[1:11:23] # Modeling
公式中的 a,b,c都是2D的向量。

[1:12:38] # Modeling
把三个系数 a,b,c 看作是曲线的控制顶点，发现顶点的位置与曲线没有关系,不直观,不利于设计。
把幂基换成 Berstein 基，控制点与曲线的关系变得直观。

回顾：曲面重建

建模(modeling)：设计与重建

  • 曲面设计(Design)
    • 不存在的物体：通过人工交互凭空设计出新的物体
      • CAGD (NURBS)、mesh modeling
    • 存在的物体：通过人工交互编辑修改构建出新的物体
    • Editing, deformation
  • 曲面重建(Reconstruction)
    • 存在的物体：对其采集并进行数字化构建
    • 也称为：逆向工程、扫描重建
      • Reverse engineering, scanning

Surface Editing

Design Modeling

  • Design from zero
    • Create a shape by a set of 3D design operators such as extrusion or revolution etc.

  • Design from a given shape (Mesh editing)
    • Select a base shape
    • Select editing elements and editing operators
    • Deform the shape to obtain a new shape

Mesh Surface Editing

Interactive shape modeling

  • Modeling is an interactive, iterative process
    • Tools need to be intuitive (interface and outcome)
    • Allow quick experimentation
    • Preserve shape properties

User Interaction (UI)

  • User specifications: Intuitive, easy‐to‐use
    • Dragging handles ‐‐ vertices, features, ROI, …
  • Deformed shape: adapt to user intents

Challenges:
• Operations
• Preservation of properties
• Semantics

Methodology

  • Set a proxy P for the input shape S
    • P is simpler/easier/more semantic than S
    • Find a map between P and S: S=g(P)
      • g is also called an embedded space
  • User interacts and deforms the proxy P to P’
    • Find a deformation map: P’=h(P)
  • Compute a new shape S’ from P’: S’=g(P’)

Key Problem:
• find a good map g

  • 第一步：Set a proxy P for the input shape S
    P is simpler/easier/more semantic than S
  • 第二步： Find a map between P and S: S=g(P)
    g is also called an embedded space

find a good map g 是关键

  • 第三步：User interacts and deforms the proxy P to P’
    Find a deformation map: P’=g(P)
  • 第四步：Compute a new shape S’ from P’: S’=g(P’)

Proxy Shapes (handles)

  • Points
    • Points, vertices, …
  • Lines/Curves
    • Sketches, skeletons, silhouettes, wires, …
  • Meshes
    • Bezier nets, lattices, cages, …
  • Other shapes
    • Deformation transfer: learning deformation from other shapes

本文出自CaterpillarStudyGroup，转载请注明出处。 https://caterpillarstudygroup.github.io/GAMES102_mdbook/