Part I Geometry -- A Geometric Approach to Elasticity, Contact and Design -- Computer Graphics in Minimal Surface Theory -- Explicit Formula and Extension of the Discrete Power Function Associated with the Circle Patterns of Schramm Type -- On Connectivity of Discretized 2D Explicit Curve -- Part II Animation -- Fast Implicit Simulation of Flexible Trees -- Probe-type Deformers -- Controllable Skeleton-sheets Representation via Shape Diameter Function -- Super resolution from Principal Component Models by RKHS Sampling -- Part III Visual Perception and Illusion -- From Mathematical Study of Visual Information Processing in the Brain to Image Processing -- Computational Creation of a New Illusionary Solid Sign with Shading Effect -- Part IV Simulation and Sampling -- Mathematical Model for Epidermal Homeostasis -- A Prior Reduced Model of Dynamical Systems -- Real-time Volume Visualization for Large-scale Grid-based Fluid Simulations on Distributed Multi-GPU Systems -- Importance Sampling for Cloth Rendering under Environment Light.