Web Site: https://www.victella.me

e-mail: email@victella.me

Victella©

The Personal Website of
Victor Vella

Site Last Updated:  25 October 2019

Victella Website

This website is intended to hold articles and other information that may be useful to some members of the public.  Currently, there are only two articles.  However, the sub-website, ETAC, contains the details and download of a new programming language.

NOTE: This website is written in Australian English.

Articles

There are currently only two articles to download.

An Analysis of B-splines

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This document presents an analysis of B-splines, especially uniform B-splines.  It explains the nature of B-splines and how they are constructed, and also how B-splines can be merged, joined, and separated.  The nature of B-splines is presented mathematically and geometrically.  Methods for converting B-spline control points to Bezier control points are also presented, as well as emulating arbitrary curves by means of B-splines.  A number of algorithms to implement B-splines is presented in an Appendix.  The document also contains an appendix discussing Bezier curves and splines. Some familiarity with mathematics is a prerequisite.

To download the free article (An Analysis of B-splines), click the following link.

Download: An Analysis of B-splines (655 kB)

The Collapse of Transfinite Cardinals

This is a free article of interest mainly to pure mathematicians.  The purpose of the article is to prove, rigorously, that the existence of transfinite cardinal numbers is untenable at this point in time because the traditional “proofs” of their existence are logically invalid.  The only transfinite cardinal number that may be admitted is À0.  The definition of transfinite cardinal numbers depends upon Cantor's theorem and the non-denumerability of the real numbers.  The “proofs” of those theorems depend upon Cantor's diagonal method.  The article proves that the diagonal method is self-contradictory, and consequently, the existence of transfinite cardinal numbers is untenable (except for À0).  The article does not prove, with certainty, that the transfinite cardinal numbers do not exist, but that they have not yet been validly proven to exist.  (Note that the word “exist” here has nothing to do with metaphysics; the word is a purely logical concept.)

To download the free article (The Collapse of Transfinite Cardinals), click the following link.

Download: The Collapse of Transfinite Cardinals (216 kB)

Websites

ETAC

This is the official sub-website for the ETAC programming language.