related? Can be this rather simple (from a pure math viewpoint) research program doable and moreover DONE by anybody?
Let me explain. My wonder came after searching with google for
– “Digital materialization” AND “euclideon” – no answers
– “Digital materialization” AND “Fractal image compression” – no answers
– “Fractal image compression” AND “euclideon” – no answers
1. Cite from the Digital Materialization Group homepage:
Digital Materialization (DM) can loosely be defined as two-way direct communication or conversion between matter and information that enable people to exactly describe, monitor, manipulate and create any arbitrary real object. DM is a general paradigm alongside a specified framework that is suitable for computer processing and includes: holistic, coherent, volumetric modeling systems; symbolic languages that are able to handle infinite degrees of freedom and detail in a compact format; and the direct interaction and/or fabrication of any object at any spatial resolution without the need for “lossy” or intermediate formats.
DM systems possess the following attributes:
- realistic – correct spatial mapping of matter to information
- exact – exact language and/or methods for input from and output to matter
- infinite – ability to operate at any scale and define infinite detail
- symbolic – accessible to individuals for design, creation and modification
As far as I understand, this works based on Function Representation (FREP), see HyperFun.org . The idea is to define an object in say, by a function , which describes the object as the set of points where . Start with a small library of functions (for example polynomials) and then construct other functions by using min, max, and so on. Therefore an object is described by a tree, with leaves decorated by functions and nodes decorated by min, max, … , operations. This is a very simplistic, but fundamentally precise description. The main point is that there is no object (defined for example by a mesh in space), but instead we may check if a point in space belongs or not to the object by evaluating the sign of . Moreover, translations, rotations, dilations (or any other easy to implement change of parametrization of the space) are implemented by composition with the function which describes the object.
In particular, we may easily pass to polar coordinates based on the point of view and stay in this coordinate system for visualization.
2. Fractal image compression is based on the fact that any compact set (like an image, described as a compact set in the 5D space = 2D (spatial) times 3D (RGB levels)) can be described as a fixed point of an iterated function system.
This brings me to
PROBLEM 1: Is there any version of the Hutchinson theorem about fixed points of IFS, with the space of compact sets replaced by a space of FREP functions? Correspondingly, is there a “FREP compression algorithm”?
My guess is that the answer is YES. Let’s assume it is so.
Hi every one , I’m Bruce Dell (though I’m not entirely sure how I prove that on a forum)
Any way: firstly the system isn’t ray tracing at all or anything like ray tracing. Ray tracing uses up lots of nasty multiplication and divide operators and so isn’t very fast or friendly.
Unlimited Detail is a sorting algorithm that retrieves only the 3d atoms (I wont say voxels any more it seems that word doesn’t have the prestige in the games industry that it enjoys in medicine and the sciences) that are needed, exactly one for each pixel on the screen, it displays them using a very different procedure from individual 3d to 2d conversion, instead we use a mass 3d to 2d conversion that shares the common elements of the 2d positions of all the dots combined. And so we get lots of geometry and lots of speed, speed isn’t fantastic yet compared to hardware, but its very good for a software application that’s not written for dual core. We get about 24-30 fps 1024*768 for that demo of the pyramids of monsters. The media is hyping up the death of polygons but really that’s just not practical, this will probably be released as “backgrounds only” for the next few years, until we have made a lot more tools to work with.
Assuming that we take a database representing a 3D very complex object (like a piece of landscape) and we convert it, by using a FREP compression algorithm, into a tree as described at point 1, then it becomes easy to imagine how the Unlimited Detail algorithm might work.
Problem 2: Given a FREP representation of a collection of 3D objects, describe an efficient sorting algorithm which uses the representation and outputs the part of the union of object visible from a given point at infinity.
Conclusion: unless this is utter giberish, the modus operandi of an “unlimited detail” algorithm could be the following:
1)- start with a database of a collection of 3d objects and compress it into a FREP format
2)- perform a “mass 3d to 2d conversion”, by using a solution of the problem 2, in polar coordinated from the viewpoint.