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Simulation and scientific computing
flight-training-simulator
certified full-flight simulators for pilot training
CAE 7000XR, L3Harris RealitySeven, FlightSafety
System
Techniques · 10
Primitives · 43
flight-training-simulat…
Motion cueing washout
control · medium: Map vehicle accelerations to simulator platform motion with high-pass washout filters, tilt coordination and workspace limits
Clock synchronization
distributed · medium: Estimate a clock's offset from four timestamps, filter out queueing noise, and steer the clock smoothly; NTP gets about a millisecond, PTP with hardware timestamps under a microsecond.
›
Asset streaming priority
graphics · medium: Prioritized async loading of assets by distance and visibility under a memory budget with eviction
Frustum occlusion culling
graphics · medium: Frustum tests on bounds, hierarchical-Z occlusion and GPU culling passes
Physically based shading (microface…
graphics · medium: Cook-Torrance microfacet BRDF with GGX distribution, height-correlated Smith masking and Schlick Fresnel, driven by base colour, metallic and roughness; the standard surface model of real-time and film renderers.
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Impedance control
robotics · medium: Make a robot behave like a spring-damper at the contact point for safe interaction
Inverse kinematics
robotics · medium: CCD/FABRIK/Jacobian solvers posing joint chains to reach targets
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
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Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
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Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
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Shared memory ipc
concurrency · low: Shared memory rings and futex signalling between processes
Record replay
distributed · low: Record every nondeterministic input (time, randomness, I/O, model and tool outputs, per-tick player input) and re-execute deterministically for debugging, replays and state rebuild
Map tile pyramid
geometry · low: Z/x/y tile pyramids, quadkeys and overviews for multi-resolution maps and imagery
Floating origin rebasing
graphics · low: Shift the world origin near the camera to keep float precision in huge worlds
Image warping remap
graphics · low: Resampling with lookup maps: resize, lens undistortion, homographies, bilinear/bicubic
Vsync frame pacing
graphics · low: Vsync, swapchain presentation modes, frame pacing, latency and variable refresh
Audio mixing
media · low: Summing many streams with gain, clipping control and per-listener minus-one mixes
Runge-Kutta 4
numerics · low: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.
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Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Rigid-body dynamics
physics · low: Advance one 3D rigid body per step from force and torque: semi-implicit Euler for position, an inertia tensor in the body frame, and quaternion orientation updated by the exponential map.
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IIR and FIR filters
signal-processing · low: Two ways to shape a sampled signal's spectrum: FIR (finite taps, always stable, exact linear phase) or IIR (feedback, a few coefficients, cheap but phase-distorting).
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Phase-locked loop (digital)
signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.
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Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
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+ 3 more techniques
+ 27 more primitives
System
Techniques · 10
Primitives · 43
flight-training-simulat…
Motion cueing washout
control · medium: Map vehicle accelerations to simulator platform motion with high-pass washout filters, tilt coordination and workspace limits
Clock synchronization
distributed · medium: Estimate a clock's offset from four timestamps, filter out queueing noise, and steer the clock smoothly; NTP gets about a millisecond, PTP with hardware timestamps under a microsecond.
›
Asset streaming priority
graphics · medium: Prioritized async loading of assets by distance and visibility under a memory budget with eviction
Frustum occlusion culling
graphics · medium: Frustum tests on bounds, hierarchical-Z occlusion and GPU culling passes
Physically based shading (microface…
graphics · medium: Cook-Torrance microfacet BRDF with GGX distribution, height-correlated Smith masking and Schlick Fresnel, driven by base colour, metallic and roughness; the standard surface model of real-time and film renderers.
›
Impedance control
robotics · medium: Make a robot behave like a spring-damper at the contact point for safe interaction
Inverse kinematics
robotics · medium: CCD/FABRIK/Jacobian solvers posing joint chains to reach targets
System identification
robotics · medium: Fit dynamic models (ARX, state space) from measured input and output data
Levenberg marquardt
numerics · medium: Damped Gauss-Newton nonlinear least squares for model calibration
Rigid body dynamics algorithms
physics · medium: Featherstone RNEA/ABA/CRBA for articulated-body inverse and forward dynamics
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
›
Shared memory ipc
concurrency · low: Shared memory rings and futex signalling between processes
Record replay
distributed · low: Record every nondeterministic input (time, randomness, I/O, model and tool outputs, per-tick player input) and re-execute deterministically for debugging, replays and state rebuild
Map tile pyramid
geometry · low: Z/x/y tile pyramids, quadkeys and overviews for multi-resolution maps and imagery
Floating origin rebasing
graphics · low: Shift the world origin near the camera to keep float precision in huge worlds
Image warping remap
graphics · low: Resampling with lookup maps: resize, lens undistortion, homographies, bilinear/bicubic
Vsync frame pacing
graphics · low: Vsync, swapchain presentation modes, frame pacing, latency and variable refresh
Audio mixing
media · low: Summing many streams with gain, clipping control and per-listener minus-one mixes
Runge-Kutta 4
numerics · low: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.
›
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Rigid-body dynamics
physics · low: Advance one 3D rigid body per step from force and torque: semi-implicit Euler for position, an inertia tensor in the body frame, and quaternion orientation updated by the exponential map.
›
IIR and FIR filters
signal-processing · low: Two ways to shape a sampled signal's spectrum: FIR (finite taps, always stable, exact linear phase) or IIR (feedback, a few coefficients, cheap but phase-distorting).
›
Phase-locked loop (digital)
signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
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Buffer pools for zero-allocation I/O
hardware-os · low: Preallocate a fixed set of aligned I/O buffers and recycle them through a free list, so the hot path never mallocs, faults or unmaps. The bounded count doubles as back pressure.
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LRU and CLOCK
systems · low: LRU evicts the least recently used entry via hash map plus linked list; CLOCK approximates it with a reference bit, so hits take no lock.
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Homogeneous transforms
geometry · low: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matrices
Image pyramids
graphics · low: Gaussian/Laplacian pyramids and tiled multi-resolution images for zoom and blending
GPU compute shaders
ml-training · low: The vendor-neutral GPU launch model of Metal, Vulkan and WebGPU: a grid of workgroups, shared memory, barriers and subgroups, driven by recorded command buffers.
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Bounding volume hierarchy
physics · low: Binary tree of nested bounding boxes; prunes overlap and ray queries to O(log n) for any size distribution, and supports cheap insert/remove for moving objects.
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Color space conversion
graphics · low: Convert pixels between transfer curves (sRGB, linear light), primaries (sRGB, Display P3, XYZ) and Y'CbCr, using tables for the curve and 3x3 matrices for the rest.
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Tone mapping (HDR to display range)
graphics · low: Compress scene-referred linear light to a display's range in three steps: expose, apply a curve to luminance, then encode (sRGB, PQ or HLG) and dither.
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PCA and SVD
machine-learning · low: Find orthogonal directions of maximum variance by an SVD of the centred data; randomized SVD gets the top k components in a few passes.
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Rigid-body transforms (SE(3) poses)
robotics · low: Represent, compose, invert, integrate and interpolate 3D poses as unit quaternion plus translation, with exp/log maps for small motions and uncertainty.
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Linear and logistic regression
machine-learning · low: Fit a weighted sum of features to a number (least squares) or a probability (logistic); the baseline every model must beat.
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Fast Fourier transform
numerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.
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Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
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LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
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Memory ordering
concurrency · low: What Relaxed, Acquire, Release and SeqCst atomics actually guarantee, what they cost on x86 and ARM, and which one each pattern needs.
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Dma transfers
embedded · low: DMA controllers: descriptors, circular buffers, cache coherence for zero-CPU data movement
PWM generation
embedded · low: A timer's counter, period and compare registers draw the pulse train; preload, dead time and DMA make duty changes glitch-free, shoot-through-free and cheap.
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Fixed timestep loop
graphics · low: Fixed simulation dt with accumulator, render interpolation, spiral-of-death guard
fsync, O_DSYNC and O_DIRECT
hardware-os · low: What fsync, fdatasync, O_DSYNC, O_DIRECT and F_FULLFSYNC really guarantee on Linux and macOS, and the exact call sequences for crash-safe files.
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Loss functions
machine-learning · low: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.
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Chroma subsampling
media · low: 4:2:0/4:2:2 colour plane downsampling and siting
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
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L-BFGS
numerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.
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Semi-implicit Euler
numerics · low: Update velocity from forces first, then position with the new velocity: explicit Euler cost, but symplectic and stable; the default game-physics integrator.
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Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
Biquad filters
signal-processing · low: Second-order IIR sections (RBJ cookbook): low/high pass, peaking EQ; stable cascades
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