CAD → CAE → CAM
Feature-based models, assemblies, tolerances, simulation, toolpaths, inspection, and manufactured parts.
Origins
Immersive University · Engineering studio 01
Geometry is not a picture. It is a system.
Begin the courseGrades 10–12 and postsecondarySelf-paced interactive STEAM course
Build geometric understanding by changing control points, parameters, continuity, topology, materials, and light—then explain how each decision changes the model.
- 6
- connected modules
- 33
- short lessons
- 6
- live studios
Course connections
Geometry becomes a language for engineering and digital art.
Curriculum connections include Common Core HSG-MG.A.1–3 for modeling with geometry and NGSS HS-ETS1 engineering-design practices involving criteria, constraints, modeling, testing, and refinement.
The course reconstructs graduate-level special-topic work completed in Georgia Tech’s mechanical engineering program under the direction of Dr. David W. Rosen, with additional faculty guidance from Dr. Farrokh Mistree. It is a free self-paced resource and does not award academic credit.
One mathematical language
Two worlds grow from the same geometry.
The early mathematics is shared. Design intent and tolerances lead toward engineering, analysis, and manufacturing. Expressive form, materials, cameras, and light lead toward animation, games, and visual storytelling.
Geometry → CGI → XR
Organic forms, animation, procedural worlds, materials, physically based light, games, and immersive experience.
Course map
From the first coordinate to a rendered world.
Each module is built from short explanations, mathematical forms, and a live studio. The sequence follows the original project’s logic and extends it through modern CAD and graphics practice.
- 015 lessons
Foundations
Coordinates · vectors · parametric form · basis functions · transforms
- 027 lessons
Curves
Hermite · Bézier · de Casteljau · continuity · B-splines · NURBS
- 035 lessons
Surfaces
Tensor products · bicubic patches · control nets · seams · trimming
- 045 lessons
Topology
Tessellation · boundaries · manifold models · normals · Euler checks
- 055 lessons
Solids
Sweeps · Booleans · B-rep · features · CAD/CAE/CAM/CGI
- 066 lessons
Rendering
Projection · normals · materials · lighting · ray tracing · PBR
The complete interactive course
Learn by changing the geometry.
Choose a lesson, adjust its variables, and watch the model respond. Progress is saved only in this browser. No account, plug-in, or installation is required.
Module 01 · Lesson 1 of 5
Points and coordinate systems
Live geometry studio
Principle
A point records a location. A coordinate system gives that location meaning.
Mathematical form
P = [x, y, z]
Try it
Move t to locate a point between the two anchors.
Capstone path
Design one object. Follow it through the entire system.
Use the six modules to build a small controlled form, test whether its mesh is valid, express its design intent, and communicate it through light and material.
- 01Define
Place points and choose a coordinate frame.
- 02Shape
Build a continuous profile with local control.
- 03Surface
Extend the profile into a controlled patch.
- 04Validate
Inspect boundaries, normals, and manifold topology.
- 05Realize
Add features and select an engineering pipeline.
- 06Communicate
Use a camera, material, and light to explain the result.
Recovered artifact · original course menuThe original artifact
The period interface remains evidence.
The recovered 800-by-600 project was built for Internet Explorer and Macromedia Flash 6. It organized mathematics, curves, surfaces, and solids around 20 named lessons and 25 interactive Flash demonstrations.
This modern course preserves that architecture and its instructional idea—make abstract geometry visible—while replacing the obsolete player with responsive HTML5 Canvas and expanding the curriculum through NURBS, topology, model intent, and modern rendering.
The through-line
From geometric systems to learning systems.
Curves, surfaces, manufactured parts, digital worlds, and immersive learning connect through the same practice: reveal the system, let learners change it, and make complex relationships understandable.