, stream reassembler, TCP receiver, and TCP sender without publishing full solutions.

Explains the dynamic counting idea for Codeforces 1774C by tracking the last change in a binary string and computing the answer for every prefix.

Derives backpropagation for a dense neural network and implements MNIST digit recognition, including forward propagation, gradients, and training.

Study notes and extensions for Ray Tracing The Next Week, covering BVH, textures, Perlin noise, transforms, fog, and multithreading.

Explains the camera implementation in Ray Tracing in One Weekend, including orientation, field of view, aperture, focus, and depth of field.

Explains Lambertian materials in Ray Tracing in One Weekend through radiometry, the cosine law, diffuse reflection, and the corresponding code.