The Periodic Temple of Primitives

rolliebollocks · Post by **rolliebollocks** » Jul 06, 2010 5:42

Generating Sin/Cos for Line Segments

The sin or cos of a line is a function which returns any value between the lower and upperbounds given some "angle" theta. The sine of line returns a point. The cos of a line returns a point. The tangent of a line also returns a point. Behold:

Proposition 1: The sin and cos of a line can be expressed like this:

rSIN(theta).x = (theta mod delta_x) + x_lowest_bound
rSIN(theta).y = (theta mod delta_y) + y_lowest_bound
rCOS(theta).x = x_highest_bound - (theta mod delta_x)
rCOS(theta).x = x_highest_bound - (theta mod delta_y)
rTAN(theta).x = y.x / x.x *(x.x<>0)
rTAN(theta).y = y.y / x.y *(x.x<>0)

<Results>

A line can be generated with

rSIN(0->length-1)
rCOS(length-1->0)

And I have no idea what TAN is going to do.

<EDIT>

Fixed mistake in iterator.

Please note, the purupose of this code is to figure out a way to iterate from one end of the line to the other, iterate along the sides of polygons, iterate for the pure joy of iteration, iterate to fill polygons, iterate to fill polygons with pixel data, iterate for the children who will never know the joys of iteration...

rolliebollocks · Post by **rolliebollocks** » Jul 06, 2010 23:50

Olestra: A New Constant

Proposition 1-n :

Let's say we have a unit circle, and we make a node at the North, South, East and West Poles such that:

NorthPole = center.x, center.y-radius
SouthPole = center.x, center.y+radius
East = center.x+radius, center.y
West = center.x-radius, center.y

Let's say we draw some square which connects Never Eat Shreaded Wheat in that order.

The ratio of any side, to the corresponding Arc (the arc made from the chord) is about: .9003136

I call it: The Olestra after the single most diarrhetic substance I have ever known.

Richard · Post by **Richard** » Jul 07, 2010 1:21

Quite fascinating; from both the mathematical and the psychological viewpoints.

rolliebollocks · Post by **rolliebollocks** » Jul 07, 2010 13:41

You know Richard, it isn't nice to make fun of bi-polar people like that.

:)

dodicat · Post by **dodicat** » Jul 07, 2010 16:34

rolliebollocks wrote:Olestra: A New Constant

Proposition 1-n (Steinerized by dodicat) :

Let's say we have a unit circle, and we make nodes all around us , scattered right around the horizon, beyond land and sea:

each node = center.polar(x), center.polar(y)

Let's say we draw some polygon edge which connects one node to the next, until it gets back to the first, all the bleeding way round and manages to make itself regular.

The ratio of half the length of the polygon edge multiplied by the number of sides of the polygon -- to the distance of the node tends to PI with ever increasing nodes

I call it: SCOTCH PIE by Steiner and tribulation, after the single most diarrhetic substance I have ever known.

Code: Select all


dim as integer xres,yres
screeninfo xres,yres
screenres xres,yres
dim as double r,bigr,num,x,y,cx,cy,k
cx=xres/2 'centre of ring
cy=yres/2
k=200  'size of ring
dim n as integer  'number of circles
dim as double pi=4*atn(1)
#define rad *pi/180
start:
print
input "How many nodes do you wish? ",n
if n<=1 then end
cls
 for z as double=0 to 2*pi step 2*pi/n
  num= (45*(2*n-4)/n) rad
    num=cos(num)
    r=num/(1+num)
    bigr=((1-r))*k  'radius of ring
    
    r=(r)*k 'radius of circles
    x=cx+bigr*cos(z)
    y=cy+bigr*sin(z)
    
    circle(x,y),r
    
next z
print"SCOTHH PIE RATIO"; n*r/(bigr)
goto start
'next n

sleep

rolliebollocks · Post by **rolliebollocks** » Jul 07, 2010 17:12

Oh dude that's awesome. I was just working on something like that.

A quick thing on polar coordinates and then correlaries of Olestra...

I wiki'd polar coordinates, in idea space this is really different. Bipolar coordinates really are appropo here. Instead of defining something in terms of it's center, we define it in terms of its range of value and distance from the upper and lower bounds. I'm too amused by the irony of that.

I can express a circle like this too, and polygons are implicit in lines. But...

A new shape has emerged from Olestra. If we take the unit circle, and unit square in circle and then draw lines from North to South and East to West... We have four right triangles. If we lose the hypotenous, and add the arc, we have some new shape...

a^2+b^2 = c^2/Olestra

:)

Bipolar coordinates...

agamemnus · Post by **agamemnus** » Jul 07, 2010 18:01

PS... it's primitives...

rolliebollocks · Post by **rolliebollocks** » Jul 07, 2010 20:06

@Agamemnus

You're right thanks. The root of the term is primate, thus I forget. It's also why anthropolgists say "traditional" as opposed to "primitive" cultures, because you are essentially describing them (and yourself) in degrees of apishness.

dodicat · Post by **dodicat** » Jul 07, 2010 20:36

Hi Rollie~
Glad to see you are investigating this branch.
The above ring formations are actually a primitive (agamemnus is right), simulation of the station taken by the orbs in times of defence or protection, or if anything untoward is encountered.
They can hold station for hundreds of years, they utilise space detritus from the interstellar winds, as an anenome on the seabed, they waft in the cosmic breeze, and catch what they can without breaking formation.
To further conserve resources, they communicate with each other by osmosis.
They once stood the ring for 23,000 years.
They were exploring near the Lagrange point between Polaris and it's big planet, Bluto.
Orb 17 was in charge, Alias Captain Pugwash.
They encountered a space system paradox, they stumbled across a small black hole quite close to the Lagrange point, but on further investigation, they noticed that it was in fact green.
They immediately formed ring around the paradox and stood to.
They held station for 23,000 years, then one evening Pugwash noticed a motion within the paradox, it appeared to open up, unfold if you like.
Turned out that it wasn't a paradox at all, but Paddy Murphy awakening from a self induced type 3 space torpor.
Paddy got quite a shock to see he was surrounded by the ring, but he made his way over to orb 17, and from under his shirt, pulled out his medallion, which he always kept near his heart.
He showed it to Pugwash, and all was now clear.
On it was inscribed : Patrick Murphy: All Ireland interstellar hide and seek champion: dated October 350013.
No snakes can be seen in Ireland, and since the day and hour that Paddy woke up, no orbs have been seen in Ireland.

rolliebollocks · Post by **rolliebollocks** » Jul 08, 2010 2:04

@Dodicat

I read your thing like four times, and then had my girlfriend come over and read it. We both thought it was brilliant. There's a genre called flash fiction, short short stories I dunno if you've heard of it or read any. Most of what I've read is crap, but I hardly blame the genre for it.

There are a few places that might be interested in publishing it, but I don't think they'd pay you for it because the only people who are interested in flash fiction are writers. Same goes for poetry nowadays too.

At any rate, the only work I've been doing has involved moving, an awful process in an unseasonably warm july in Buffalo, NY. We moved in a rush because there was sewage coming up from the basement and the pumbing was poory constructed causing a build up feces in the basement.

That hasn't stopped me from doing notebook stuff on the bipolar line consequences.

I have decided the the new shape should be called PIE. Because it looks like a Pie, and Pies cause diarrhea , especially when they are inproperly stored.

I'm going to start my discoveries of this in a new post...

rolliebollocks · Post by **rolliebollocks** » Jul 08, 2010 2:43

PIE Corrollaries
~~~~~~~~~~

The are 4 PIE in a circle

If we remove the triangular portion of PIE we are left a half ellipse and we can derive the height using the Olestra constant and the pythagorean theorem.

We can derive any of this so long as we know either

1. the radius of the circle
2. the length of the side of the square

Is it a line or a circle?

It's a line... except that lbound-1 = ubound and ubound+1 = lbound. Therefor it is also a circle. If you remember the game Combat (Atari 2600), it was played on the surface of a 2d sphere. Continuity between extremes means circle.

But wait, it is definitely a line because it is iterated from a lower extreme toward an upper extreme, in fact defined in terms of its place and sequence on the line.

This is what happens to a circle when you try to fit into a one dimensional space. The component that would be it's height, is collapsed and forced into a temporal dimension. So the circle never really stops being a circle, it merely loses its extension in one dimension so that it can gain extension in another. Thus the periodic temple of primitives...

The the modular iterator functions like a time step looping back to position one as it passes beyond it's own length...

Therefore, we can say with some certainty, that it is a circle, and that circles can be used to express lines.

At any rate, tomorrow I'll work on the polygon filler. We'll see if its as fast as all that, and try to test mod functions against, a mul variant that does the same thing, and the fmod function.

This appears to be a lot less work than a ray caster would have to do.

Can other dimensions besides time be used?

Any dimension you can think of... Any property can be considered a dimension. You can stick any data into any place, any time... Let your imagination run wild. Anything can be a dimension (if you hold it right).

rolliebollocks · Post by **rolliebollocks** » Jul 08, 2010 17:22

Crap... this modulus formula only works inside the box (45 degree angles)...

Anyway... this doesn't negate the theory, it merely means I need more time in the notebook.

I will use the normals to calculate the sequence's data...

It will easier to translate this mini-bipolar system into polar coordinates also... In fact, it could replace the need for them entirely, considering the normals are sloping information that contain data that can be translated angularly.

@Dodicat

The beauty of your example, is that it's a polygon made up of circles with diameter length sides.

It's dressed like a circle. Very artistic. Math and Poetry will become one, and a higher reasoning shall emerge.

I think Nostradamus said something to that effect, maybe it was science and religion... Same difference really. Isomorphically speaking.

rolliebollocks · Post by **rolliebollocks** » Jul 08, 2010 17:48

For the record, in case anyone is curious.

I had at one point intended to write paper on Sh!t being isomorphically related to remainder and difference...

I do a lot of things that sound ridiculous but are actually related to stuff. Unfortunately it means that sometimes people think I'm mocking their field of learning, when in fact, I'm merely amusing myself at their expense.

Like the one time I wrote a paper on 4 dimensional objects/temporal objects relating it to the castration of freud...

If we castrate freud at t[0] then Freud is less than Freud at t[-1] and yet has gained the quality of testicallessness.

In fact the ball-less Freud is not(Freud) and Freud can only be understood relative to some temporal spot...

(sound familiar?) it's my line sequencer

The professor was not impressed.

B-

rolliebollocks · Post by **rolliebollocks** » Jul 08, 2010 18:10

*blush*

This works perfectly:

Code: Select all

dim as point2d res = (theta mod length) * this.DirectionVector01

rolliebollocks · Post by **rolliebollocks** » Jul 08, 2010 19:04

Proof of concept is completed:

http://www.imakegames.com/rolliebollocks/_RB_LIB.zip

Root/Examples/Polygon Demo 2.bas

I'm going to rename it a line demo... Has little to do with polygons really.

*sigh of relief*