Comprehensive 3D Simulation Learning Roadmap

Mathematics Prerequisites

Linear Algebra

• Vectors and vector operations
• Matrices and matrix transformations
• Dot product, cross product
• Eigenvalues and eigenvectors

Calculus

• Derivatives and integrals
• Partial derivatives
• Gradient, divergence, curl
• Numerical differentiation and integration

Geometry

• Coordinate systems (Cartesian, polar, spherical)
• Transformations (translation, rotation, scaling)
• Quaternions for rotation
• Homogeneous coordinates

Physics Basics

• Newtonian mechanics
• Kinematics and dynamics
• Forces, energy, momentum
• Conservation laws

Programming Fundamentals

Core Programming (Python/C++)

• Object-oriented programming
• Data structures (arrays, linked lists, trees, graphs)
• Algorithms (sorting, searching, optimization)

Computer Graphics Basics

• Rendering pipeline
• Coordinate transformations
• Camera models and projections
• Rasterization vs ray tracing

3D Graphics Programming

Graphics APIs

• OpenGL/WebGL fundamentals
• Shaders (vertex, fragment, geometry)
• Texture mapping and materials
• Lighting models (Phong, Blinn-Phong, PBR)

3D Model Representation

• Mesh structures (vertices, edges, faces)
• Polygonal modeling
• Subdivision surfaces
• Implicit surfaces and volumetric representation

Rendering Techniques

• Z-buffering and depth testing
• Back-face culling
• Shadow mapping
• Ambient occlusion
• Screen-space techniques (SSAO, SSR)

Animation Fundamentals

Keyframe Animation

• Interpolation methods (linear, cubic, Bezier)
• Easing functions
• Animation curves and timelines

Skeletal Animation

• Rigging and skinning
• Bone hierarchies
• Inverse kinematics (IK)
• Forward kinematics (FK)
• Blend shapes and morph targets

Rigid Body Dynamics

Core Concepts

• Mass, center of mass, inertia tensors
• Linear and angular velocity
• Force and torque application
• Numerical integration (Euler, RK4, Verlet)

Collision Detection

• Bounding volumes (AABB, OBB, spheres)
• Spatial partitioning (octrees, BVH, grid-based)
• Narrow-phase detection (SAT, GJK)
• Continuous collision detection

Collision Response

• Impulse-based resolution
• Constraint-based resolution
• Friction models (Coulomb friction)
• Restitution coefficients

Soft Body Dynamics

Mass-Spring Systems

• Spring forces (Hooke's law)
• Damping
• Structural, shear, and bend springs

Finite Element Method (FEM)

• Continuum mechanics
• Stress and strain tensors
• Material models (linear elastic, neo-Hookean)
• Mesh discretization

Position-Based Dynamics (PBD)

• Constraint projection
• Solver iterations
• Collision handling

Fluid Simulation

Particle-Based Methods

• Smoothed Particle Hydrodynamics (SPH)
• Neighbor search algorithms
• Pressure and viscosity forces
• Surface reconstruction (marching cubes)

Grid-Based Methods

• Navier-Stokes equations
• MAC grid and staggered grids
• Pressure projection
• Semi-Lagrangian advection
• FLIP/PIC methods

Special Effects

• Smoke and fire simulation
• Level sets for interface tracking
• Vorticity confinement

Cloth Simulation

• Continuum-based approaches
• Discrete models (mass-spring, PBD)
• Self-collision handling
• Wrinkling and buckling
• Two-way coupling with rigid bodies

Hair and Fur Simulation

• Hair strand modeling
• Guide hair and interpolation
• Collision detection for thin structures
• Wind and dynamic forces
• Rendering techniques (Kajiya-Kay model)

Destruction and Fracture

• Voronoi fracturing
• Constraint networks
• Progressive damage models
• Debris simulation
• Connection graphs

Vehicle Dynamics

• Tire models (Pacejka, brush model)
• Suspension systems
• Drivetrain modeling
• Aerodynamics
• Terrain interaction

Crowd Simulation

• Steering behaviors
• Path planning and navigation
• Social forces model
• Flow fields
• Behavioral animation

Real-Time Simulation

• Level of Detail (LOD) systems
• Temporal coherence
• Asynchronous simulation
• GPU acceleration techniques
• Performance profiling and optimization

Machine Learning Integration

• Neural network-based physics prediction
• Learned simulation models
• Motion synthesis and style transfer
• Differentiable simulation
• Reinforcement learning for animation

Integration Methods

• Explicit Euler
• Semi-implicit (Symplectic) Euler
• Runge-Kutta methods (RK2, RK4)
• Verlet integration
• Leapfrog integration
• Implicit integration methods

Collision Detection

• Sweep and Prune (SAP)
• Gilbert-Johnson-Keerthi (GJK)
• Expanding Polytope Algorithm (EPA)
• Separating Axis Theorem (SAT)
• Bounding Volume Hierarchies (BVH)
• K-D trees and octrees
• Dynamic AABB trees

Constraint Solvers

• Sequential Impulses (SI)
• Projected Gauss-Seidel (PGS)
• XPBD (Extended Position-Based Dynamics)
• Lagrange multiplier methods
• Interior point methods

Optimization Algorithms

• Gradient descent
• Newton-Raphson method
• Conjugate gradient
• BFGS and L-BFGS
• Levenberg-Marquardt

Rendering Algorithms

• Ray tracing and path tracing
• Rasterization pipeline
• Deferred rendering
• Forward+ rendering
• Screen-space reflections
• Temporal anti-aliasing (TAA)

Physics Engines

3D Graphics Frameworks

• Three.js (JavaScript/WebGL)
• Babylon.js (JavaScript/WebGL)
• OpenGL/Vulkan (low-level APIs)
• DirectX (Windows)
• Metal (Apple platforms)

Game Engines

• Unity (C#, versatile)
• Unreal Engine (C++, high-fidelity)
• Godot (open-source)
• CryEngine
• O3DE (Open 3D Engine)

Specialized Simulation Software

• Houdini (VFX, procedural)
• Maya (animation, rigging)
• Blender (open-source, all-in-one)
• Cinema 4D (motion graphics)
• RealFlow (fluids)
• FumeFX (smoke/fire)

Scientific/Engineering Tools

• COMSOL (multiphysics)
• ANSYS (finite element analysis)
• OpenFOAM (computational fluid dynamics)
• ParaView (visualization)
• MATLAB/Simulink (prototyping)

Libraries & Frameworks

• Eigen (C++ linear algebra)
• GLM (OpenGL Mathematics)
• NumPy/SciPy (Python scientific computing)
• PyTorch3D (3D deep learning)
• Open3D (3D data processing)

Project 1: Bouncing Ball Simulator

• Implement basic gravity and ground collision
• Add different materials (basketball, golf ball, rubber)
• Visualize using simple 3D library

Skills: Basic physics, numerical integration, rendering

Project 2: Solar System Simulation

• N-body gravitational simulation
• Implement orbital mechanics
• Add camera controls

Skills: Vector math, physics laws, 3D transformations

Project 3: Particle System

• Create fire, rain, or fountain effects
• Implement particle lifecycle
• Add basic forces (gravity, wind)

Skills: Particle dynamics, instanced rendering

Project 4: Simple Cloth Flag

• Mass-spring network (10x10 grid)
• Wind forces and interaction
• Fixed corner constraints

Skills: Spring physics, constraint solving

Project 5: Rigid Body Stack

• Stack of cubes/objects with collision
• Implement friction and restitution
• Compare different integration methods

Skills: Rigid body dynamics, collision resolution

Project 6: Rope/Chain Simulation

• Verlet integration for stability
• Distance constraints
• Interactive dragging

Skills: Constraint-based dynamics, numerical stability

Project 7: Water in a Glass

• SPH fluid simulation
• Container boundaries
• Surface tension effects

Skills: Particle-based fluids, neighbor search

Project 8: Ragdoll Physics

• Articulated body with joints
• Joint constraints (hinge, ball-socket)
• Collision with environment

Skills: Skeletal systems, joint simulation

Project 9: Vehicle Physics Simulator

• 4-wheel vehicle with suspension
• Basic tire model
• Steering and acceleration

Skills: Complex rigid bodies, specialized physics

Project 10: Destruction Simulator

• Voronoi fracturing algorithm
• Constraint-based breaking
• Debris generation and simulation

Skills: Procedural geometry, fracture mechanics

Project 11: Soft Body Deformation

• Tetrahedral mesh-based FEM
• Real-time deformation
• Two-way coupling with rigid bodies

Skills: Continuum mechanics, FEM, numerical methods

Project 12: Fluid-Structure Interaction

• Boat on water simulation
• Grid-based fluid + rigid bodies
• Buoyancy and drag forces

Skills: Multi-physics coupling, advanced fluids

Project 13: Crowd Evacuation Simulator

• Path planning with A* or RRT
• Social forces model
• Obstacle avoidance
• Heat maps and analytics

Skills: AI behaviors, agent-based simulation

Project 14: Hair/Fur Simulation

• Strand-based hair model
• Collision with character body
• Dynamic wind interaction
• Rendering with anisotropic shading

Skills: Thin structure simulation, specialized rendering

Project 15: Real-Time Smoke Simulator

• Grid-based Navier-Stokes solver
• Vorticity confinement
• GPU acceleration (compute shaders)
• Volumetric rendering

Skills: CFD, GPU programming, advanced rendering

Project 16: Machine Learning-Enhanced Physics

• Train neural network to predict cloth behavior
• Compare performance vs. traditional solver
• Implement hybrid approach

Skills: Deep learning, physics ML, optimization

Project 17: Multi-Physics Engine

• Integrated rigid, soft, fluid simulation
• Universal collision detection system
• Scene graph with different physics objects
• Performance profiling and optimization

Skills: Engine architecture, advanced algorithms

Project 18: Digital Twin Application

• Real-world system replication (e.g., factory)
• Sensor data integration
• Predictive simulation
• Real-time visualization dashboard

Skills: System integration, IoT, full-stack development

Project 19: Differentiable Simulator

• Build simulation with automatic differentiation
• Inverse problems (parameter estimation)
• Gradient-based optimization

Skills: Advanced math, autodiff, optimization

Project 20: VR Physics Sandbox

• Room-scale VR physics playground
• Hand tracking for interaction
• Haptic feedback integration
• Multiple physics phenomena

Skills: VR development, real-time systems, UX design