Presentation
Inverse Tiling of 2D Finite Domains
DescriptionA K-hedral tiling of a 2D finite domain is a covering of the domain with tiles without gaps or overlaps, where each tile is congruent to one of the K distinct shapes called prototiles. K, the number of prototiles, is preferred to be as small as possible for congruent tiling appearance and reducing fabrication cost, e.g., by molding. Typically, a forward approach is adopted to produce Khedral tilings by prescribing a set of prototiles and placing prototile instances (i.e., tiles) to cover the input domain. However, the prescribed prototile set may not be sufficient to tile the domain (for small K) or may lead to tiling results with excessive prototiles more than needed (for large K).
In this work, we formulate a new tiling problem called inverse tiling for producing K-hedral tilings in 2D finite domains, where the prototile set is inversely modeled to fit the input domain instead of being prescribed. Since the prototile set is unknown, inverse tiling allows exploring a large search space to discover a minimized number of prototiles for tiling the input domain. To solve the inverse tiling problem, we propose a computational approach that progressively builds the prototile set while tiling the input domain, starting from a prototile set with a single element. Once a tiling result is obtained, the approach further reduces the number of prototiles by locally re-tiling the input domain to eliminate prototiles with few instances. We demonstrate the effectiveness of our inverse tiling approach on a variety of finite domains, evaluate its performance in scalability and K minimization, and compare it quantitatively with forward tiling approaches.
In this work, we formulate a new tiling problem called inverse tiling for producing K-hedral tilings in 2D finite domains, where the prototile set is inversely modeled to fit the input domain instead of being prescribed. Since the prototile set is unknown, inverse tiling allows exploring a large search space to discover a minimized number of prototiles for tiling the input domain. To solve the inverse tiling problem, we propose a computational approach that progressively builds the prototile set while tiling the input domain, starting from a prototile set with a single element. Once a tiling result is obtained, the approach further reduces the number of prototiles by locally re-tiling the input domain to eliminate prototiles with few instances. We demonstrate the effectiveness of our inverse tiling approach on a variety of finite domains, evaluate its performance in scalability and K minimization, and compare it quantitatively with forward tiling approaches.
Event Type
Technical Papers
TimeTuesday, 16 December 202511:23am - 11:34am HKT
LocationMeeting Room S421, Level 4