Supanut Chaidee

Chiang Mai University | CMU · Department of Mathematics

This paper presents a method for approximating spherical polygonal tessellations with spherical Laguerre Voronoi diagrams when the generators of the tessellations are not available. The approximation method uses a polyhedron corresponding to the spherical Laguerre Voronoi diagram, and the problem is reduced to an optimization problem. The method is...

We propose a model for generating tessellation patterns on the sphere using the spherical Laguerre Voronoi diagram which satisfies the real-world assumptions. The generator pushing model is presented to generate the tessellation dynamically. The simulations were done for the different distribution of spherical circles on the sphere, and the results...

Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained vertex norms are distinct or repeated for, at most, four points. However, we proved that there always exists a convex configuration in the three-dime...

The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them. Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to achieve land-use optimization. However, such algorit...

This paper investigates the properties of Voronoi diagrams in which the generators are on an Archimedean spiral curve with various divergence angles. We apply geometrical properties to construct algorithms to recognize whether the given Voronoi diagram is the Archimedean Voronoi diagram from linear parastichy patterns.

We propose the necessary and sufficient conditions which fit a square in a trapezoid when the trapezoid is cut from a triangle parallel to its base. The conditions are presented in the form of the largest fitting square on each trapezoid side when the original triangle is right and acute triangle such that the sum of base angle is greater than π/2.

Climate change is a crucial cause of health issues, as reported in many studies. Temperature is one of the important factors related to extreme weather. Chiang Mai, the center of the north of Thailand, is also affected by temperature changes that have led to many outpatient visits. Better information will help the health service to be well-prepared...

Given a set of radii measured from a fixed point, the existence of a convex configuration with respect to the set of distinct radii in the two-dimensional case is proved when radii are distinct or repeated at most four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we ca...

In this work, we devise an efficient method for the land-use optimization problem based on Laguerre Voronoi diagram. Previous Voronoi diagram-based methods are more efficient and more suitable for interactive design than discrete optimization-based method, but, in many cases, their outputs do not satisfy area constraints. To cope with the problem,...

In nature, there are many tessellation patterns on curved surfaces that look like Voronoi diagrams. Typical examples are the patterns found on fruit skins. Verifying that a given tessellation is a Voronoi diagram will be useful for constructing mathematical models of polygonal patterns. However, the data are usually obtained as a 2D projected image...

In this paper, we construct an algorithm for determining whether a given tessellation on a sphere is a spherical Laguerre Voronoi diagram or not. For spherical Laguerre tessellations, not only the locations of the Voronoi generators, but also their weights are required to recover. However, unlike the ordinary spherical Voronoi diagram, the generato...

There are many natural phenomena displayed as polygonal tessellations on curved surfaces, typically found in fruit skin patterns. The paper proposes a method to fit given tessellations with spherical Laguerre Voronoi diagrams. The main target of this paper is fruit skin patterns such as jackfruit and lychee covered by tessellation patterns in which...

Optimal partitioning of a square is the search for the least-diameter way to partition a unit square into n pieces. The problem is here solved for some small n values. Although this problem has recently been approached by transforming the problem into a graphical enumeration, the algorithm had too large a computational cost for cases of n >= 7. In...

There are many phenomena that generate polygonal tessellations on surfaces of 3D objects. One interesting example is the jackfruit, a multiple fruit found in the tropics. A recent study found the best-fit spherical Voronoi diagram from a photo of jackfruit skin, but the optimization was relative to the radius of the sphere and the height of the spi...

Optimal partitioning of a square problem is the search for the least-diameter way to partition a unit square into n pieces. In 1958, Wanceslas solved the problem for n = 3 in [6]. Later in 1959, Page settled the case n = 5 in [5]. In 1965, Graham studied a similar problem on partitioning an equilateral triangle into n pieces for n up to 15. It is w...

Optimal partitioning of a square problem is the search for least-diameter way to partition a unit square into n pieces. The problem has been settled for some cases. Unfortunately, the proof for each n has its own unique trick with no relation to the proof for the other cases. In this work, we introduce a new approach to this problem. We construct a...