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Mathematical Progress in Expressive Image Synthesis II

Part of the Mathematics for Industry Book Series (volume 18)

Editors: Ochiai, Hiroyuki; Anjyo, Ken

DOI: 10.1007/978-4-431-55483-7

ISBN: 978-4-431-55482-0

Publisher: Springer Japan - Springer Journals

Jun 11, 2015

1 - 10 of 14 Chapters

Available

A Geometric Approach to Elasticity, Contact, and Design

Grinspun, Eitan

Pages: 3 –7

[Computer graphics and animation applications require mathematical models and simulation codes that capture the qualitative, characteristic behavior of a physical system, even at very coarse discretizations. We describe numerical tools based on ideas from discrete differential geometry (DDG) and...
Available

Computer Graphics in Minimal Surface Theory

Fujimori, Shoichi

Pages: 9 –18

[We give a summary of the computer-aided discoveries in minimal surface theory. In the later half of the 20th century, the global properties of complete minimal surfaces of finite total curvature were investigated. Proper embeddedness of a surface is one of the most important properties amongst...
Available

Explicit Formula and Extension of the Discrete Power Function Associated with the Circle Patterns of Schramm Type

Ando, Hisashi; Hay, Mike; Kajiwara, Kenji; Masuda, Tetsu

Pages: 19 –31

[We consider the discrete power function introduced by Bobenko, which is associated with the circle patterns of Schramm type. We first present an explicit formula in terms of the hypergeometric τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}...
Available

On Connectivity of Discretized 2D Explicit Curve

Sekiya, Fumiki; Sugimoto, Akihiro

Pages: 33 –44

[Preserving connectivity is an important property commonly required for object discretization. Connectivity of a discretized object differs depending on how to discretize its original object. The morphological discretization is known to be capable of controlling the connectivity of a discretized...
Available

Fast Implicit Simulation of Flexible Trees

Aubry, Jean-Marie; Xian, Xiao

Pages: 47 –61

[We present a model for flexible trees using constrained elastic rods, that can be solved implicitly in linear cost. We also demonstrate how to solve frictional hard contacts, as well as the inverse static equilibrium problem.]
Available

Probe-Type Deformers

Kaji, Shizuo; Liu, Gengdai

Pages: 63 –77

[Fast and easy-to-use deformers to warp 3D space are vital tools for both modeling and animation. In this paper, we introduce interactive and easy-to-manipulate shape deformers based on interpolation of affine transformations. We devise a new interface with probes, which are metaphors of...
Available

Controllable Skeleton-Sheets Representation Via Shape Diameter Function

Ďurikovič, Roman; Madaras, Martin

Pages: 79 –90

[The Shape Diameter Function (SDF) is a scalar function defined on the mesh surface expressing a measure of the diameter of the objects volume in the neighborhood of each point on the surface. In our approach we propose to compute internal skeleton, from which every mesh vertex is visible. There...
Available

Superresolution from Principal Component Models by RKHS Sampling

Lewis, J. P.; Anjyo, Ken; Rhee, Taehyun

Pages: 91 –102

[Principal component analysis (PCA) involves a signal that is sampled at some arbitrary but fixed and finite set of locations. Radial Basis Function (RBF) regression interpolates a-priori known data to arbitrary locations as a weighted sum of a (radial) kernel function centered at the data...
Available

From Mathematical Study of Visual Information Processing in the Brain to Image Processing

Arai, Hitoshi

Pages: 105 –110

[In this survey paper we will deal with applications of our study of mathematical models of visual information processing in the brain. In particular, we will show some of our results on sharpening, edge enhancement and extraction of contours of objects in an image.]
Available

Computational Creation of a New Illusionary Solid Sign with Shading Effect

Tomoeda, Akiyasu; Sugihara, Kokichi

Pages: 111 –116

[We present a computational method to create new illusionary solid signs inspired by two kinds of illusions; “hollow mask illusion” and “crater illusion”. The three-dimensional vertices of the illusionary solid sign are obtained by the straight line Voronoi diagram for a given base shape. Then,...

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