LOD HIERARCHIES

• SCENE: a collection of individual models (chairs, cars, teapots, etc).
• LOD Hierarchy for (an original) model M₀: H=(M_0, M_1, ..., M_k) where each M_i is a simplification of M_i-1.
• Typically, k5.
• SIMPLIFICATION ALGORITHM:
  M_iM_i-1 by an application of algorithm.
• MEASURE OF DISTORTION:
  - distance function d(M₀,M_i)
  - E.g. Hausdorff Measure
• MEASURE OF SIMPLICITY:
  - SIZE, K_i=|M_i| = number of vertices, edges and faces.
  - (simplification target) K_i< c.K_i-1 for some 0<c<1.
• TRADEOFFS BETWEEN THE TWO MEASURES:
  - minimize distortion eps and maximize simplicity K.
• TWO KINDS OF SIMPLIFICATION PROBLEMS:
  - MIN-DISTORTION PROBLEM: Given M₀ and K, find M₁ of minimal size subject to |M₁| <K.
  - MIN-SIZE PROBLEM: Given M₀ and eps, find M₁ of minimal distortion subject to d(M₀,M₁) <eps.
• USING LOD MODELS:
  Choose M_i based on perceptual Importance of model in scene.
• MEASURES OF PERCEPTUAL IMPORTANCE?
  - (usually) Real estate on screen when rendered.
  - (propose) Distance from gaze point.
• Parameter for Simplification:
  - Target complexity (K>0)
  - or, Bound on distortion (eps>0)