Geometric_Modeling-Feb2021

Project 1 - Mesh Subdivision & 3D Check Board Texturing

1.1 Mesh Subdivision

10k Tris	40k Tris	160k Tris

1.2 3D Check Board Texturing

L = 1	L = 0.5	L = 0.25

Project 2 - Mesh Smoothing & 3D Heat Diffusion & 3D Texture Synthesis

2.1 Mesh Smoothing

Method	Angle View	Side View	Front View	Bottom View
Uniform scheme
Cord scheme
Mean Curvature Flow scheme
Mean Value Coordinates scheme

2.2 3D Heat Diffusion

Iterating Solver	Result	Time cost
Gauss-Seidel (10000 times)		457.678s
Explicit (10000 times)		442.608s
Implicit (10000 times)		7.67s

2.3 3D Texture Synthesis

Texture	Left-Side View	Front View	Right-Side View

Project 3 - Sketch Stylization & Curvature Tensor

3.1 Curvature Tensor Visualization

Curvature Type	Donut Surface	Dragon Surface
Mean curvature
Gaussian curvature

Before Smoothing

Eigen Vector Type	Donut Surface	Dragon Surface
Minor principle
Major principle
Duplicate principles

After Smoothing

Eigen Vector Type	Donut Surface	Dragon Surface
Minor principle
Major principle
Duplicate principles

3.1 Sketch Stylization

Mesh Type	Curvature Regression Line	Add Silhouette Stroke	Turn on Light
Donut
Bunny
Feline
Dragon
Budda

Project 4 - Linear Rotation Invariant for Meshes Deformation

Transformation Results

Transformation	Bunny Before	Bunny After
Rotate
Scale
Translate