Points and Vectors in 3D

[Simen kjaeraas]

Spacen Jasset <spacenjasset at yahoo.co.uk> wrote:

> On 13/03/2011 00:06, Bekenn wrote:
>> On 3/12/2011 2:20 PM, Simon wrote:
>>> I've done lots of 3d over the years and used quite a lot of different
>>> libraries and I've come to prefer code that makes a distinction between
>>> points and vectors.
>>
>> Agreed. This has some nice benefits with operator overloading, as well:
>>
>> vec v = ...;
>> pt p = ...;
>> auto p2 = p + v; // p2 is pt
>> auto p3 = p + p2; // error
>> auto v2 = v + v; // v2 is vec
>>
>> ...and with properties:
>>
>> p.x = 5; // p is pt, sets p._vals[0]
>> v.dx = 3; // v is vec, sets v._vals[0]
> Would you then go on to define things like a cross product as an  
> operator overload?

Can't see a fitting operator in D. Multiplication (*) is ambiguous at best
and no other operator seems fitting.

I'd like to have more of unicode's mathematical operators and symbols[1]
as operators in D, but currently that's beyond the horizon.

Use cases:

Vector a, b;

auto angle = a ∠ b;
assert( a == (b ∓ .1) );
assert( ( a ∟ b ) == ( angle == degrees( 90 ) ) );
assert( a ∥ b );
auto v = a ⋅ b;


Set c = ∅, d = ∅;

auto union = c ∪ d;
auto intersection = c ∩ d;

assert( "foo" ∈ c );
assert( "foo" ∉ d );
assert( d ∌ "foo" );
assert( c ∋ "foo" );

assert( d ⊂ c );
assert( d ⊅ c );

assert( ∏[1,2,3] == ∑[1,2,3] );

Of course, this requires a method for typing these symbols, something
which TeX has already solved for us.


[1]:  
http://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode

-- 
Simen