We organized the seminar in which we had a discussion on the relation between Invariant Theory (via Computational Invariant Theory) and CG from the viewpoint of known results in standard textbooks. However, we reached a conclusion that there still exist some unknown problems (e.g. practical effectiveness, computational time, quality and their relations). In this workshop following the previous one, we would like to have some further discussions on these topics (including with Renderman) with an expert in Computational Invariant Theory. Moreover, if possible, we will discuss on some possibilities of shading model, match move, compositing and the theory of sub surface scattering.
As noted in the front page of seminar, if 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 take a look at the following information for participants, to have better discussions.
One of the purpose of our current production is to give an "easily lose impression". To do this, we adapt ordinary methods together with repressed visual effect in screen space.
As a suggestion of later discussion, we talk about a way to reduce several methods of visual effect to inconspicuous methods in screen space.
This short talk gives an issue of the specification of EXR2.0 from the viewpoint of Symbolic Algebraic Computations.
We start with examples of invariants under an appropriate class of transformations, i.e., invariants of rotation, invariants of scalling, the discriminant of a quadratic form, etc. Next, we give a survey of plane projective invariants, e.g., cross ratio, etc.
We recall computational invariant theory for reductive groups due to Derksen. Using examples, we explain concretely the process of computing generators of invariant rings for reductive groups.
Transforming an object rigidly by rotation and translation, its image on a screen with a viewpoint changes. Perspective distorsion affects angles and lengths. For example, circles as object become ellipses as image. So, imaging the object in the transformation to the screen, neither angles nor lengths are not invariant. However the value of a projective invariant is unchanged by the imaging transformation. We reconstruct certain projective invariants in terms of computational invariant theory.
In the previous seminar, we had a discussion on some relations between Invariant Theory (and Computational Invariant Theory) and CG (e.g. rendering equation, shading techniques and so on). In this discussion, we would like to think about an expansibility of those relations including artistic techniques.
We would like to deepen the discussion in KSS, 2014. Therefore, we try to prepare the information on the topic before the discussion at the seminar. Please take a look at the followings for your preparation. If you know the original Studio Phones Seminar organized by Studio Phones, we follow the same scheme that all the participants are expected to prepare the everything.
The organizers have been interested in the following papers from the viewpoint of CG.
We think that materials and topics given in the following workshop and talks will be useful.
We recommend you to read the followings from the practical viewpoint.
Please refere the following softwares if you would like to use the actual one.
The organizers recommend you to read the following book from the mathematical viewpoint.