Lectures in course CS-457: Geometric computing

Blender Basics: Modeling and Animation

Introduces Blender basics, including modeling with NurbsCurve and BezierCircle, and animation techniques like keyframing.

Deformation Analysis in Elastic Solids

Explores manipulation of 3D arrays, barycenters, shape matrices, Jacobians, eigendecomposition, and visualization in elastic solids.

Make it Stand: Geometric Computing

Explores static equilibria, geometric data representations, and shape optimization to make a geometric object stand.

Quadratic Fitting: Coefficients and Solutions

Covers the computation of matrices for mesh processing and the Laplace equation solution for mesh deformation.

Minimal Surfaces and Discrete Differential Geometry

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Remeshing

Explores remeshing in geometric computing, emphasizing equal edge lengths and valence close to 6.

Geometric Computing Laboratory: Inverse Design Optimization

Explores inverse design optimization in geometric computing, covering topics such as deployable structures, material-aware design, and programmed materials.

Shape Preservation in Deformation

Explores shape preservation in deformation using elastic energy and spring-based modeling to optimize object stability and form integrity.

Optimization Basics: Unconstrained Optimization and Gradient Descent

Covers optimization basics, including unconstrained optimization and gradient descent methods for finding optimal solutions.

Convergence Criteria: Necessary Conditions

Explains necessary conditions for convergence in optimization problems.

Newton's Method: Optimization Techniques

Explores optimization techniques like gradient descent, line search, and Newton's method for efficient problem-solving.

Elastic Deformation: Intro

Covers elastic deformation in materials, shaping objects subject to weight or forces, and its application in architecture.

Elastic Deformation: Material Properties

Explores material properties, stress, strain, and deformation gradient in elastic deformation.

Solid Mechanics II + Material Models

Explores material models for elastic objects, including inverse shape optimization and hyperelasticity.

Energy Equilibrium and Newton CG Method

Covers continuum mechanics, linear elasticity, force balance, divergence, finite element discretization, energy minimization, and Newton's method.

Inverse Design and Sensitivity Analysis

Explores optimal transport, transforming light, inverse design optimization, and sensitivity analysis for shape optimization.

Elastic Energy: Implementation and Analysis

Explores the implementation and analysis of elastic energy in hyperelastic materials, including strain and stress tensors.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Vectorizing Functions for Optimization

Demonstrates how to optimize code by vectorizing functions for efficient problem-solving.

Computing Centroids and Tolerances

Addresses common problems in computing centroids and the importance of tolerances.