Topics covered:

Volume 2:
Linear Algebra & Matrix Decompositions
• Principal Component Analysis [PCA], Singular Value Decomposition [SVD]
• Eigenvalue Decomposition [EVD], Eigenvalues, Eigenvectors, Eigenbasis
• Polar Decomposition, Orthogonality, Diagonalization
• Matrix Transposition, Diagonal Matrices, Orthogonal Matrices, Orthonormal Matrices
• Matrix Pseudoinverse [Generalized Inverse], Moore-Penrose Inverse, Projection Matrix
• Matrix Norms, Matrix 1-Norm, Matrix Infinity-Norm, Matrix Max-Norm, Frobenius Norm, Spectral Norm
• Tensors, Vector Spaces

Vector Field Dynamics: Deformation Analysis & Transformations
• Fluid Dynamics, Continuum Mechanics, Stress Tensor Analysis
• Velocity Gradient Tensor [VGT], Fluid Flow Analysis, Field Distortion & Volume Change
• Deformation Gradient Tensor, Principal Deformations & Principal Deformation Directions
• Strain Tensor, Strain Rate Tensor, Vorticity Tensor, Symmetric & Anti-Symmetric Parts of VGT
• Material Point Method [MPM]
• Galilean invariance

Fitting & Principal Analysis
• Regression Analysis, Data Fitting Techniques, Multivariate Analysis, Dimensionality Reduction
• Best Fit Line, Best Fit Plane, Rigid Transform Matrix Computation
• Outer Product, Covariance Matrix, Point Cloud Normal Estimation
• Linear Least Squares [LLS], Principal Axis Computation
• Anisotropy-Aware Sheet Refinement and Gap Filling in Thin FLIP Fluids
• Spectral Analysis

Curvature, Surface & Shape Analysis
• Differential Geometry, Topological Analysis, Computational Geometry, 3D Surface Analysis
• Curvature, First Partial Derivative, Second Partial Derivatives
• Hessian Matrix/Tensor, First Fundamental Form, Second Fundamental Form
• Shape Operator, Weingarten Map, Smoothing the Shape Operator, Shape Index, Willmore Energy
• Maximum/Minimum Principal Curvatures & Directions
• Mean Curvature, Gaussian Curvature, Normal Curvature, Curvedness, Difference of Principal Curvatures
• Monoclastic, Synclastic & Anticlastic Surfaces
• Geomorphology, Geomorphometric Analysis, Terrain Analysis, Heightfield Analysis
• Asymptotic Lines, Asymptotic Curves, Asymptotic Directions
• Minima, Maxima, Umbilical Points
• Curvature Tensor, OpenSubdiv Curvature, Analytic Differential Curvature
• OpenSubdiv Derivatives, OpenSubdiv Normals, Intrinsic UVs
• Minimal Surface
• Intrinsic Distance Metrics: Geodesic Distance, Biharmonic Distance, Diffusion Distance
• Shape Relaxation and Smoothing

Geometric Transformations
• Affine Transformations, Homogeneous Coordinates, Coordinate Systems
• Point Line Projection, Computing Arbitrary Linear Transformation Between 2 Point Clouds
• Shape Matching, Rigid Transform Matching
• Iterative Closest Point [ICP], Point Cloud Registration
• Boundary Conditions, Dirichlet Boundary Conditions, Neumann Boundary Conditions

Bounding Geometries, Geometric Decomposition & Convex Hulls
• Collision Detection, Geometric Primitives, Geometric Optimization
• Oriented Bounding Box [OBB], Oriented Bounding Cylinder [OBC]
• Minimum Volume Box [MVB], Minimum Volume Cylinder [MVC], Minimum Area Rectangle [MAR]
• Temporal Oriented Bounding Box, Temporal Oriented Bounding Cylinder
• Rotating Calipers, 2D Convex Hull, 3D Convex Hull

Differential, Vector, Scalar Fields Analysis, Partial Differential Equations
• Partial Differential Equations [PDEs]
• Gradient, Divergence, Curl, Vorticity
• Laplacian, Biharmonic Operator, Biharmonic Equation
• Vector Calculus, Differential Operators, Differential Equations
• VDB Analysis, Volume Analysis, Derivatives
• Helmholtz Decomposition, Solenoidal Fields, Irrotational Fields, Harmonic Fields, Helicity
• Gradient Matrix/Tensor, Jacobian, Field Transformations
• Vector Field Visualization, Scalar Field Analysis, Flow Fields
• Geometric Integration, Gaussian Derivatives, Root Finding
• Q-criterion, Lambda2 Method
• Quadratic Equations
• Discrete Linear Systems [A·x = b]

Sampling, Interpolation Methods & Finite Difference Methods
• Cubic Volume Sampling, Smooth Volume Sampling
• Tricubic Interpolation, Trilinear Interpolation, Matrix Interpolation, Closest Point
• Finite Difference Methods [FDM]
• Discrete Laplacian Stencils
• Volume Discretization [Lattice Structure]
• Smooth Spherical Linear Interpolation Solver, SLERP, Attribute Interpolation/Fill

Software: Houdini 22
Length: Over 11 hours (~19-20h with upcoming content)
Number of Videos: 151 (216 with upcoming content)

Special thanks to Omar Zarifi, Tiago Novello, Cameron White, Jeff Lait, White Dog, Jake Rice.

Volume 1:
Point Clouds & Geometry Distribution
• Point Clouds, Smooth Point Cloud Filtering, Grid Based Point Cloud Lookup [pgfind]
• Camera Based Occlusion with Variable Pscale
• Point Relaxation, Uniform Point Distribution over Polygonal Surfaces, Self Proximity, Tighter Packing
• Clustering, Geometric Advection

Optimization, Kernel Processing & Hashing
• Multithreading Geometry Creation, Unique Pair Matching, Operator Decoupling
• Kernel Code Generalization, Generic VEX Kernels, Unrolling For Loops
• Convolution Kernels, Blurring Attributes, Sharpening Attributes
• Cubic Hermite Interpolation [smoothstep], Shaping Functions
• Hashing

Field Analysis, Geometry Dynamics & Tracing Techniques
• Attribute Gradient, Gradient Descent & Contour Lines [Isolines] on Arbitrary Geometry & Heightfields
• Streamlines, Flowlines, Geometry Traversal
• Backward Tracing, Forward Tracing, Tracing Curves

Flow Analysis & Visualization
• Flow Fields, Flow Field Visualization, Vector Fields, Direction Fields

Edge Operations & Analysis
• K-Depth Neighbours Using Edges & Primitives, Half-Edges, Splitting Edges, Optimizing Edge Operations

Subdivision Surfaces, Limit Surfaces, Adaptivity & Geometric Refinement
• Catmull-Clark Subdivision, Bilinear Subdivision, Improved OpenSubdiv CC Subdivision Surfaces Algorithm
• Adaptive Subdivision, Boundary Rules
• Subdivision Limit Surface, Limit Surface Sampling, Isoline Display
• Orthonormalization, Quadtrees

Attributes, Group Handling & Fusing
• Custom Fusing in VEX, Attribute Preservation & Interpolation, Group Preservation

Light & Reflection
• Sea Caustics, Pool Caustics

Performance, Profiling & Design Principles
• Performance Profiling, Aggressive Performance Optimizations
• Generic HDA Design

Software: Houdini 21
Length: Over 15 hours
Number of Videos: 163

Special thanks to Jeff Lait and Mark Elendt.

Korean translation (WIP) by Seona Hwang.

Rendered using Redshift.