It is important for expanding our flexibility in the practical production, that we continue discussions on several research topics related to practical pipelines for film making in computer graphics. In this seminar, we invite researchers in Geometry and Topology and they give us talks about a relationship between their research topics and computer graphics. We also have a discussion on practical possibilities of film making tools from the mathematical viewpoint. We expect that all the participants are researchers in Mathematics, Computer Science, or Computer Graphics, or students studying these subjects.
If you are not any specialist as noted above and you'd like to attend our seminar, please contact to the corresponding organizer: Kosaku Nagasaka in advance. We will give you more detailed information on our seminar.
Please note that this workshop is co-organized with Kobe Studio Seminar for Studies with Renderman.
For the participants, we would like to cite the following books for your preparations in advance.
The following papers are related to the talks, and are helpful for your preparations in advance.
In addition to the above documents, the following sites and paper may be useful.
The following papers are useful for the participants (this information added after the workshop).
Our current movie script required a challenge of story-telling method accompanied with a specialized appearance by shading. In this short talk, I give a brief review of our reconstructed in-house package for production and research tools of both math and CG, to realize the main idea of this production.
Eversing a spheare means to turn a sphere in the 3-space inside out. It is allowed that a surface passed though itself, but punching and pinching are forbidden. S. Smale first proved in 1958 that it is possible to evert a sphere. Since then several visualizations are given. In this talk, we describe a new way of eversion where the behavior of apparent counter is quite simple. We also visualize how the curves of self-intersection are deformed. This is a joint work with Minoru Yamamoto (Hirosaki University).
In Euclidean 3-space, a ruled surface is called developable if it has zero Gaussian curvature. A developable surface is a mathematical model of a surface crafted by 'paper', such as a plane, a cylinder and a cone. In this talk, I will introduce topics of developable Möbius strips related to the geometry, topology and singularity.
3D-XplorMath is a freely available Mathematical Visualization program developed by Richard Palais (UC Irvine), Hermann Karcher (Univ. Bonn) and their collaborators. 3D-XplorMath is designed to make it easy for anyone to see concrete visualizations of many kinds of mathematical objects. In this talk, I would like to introduce 3D-XplorMath project. I will also show some examples of utilization of 3D-XplorMath in education and research. 3D-XplorMath is contained in a Linux system "MathLibre". I will introduce MathLibre project and math softwares contained in it.
A surface in 3-dimensional Euclidean space R^3 is called a minimal surface if it is a critical point of the area functional. Equivalently its mean curvature vanishes. On the other hand, a critical point of the Willmore functional, which is a conformal invariant, is called a Willmore surface. In this talk we discuss the relationship between compact Willmore surfaces and minimal surfaces with flat-type ends. I would like to explain visualization of minimal surfaces and Willmore surfaces applying the Weierstrass-Enneper representation formula.
In 1950s Fermi-Pasta-Ulam conducted numerical experiment of mode energy of non-linear lattice model. Surprisingly they observed a quasi-periodic phenomenon. Their experiment suggested that their non-linear model is close to an integrable system. In fact, in 1970s M. Toda discovered a completely integrable non-linear lattice, which is nowadays called a Toda lattice. In this talk we will discuss integrability and non-integrability of non-linear lattices using 3D-XplorMath.
We are interested in reviewing the fundamental technologies for CG from the theoretical viewpoint, reviewing technologies for mathematical objects from the both of theoretical and technical viewpoints, and reviewing relations between technologies for CG and Mathematics. It may require a bit complex discussion to state some relationship among their technologies and methodologies, hence we hope that their crossing point may have a lot of informations. In this short discussion, we would like to have many frank comments for CG from mathematicians, comments for mathematical objects from the viewpoint of CG, and discussions on how to continue to study the relation between CG and Mathematics.
On 29th June, a proposal talk will be given, which is of KSS Projects for Communication: Low Dimensional Topology and Computer Graphics. We will have discussions on this topic at the workshop on October 25-26th.
There are several ways how one is interested in visualizing deformations of surfaces such as the sphere eversion mentioned in my previous talk on June 28. My initial interest came from the study of knots and surfaces. We discuss how to understand the shape and characteristics of surfaces by drawing them.