Efek Diskritisasi pada Modifikasi Hypocycloid Menjadi CSCPP (Curve Stitching Connected Pseudo Polygon)

Tulisan ini membahas tentang pembuatan Curve Stitching berdasarkan efek diskritisasi kurva Hypocycloid yang dimodifikasi. Kurva yang dihasilkan dinamakan Connected Pseudo Polygon (CPP) karena berupa segibanyak yang berbentuk berdasarkan urutan cara menggambar serta diskritisasi titik yang digunakan. Yang dimaksud Curve Stitching disini adalah pembuatan ornamen dengan papan dan benang. Desain ini digunakan sebagai media bermain dalam kegiatan pelajaran atau kuliah matematika. Selain dengan benang, CPP juga dibentuk dengan kawat dan sedotan agar Desain yang sama dapat dibentuk dengan beberapa material yang cocok untuk penyusunan CPP. CPP ini digunakan sebagai media untuk mengilustrasikan inovasi matematika atau ornamen matematika

Bichromatic compatible matchings

ABSTRACT For a set R of n red points and a set B of n blue points, a BR-matching is a non-crossing geometric perfect matching where each segment has one endpoint in B and one in R. Two BR-matchings are compatible if their union is also noncrossing. We prove that, for any two distinct BR-matchings M and M , there exists a sequence of BR-matchings M = M1, . . . , M k = M such that Mi−1 is compatible with Mi. This implies the connectivity of the compatible bichromatic matching graph containing one node for each BR-matching and an edge joining each pair of compatible BR-matchings, thereby answering the open problem posed by Aichholzer et al. in [5]

Bichromatic compatible matchings

Abstract For a set R of n red points and a set B of n blue points, a BR-matching is a non-crossing geometric perfect matching where each segment has one endpoint in B and one in R. Two BRmatchings are compatible if their union is also non-crossing. We prove that, for any two distinct BRmatchings M and M , there exists a sequence of BR-matchings M = M 1 , . . . , M k = M such that M i−1 is compatible with M i . This implies the connectivity of the compatible bichromatic matching graph containing one node for each BR-matching and an edge joining each pair of compatible BR-matchings, thereby answering the open problem posed by Aichholzer et al. in [6]

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

Robot Kinematics INDUSTRIAL Classical Geometry Computer Vision GEOMETRY Computer Aided Geometric Design Image Processing Abstract Transforming Spanning Trees and Pseudo-Triangulations ∗

Let TS be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph TS where two members T and T ′ of TS are adjacent if T intersects T ′ only in points of S or in common edges. We prove that the diameter of TS is O(log k), where k denotes the number of convex layers of S. Based on this result, we show that the flip graph PS of pseudo-triangulations of S (where two pseudo-triangulations are adjacent if they differ in exactly one edge – either by replacement or by removal) has a diameter of O(n log k). This sharpens a known O(n log n) bound. Let � PS be the induced subgraph of pointed pseudo-triangulations of PS. We present an example showing that the distance between two nodes in � PS is strictly larger than the distance between the corresponding nodes in PS