http://www.blacksmith-studios.dk/blog Physics, Mathematics, and Realistic Image Synthesis Wed, 26 May 2010 07:35:27 +0000 http://backend.userland.com/rss092 en Haven't produced any posts in a while (well at least not published any), I guess that's just an inevitable consequence of personal blogs! However, the explanation, as it usually is, is that I have been extremely busy with my theoretical studies and actually still am. I'm writing my dissertation over ... http://www.blacksmith-studios.dk/blog/?p=114 The derivation of the matrix for a general rotation in three dimensional Euclidean space is often encountered in strange forms. This is sometimes a bit puzzling until you have found your own way around it. In this post, I will not derive the expression, but show how the useful matrix ... http://www.blacksmith-studios.dk/blog/?p=64 In group theory Lagrange’s theorem is one of the most important in the theory of finite groups. Theorem 2.6 (Lagrange's theorem) The order of a subgroup H of a finite group G is a divisor of the order of G, i.e. |H| divides |G|. One evident, but funny, implication of the theorem ... http://www.blacksmith-studios.dk/blog/?p=55 I decided that it was probably time for a release of a graphical demo! Since I did not code up anything in relation to the participating media research I thought that this time I would do the research the other way around! This time I have done some research related ... http://www.blacksmith-studios.dk/blog/?p=19 I am proud to finally publish my article concerning analytic approaches for rendering participating medias. Enjoy! Abstract An analytical approach toward visualization of participating media is presented. The volume rendering equation is considered under the assumption that the in-scattering integral can be sampled as a Dirac delta function in the direction of ... http://www.blacksmith-studios.dk/blog/?p=5 In which direction is the development of relief mapping techniques heading? Techniques for visualizing surfaces of highly detailed geometry without exploiting the bandwidth to the stress limits by passing a huge amount of primitives down the graphics pipe have been a research topic for quite a while. Currently, techniques such as ... http://www.blacksmith-studios.dk/blog/?p=10 I was working on methods for determining the inverse of a specific function. Namely, a two dimensional bijective vector function of the following kind: In the particular problem the function is sampled on a regular grid so only a discrete map is available. It is therefore tempting to find the inverse ... http://www.blacksmith-studios.dk/blog/?p=6 I really wanted to post my newest research a few weeks ago entitled "Analytic Single Scattering in Participating Medias", but then I got stuck in a dilemma concerning the use of LaTeX in WordPress blogs, which I thought I had solved with mimetex. I will reveal the pre-abstract of the ... http://www.blacksmith-studios.dk/blog/?p=8 Before reading this very first blog entry I will like to inform the reader that knowledge about the radiosity algorithm may be helpful in order to follow the various discussions and derivations. Introduction In this entry I will show that the classical radiosity equation always can be rewritten such that the linear ... http://www.blacksmith-studios.dk/blog/?p=4 This is the first entry of this blog! In the time to come I will try and post various thoughts in the subjects of physics, mathematics, and computer graphics regularly, which I hope people will gain some motivation and benefits from. Since our server do not have LaTeX installed I ... http://www.blacksmith-studios.dk/blog/?p=1