visualization
education

Math Visual Studio

A local web app for visualising multivariable calculus, transformations, ODEs and PDEs, mechanisms, deformation and molecules

23 images · 2 videos · 1 min read

Open Studio Jump to gallery

Math Visual Studio

datasheet // math-studio-course

images: 23
videos: 2
formats: png, mp4, gif
text: 65 words · 1 min read
studio: /studio (gallery)
topics: calculus ×9

transforms ×3

solver ×3

deform hair ×3

molecules ×2

mechanisms ×1

atlas ×1

animation ×3

Datasheet

Workspaces: 22 (including the embedded Grapher, Desmos 2D, Desmos 3D and GeoGebra)
Syllabus Atlas: 112 chapters, 641 cited examples, each shown in 2D and 3D
Presets: Mechanisms 26, Deform & Hair 20, Molecules 15, Physics 26
Export for 3D printing: STEP, STL, 3MF, OBJ
Recording: frame-exact MP4, WebM, GIF or PNG, 720p to 4K
Runs as a local web app

My contribution

Developed (AI-assisted).

Gallery

Revolve: solid with a hole, one washer pulled out of the solid — Revolve: solid with a hole, one washer pulled out of the solid Explain Calculus and transformations

Revolve: the same solid by cylindrical shells, one shell unrolled — Revolve: the same solid by cylindrical shells, one shell unrolled Explain Calculus and transformations

Integrals Lab: change of variables, one grid cell and its image — Integrals Lab: change of variables, one grid cell and its image Explain Calculus and transformations

Integrals Lab: spherical shell cut into wedges, one wedge shown — Integrals Lab: spherical shell cut into wedges, one wedge shown Explain Calculus and transformations

Integrals Lab: triple integral as small boxes on the unit cube, coloured by density — Integrals Lab: triple integral as small boxes on the unit cube, coloured by density Explain Calculus and transformations

Surface area: sphere cut into frustum bands, with the flatness strip — Surface area: sphere cut into frustum bands, with the flatness strip Explain Calculus and transformations

Arc length: chords inscribed in a cardioid, error against number of chords — Arc length: chords inscribed in a cardioid, error against number of chords Explain Calculus and transformations

Polar: polar cells over a disk r=2cos θ, draggable pole — Polar: polar cells over a disk r = 2cos θ, draggable pole Explain Calculus and transformations

Intersect: Steinmetz solid, two cylinders at right angles — Intersect: Steinmetz solid, two cylinders at right angles Explain Calculus and transformations

Transform: matrix columns as arrows, image of the unit square, det A=-1 — Transform: matrix columns as arrows, image of the unit square, det A = -1 Explain Calculus and transformations

Transform 3D: gimbal lock at pitch=90° — Transform 3D: gimbal lock at pitch = 90° Explain Calculus and transformations

Transform 3D: SVD of a shear as rotate, stretch, rotate — Transform 3D: SVD of a shear as rotate, stretch, rotate Explain Calculus and transformations

Solver: symbolic regression, Pareto front of complexity against loss — Solver: symbolic regression, Pareto front of complexity against loss Explain Calculus and transformations

Solver: heat equation past the stability limit (r = 0.52) — Solver: heat equation past the stability limit (r = 0.52) Explain Calculus and transformations

Solver: phase plane of x'' = -x with its equilibrium — Solver: phase plane of x'' = -x with its equilibrium Explain Calculus and transformations

Deform & Hair: head of curls, front view and 3D — Deform & Hair: head of curls, front view and 3D Explain Geometry and kernels

Deform & Hair: linear blend skinning against dual quaternions — Deform & Hair: linear blend skinning against dual quaternions Explain Geometry and kernels

Course figure: Follow-The-Leader strands against springs, segment-length error — Course figure: Follow-The-Leader strands against springs, segment-length error Explain Geometry and kernels

Molecules: H + H₂ on a LEPS potential-energy surface — Molecules: H + H₂ on a LEPS potential-energy surface Explain Quantum chemistry

Course figure: collinear H₃ contours and energy profile along the path Explain Quantum chemistry

Mechanisms: Stewart–Gough platform, six legs give six degrees of freedom — Mechanisms: Stewart–Gough platform, six legs give six degrees of freedom Explain Geometry and kernels

Atlas: the saddle z=x² - y² in 2D and 3D — Atlas: the saddle z = x² - y² in 2D and 3D Explain Calculus and transformations

Manim render: shells with a hole, strips thinning to the integral Explain Calculus and transformations

Recording from the Studio: Deform & Hair, wavy hair preset Explain Calculus and transformations

Recording from the Studio: matrix morph from the identity, det A=1 — Recording from the Studio: matrix morph from the identity, det A = 1 Explain Calculus and transformations

How to recreate this plot

Watch

A short screen capture of the Math Visualization Studio. Each step is captioned in the clip.

Steps

Open the controls panel
Raise the number of cells n to 20
Press n to infinity
Choose dx dy (rows)
Press Fubini sweep

Open the scene in the Studio Read the explanation

Code and PDF notes

Free of cost. I approve each request and reply by email.

To request the files, email me at krunalpanchal1995 [at] gmail [dot] com and mention the item id. project-math-studio-course