And last but not least if you like Xinha Here please consider making a donation to support further development using the PayPal donation button in the upper right.  I get a lot of support requests everyday but practically no donations.  If you like free software please support your free software developers.

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So what does a hypercube look like? Well obviously, due to limitations of 3-d space, we cannot see a four dimensional object. However, using the same techniques that one uses when drawing a 3 dimensional cube onto a two dimensional piece of paper we can project an image of a four dimensional hypercube (or the wire frame of one) into three dimensions.

POV-RAY is a 3-d is a ray tracer. It takes simple text file descriptions of a three dimensional scene and renders it into a graphics scene. So here is the challenge. Given a set of 4 vectors (four dimensional vectors) that represent a four dimensional object (such as a hypercube) how can these be projected into a 3-d scene.

Before we can work with 4 vectors we must first “teach” POV-RAY how to manipulate 4 vectors.

 #macro v4dot (A, B)  //4d dot product
       A.x*B.x+A.y*B.y+A.z*B.z+A.t*B.t
 #end

#macro v4len(V)  //Length of 4 vector
     sqrt(v4dot(V, V))
 #end
 
 #macro Norm4(V)  //Normalize 4 vector
     V/v4len(V)
 #end
 
#macro Cross4 (U, V, W)  // 4d cross product

    // Calculate intermediate values.

    #local A = (V.x * W.y) - (V.y * W.x);
    #local B = (V.x * W.z) - (V.z * W.x);
    #local C = (V.x * W.t) - (V.t * W.x);
    #local D = (V.y * W.z) - (V.z * W.y);
    #local E = (V.y * W.t) - (V.t * W.y);
    #local F = (V.z * W.t) - (V.t * W.z);

    // Calculate the vector components.

    #local X = ((U.y * F) - (U.z * E) + (U.t * D));
    #local Y = ((U.x * F) + (U.z * C) - (U.t * B));
    #local Z = ((U.x * E) - (U.y * C) + (U.t * A));
    #local T = (-(U.x * D) + (U.y * B) - (U.z * A));
    
    <X, Y, Z, T>
#end

The next step is to translate the 4 dimensional vectors into the 3 dimensional eye coordinates using a transformation matrix.

#macro v4to3 (A)
        #local V = v4dotM(A-From4, TM);  //Translate to eye coordinates
        #if (Per4 = 1)
                #local R = (V.t*Tp);  //4d Perspective
        #else
                #local R = v4len(From4); //4d Orthogonal
        #end        
        <V.x/R,V.y/R,V.z/R>  //3d vector
 #end

#declare Tp = tan((2*pi/360)*45);

#declare From4 = <4, 0, 0, 0>;
#declare To4 = <0, 0, 0, 0>;
#declare Up4    = <0, 1, 0, 0>; 
#declare Over4  = <0, 0, 1, 0>; 
#declare Per4 = 1;  //1- Perspective 0- Orthogonal

#declare D = Norm4(To4 - From4);
#declare A = Norm4(Cross4(Up4, Over4, D));
#declare B = Norm4(Cross4(Over4, D, A));
#declare C = Cross4(D, A, B);

#declare TM =   //Translation Matrix
array[4]
{ A, B, C, D }

#declare T = pi/2*clock;
#declare From4 = 4*<cos(T), 0, -sin(T), 0>;

#macro point3d (P, pradius, pcolor)
 sphere
 {
  P
  pradius
  pigment { pcolor }
 }
 #end
  
 #macro point4d (P, pradius, pcolor)
        point3d (v4to3(P), pradius, pcolor)
 #end 
 
 #macro vector3d (S, E, vradius, vcolor)
 #if (!((S.x = E.x) & (S.y = E.y) & (S.z = E.z)))
 cone
 {
  S, vradius,
  E, vradius
  pigment { vcolor }
 }
 #end 
 #end
 
#macro vector4d (S, E, vradius, vcolor)
 vector3d (v4to3(S), v4to3(E), segradius, vcolor)
#end

Hypercube.pov v1.0 4.57 kb

Special thanks to Steven Richard Hollasch and his Thesis on Four-Space Visualization of 4D Objects (August 1991)

The second major improvement is the Xinha Here! tool bar. This is a Xinha plugin like many others Xinha plugins except that it adds items that are only available in Xinha Here. These include “Save As” and “Open” for when you want to save and load the HTML text. This makes it very convenient to save posts for later use. Also on the Xinha Here! tool bar you have a restore feature. This will recover the last post you made using Xinha Here. Future versions may include automatic backups as you type.

In addition I have fixed a few bugs and added an auto update feature. Now you can update Xinha Here directly from the browser if you are using Firefox 1.5.

And now for some begging! I first posted Xinha Here exactly two months ago today. In the last two months I’ve seen Xinha Here grow surprisingly fast in popularity. Searching for “Xinha Here” in google returns 38,200 hits. My website traffic has gone from around 30 unique visitors per day to nearly 400. According to my count the latest version alone has been downloaded 3070 times. You may notice in the upper right hand corner of this blog is a “Make a Donation” button. I have a similar button on my extensions page. At this time I have received only two donation of $1 each (both from the same person). So while news of Xinha Here has spread quickly and my traffic is increasing I have made practically no money. Sure I know that I can never get rich making free software but I think I deserve a little more then $2! If everyone that downloaded Xinha Here gave just a little I could at least recover most hosting costs. That would be nice!

If you like Xinha Here please consider making a donation to support further development using the PayPal donation button in the upper right.

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I also wanted to mention that the next version of SpellBound (development version here) will include spell check as you type.  It works great within Xinha and Xinha Here.

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Install Xinha Here! version 0.5 (Firefox 1.0 – 1.5)

Yo Qued� Xinha Aqui!

This isn’t my first experience with a “web hit”. When Neverwinter Nights came out in 2002 I was the first to create a custom tile set within a few days of it’s release. I saw Labtek’s custom tileset spread across the Internet so fast it made my head spin. I was even recognized by Bioware for being incredibly active in the Neverwinter Nights community:

Labtek (Custom Content Builder) – Creator of the Winter Tileset and recognized for his work in cracking the Tileset mysteries, Labtek has made it possible for the community to make for significant changes to existing and new tilesets. There will always be a need for a new and different terrain and through Labtek’s pioneering work those new terrains will soon be in created and used by technical artists, modelers and module designers.

My second “web hit” was in 2003 when I developed Coordinate Exchange for MapPoint. This was a MapPoint plugin that allows users to exchange GPS data between MapPoint and many different file formats and GPS units.  I still plan on releasing a new version but now that Visual Basic 6.0 is so Pass� I’ve been delaying.

These previous “web hits” were fairly popular but had a limited audience. There were only so many MapPoint users and NWN players out there. This Firefox extension may prove to be more popular then either of these. Maybe I’ll finally reach status of web celebrity and unbelievable riches! Ok, maybe not. Giving out free software has never been successful for me. What do I expect? Well, really nothing. Does a stamp collector expect to make millions of their hobby? Well, I’m sure some do. How about model train enthusiasts or rocketry buffs? No I don’t expect to become a web celebrity (webrity?) or make anywhere near enough money to compensate for my time. Programming and blogging is a hobby and nothing more. I’ll be keeping my day job.

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Install Xinha Here! version 0.4 (Firefox 1.5 only)

In other “Xinha Here” news I spotted my extension at:

• Leon Kilat ::: The Cybercafe Experiments
• Carlton Bale�s Blog
• Slacker Manager
• New Trommetter Times
• asolo.dk
• Tecnorantes
• rumore – sideblog of redeunder

A day or so later  I noticed that Mozilla is running an "Extend Firefox" competition.  That gave me the idea… why not package Xinha as a Firefox extension.  That way not matter what site I visit I can have my favorite HTML editor handy.  Most likely not a worthy entry into the contest but an interesting project non the less.

The following weekend (ignoring pleads from my wife to clean the house or other such nonsense) I developed what I’m calling Xinha Here!  With this extension you can add HTML to any textbox or textarea on any website.  You simply select the textbox (or textarea), right click, and selected Xinha Here!  Up will pop a Xinha editor for your WYSIWYG pleasure.  Press OK and the raw HTML is pushed back to the original textbox.  Simple as that.  I would also suspect that because the Xinha source and images are located within the extension (not on the web) it may be faster to load then the web version.

Xinha Here! can be downloaded here. Beware that this is my first Firefox extension and only version 0.1 so there are bound to be some bugs.  I’ve only tested it with Firefox 1.0.7 so your mileage may vary.  The current implementation doesn’t allow any of customization of Xinha.  Enjoy!

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