page_title: Caustic (optics)
section_title: Design pipeline
hierarchical_section_title: Caustic (optics) / Caustic engineering / Optimal-transport-based caustic pattern design / Design pipeline
caption_attribution_description: English: Optimal transport pipeline
context_page_description: In optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light. Therefore, in the photo on the side, caustics can be seen as patches of light or their bright edges. These shapes often have cusp singularities.
context_section_description: Here considering only refractive caustic, the objective can be determined as follows (similar principle for reflective caustic with different output):
  Input: image of pattern to be obtained after propagating lights through the material, given the light source position.
  Output: caustic geometry on the receiver (flat solid surface, e.g.: floor, wall, etc...)
  In order to achieve the target pattern, the surface where light refracts through and exits to the outer environment must be manufactured into certain shape to achieve desired pattern on the other side of the material.
  As mentioned, given an input image, this process will produce the similar caustic pattern as the output. In principle, there are two core stages with each includes two sub-stages:
  Solving Optimal Transport Problem
  Compute Target Light Distribution
  Compute Mapping from Initial Distribution to Target Distribution
  Optimizing Target Surface
  Compute Normal Representation of Surface
  Surface Refinement
caption: Optimal-transport-based caustic design
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