World: r3wp

:-) Make function libs!

Hard to adapt the formulas in the Wikipedia article, as they're in 
radians.

>> ? arctangent 
USAGE:
    ARCTANGENT value /radians

Maybe use /radians refinement?

Maybe atan2 should also have a /radians refinement.

I like that one too.

Project: func [

 {orthogonal projection of a point P on a line AB, return coordinates 
 [x y]}
	ax ay bx by px py
	/local sx sy ux uy ratio
][
	sx: bx - ax
	sy: by - ay
	ux: px - ax
	uy: py - ay
	ratio:  sx * ux + (sy * uy) / (sx * sx + (sy * sy))
	reuse [ratio * sx + ax  ratio * sy + ay]
]

I don't remember why i didn't use pair! as coordinates

Hmm, maybe to avoid path notations

Pairs in R3 are 32bit floats, decimals are 64bit.

I was for R2

and pairs are integers

And in R2 pairs are made up of integers.

AltME is a little slow for me today.

Ok, I know why I did it now ;-)

reuse?

reuse: funco [b][head reduce/into b clear []]

weird, I don't think anymore it was for R2

Not task-safe to reuse inline blocks like that.

And I don't like anymore that reuse too :-)

We should write an extension with such math/graphs functions

Maybe Brian you could start a wiki page for that purpose

Maybe it would be better for someone more familiar with and interested 
in mathematical issues to do so. Ladislav?

advise on how to colorize individual countries in a worldmap?
take a worldmap, draw background borders between the countries
and then floodfill the country via a central coordinate. 
is this a effective approach?

Not enough probably as you might jave country border touching other 
border of the same countryy. Countries are not simple polygon !

My first though is to have a map (an image) of countries where each 
country has its own color (call it a color-map) and another map of 
the same size that you display (diplay-map).
Then you have a block of pairs [country-name country-color].
So like this you have a relationship in any sense.


Click the displayed map => find the corresponding pixel in the color-map 
=> find the country name in the block.

To know the edge of the country you want to fill, just find all the 
pixels of this same color in the color-map and poke the corresponding 
pixel on the diplay-map.

jave=have

yes, a precolorized map would make things simpler. thx didec...