Re: point to plane projections and algebra

[Doug Lua <douglua@...>]

On 12/18/2010 12:25 AM, Dirk Laurie wrote:
> On Fri, Dec 17, 2010 at 06:39:55PM +0200, en dator wrote:
> a=point(1,1,1); b=point(4,5,6)
> print(a:norm()) -->  1.7320508075689 i.e. sqrt(3)
> print(b-a)      -->  (3,4,5)
> print(b%a)      -->  (-1,0,1), component of b orthogonal to a

I like this use of '%'; it's quite natural. I've also added the __call 
metamethod rather than :new(). I use this for all my newer libraries but 
never updated LA.

> So my recommendation is: write your own, and enjoy the feeling of
> power you get from having mastered metatables and metamethods!

Highly recommended.

I don't think my code is too difficult to read, but it is not as well 
commented as my newer packages. And I did find a major bug. Perhaps I 
should have run it through more rigorous tests. The setmetatable() call 
in Vector:new() should have Vector for its second argument rather than 
self. Similarly, Matrix:new() should have Matrix for the second argument 
to its setmetatable() call.

To get the distance between two points (points are represented by 
Vectors), add:

function Vector:distance_to(other)
   return (other - self):len()
end

To get the projection of one vector onto another, or to find an 
orthogonal vector (like b % a above), add:

function Vector:unit()
   return self / self:len()
end

function Vector:projection_onto(other)
   return other * (self:dot(other) / other:dot(other))
end

function Vector:orthogonal_to(other)
   return self - self:projection_onto(other)
end

Vector.__mod = Vector.orthogonal_to

I've updated http://www.dkrogers.com/lua/LA.zip to include these 
changes, also including Dirk's test case for '%'. See LA_test.lua for 
sample usage.

--
Doug Rogers