Mark Pauly 教授跟 Geometric Computing 應該算是我想來 EPFL 的原因之一。

• ### Dinasour

• Parameter
w = 10, obj_tol = 1E-10, theta = 1.0, beta = 0.5, c = 0.01
• Result
hit tolerance @ iter #17110 with energy 1.36E-4
• Objective function trend chart
• ### Dance

• Parameter
w = 7, obj_tol = 1E-10, theta = 1.0, beta = 0.5, c = 0.01
• Result
hit tolerance @ iter #29392 with energy 9.95E-5
• Objective function trend chart
• ### Gym

• Parameter
w = 10, obj_tol = 1E-10, theta = 1.0, beta = 0.5, c = 0.02
• Result
hit tolerance @ iter #35012 with energy 3.11E-5
• Objective function trend chart

## 3.4.3 BFGS

• ### Dinasour

• Parameter
w = 10, obj_tol = 1E-10, theta = 1.0, beta = 0.5, c = 0.02
• Result
hit tolerance @ iter #337 with energy 1.31E-4
• Objective function trend chart
• ### Dance

• Parameter
w = 13, obj_tol = 1E-10, theta = 1.0, beta = 0.5, c = 0.02
• Result
hit tolerance @ iter #494 with energy 2.01E-5
• Objective function trend chart
• ### Gym

• Parameter
w = 10, obj_tol = 1E-10, theta = 1.0, beta = 0.5, c = 0.02
• Result
hit tolerance @ iter #460 with energy 2.75E-5
• Objective function trend chart

## 3.4.4 My Shape

• ### Cat

• Parameter
w = 44, obj_tol = 1E-10, theta = 0.1, beta = 0.5, c = 0.02
• Result
hit tolerance @ iter #1433 with energy 1E-3
• Objective function trend chart

• Parameter
w = 9, obj_tol = 1e-10, theta = 0.1, beta = 0.5, c = 0.01
• Result
hit tolerance @ iter #1625 with energy 2.8e-6
• Objective function trend chart
• ### Helicopter

• Parameter
w = 150, obj_tol = 1e-9, theta = 0.5, beta = 0.5, c = 0.01
• Result
hit tolerance @ iter #1367 with energy 4.21e-4
• Objective function trend chart

## Laser Cutting

I choosed Wu-Jing (Turnip-Head) for cutting. However, the initial support line is too short for inserting a foot, so I made another one which is stronger.

## 3.5.4 Equilibrium

• Neo-Hookean elasticity model is used

### Beam

• $\rho$ = $131$
• young = $3 \times 10^8$
• poisson = $0.2$
• iteration time = $1000$
• initial step size =
• $10^{-7}$ (Gradient Descent)
• $10^{-8}$ (BFGS)

#### Linear Elasticity model

Residuals Total Energy

#### Neo-Hookean Elasticity model

Residuals Total Energy

### Dinosaur

• $\rho$ = $131$
• young = $3 \times 10^8$
• poisson = $0.2$
• iteration time = $1000$
• initial step size =
• $10^{-8}$ (Gradient Descent)
• $5 \times 10^{-9}$ (BFGS)

#### Linear Elasticity model

Residuals Total Energy

#### Neo-Hookean Elasticity model

Residuals Total Energy

### Ball

• $\rho$ = $131$
• young = $10^6$
• poisson = $0.2$
• iteration time = $1000$
• initial step size =
• $10^{-7}$ (Gradient Descent)
• $10^{-8}$ (BFGS)

#### Linear Elasticity model

Residuals Total Energy

#### Neo-Hookean Elasticity model

Residuals Total Energy

• Mesh
• Objective

• Mesh

• Mesh
• Objective

• Mesh

## Mean Curvature Flow

### Two Rings

$(\text{Max iter}, \epsilon_1, \epsilon_2) = (1000, 5 \times 10^{-2}, 10^{-3})$

Average Mean Curvature Final Mini

### Half Cube

$(\text{Max iter}, \epsilon_1, \epsilon_2) = (1000, 5 \times 10^{-2}, 10^{-3})$

Average Mean Curvature Final Mini

### Cube

$(\text{Max iter}, \epsilon_1, \epsilon_2) = (2, 1, 1)$

Average Mean Curvature Final Mini

### My Shape

$(\text{Max iter}, \epsilon_1, \epsilon_2) = (300, 0.5, 1e-2)$

Average Mean Curvature Final Mini

## Fitting Output

### Bob

Gaussian curvature Mean curvature
Principal curvature directions Asymptotic directions

### Bob

Gaussian curvature Mean curvature
Principal curvature directions Asymptotic directions