www.digitalmars.com         C & C++   DMDScript  

digitalmars.D.learn - Points and Vectors in 3D

reply Caligo <iteronvexor gmail.com> writes:
Given everything that D offers, what would be the best way to implement a
Point and a Vector type?  The same (x, y, z) can be used to represent
vectors, but a point represents a position, whereas a vector represents a
direction.  So, would you define two different structs for each? or define
and implement an interface?  a fixed array or POD members?
Mar 12 2011
parent reply Simon <s.d.hammett gmail.com> writes:
On 12/03/2011 20:51, Caligo wrote:

 Given everything that D offers, what would be the best way to implement
 a Point and a Vector type?  The same (x, y, z) can be used to represent
 vectors, but a point represents a position, whereas a vector represents
 a direction.  So, would you define two different structs for each? or
 define and implement an interface?  a fixed array or POD members?


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. Makes code easier to read and more type safe, though 
it's a bit more inconvenient when you need to mix things up.

I use:

struct pt {
   float[3] _vals;
}

struct vec {
   float[3] _vals;
}

Using the float[3] allows you to use vector ops:

pt	p0;
vec	v;

p0._vals[] += v._vals[];

You don't want an interface; you don't get anything more value type than 
points & vectors. In a modern 3d models you could be dealing with a 1/2 
million vertices.

-- 
My enormous talent is exceeded only by my outrageous laziness.
http://www.ssTk.co.uk
Mar 12 2011
parent reply Bekenn <leaveme alone.com> writes:
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]
Mar 12 2011
parent reply Spacen Jasset <spacenjasset yahoo.co.uk> writes:
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?
Mar 13 2011
parent reply "Simen kjaeraas" <simen.kjaras gmail.com> writes:
Spacen Jasset <spacenjasset 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 differen=






t

 libraries and I've come to prefer code that makes a distinction betw=






een

 points and vectors.


 Agreed. This has some nice benefits with operator overloading, as wel=




l:

 vec v =3D ...;
 pt p =3D ...;
 auto p2 =3D p + v; // p2 is pt
 auto p3 =3D p + p2; // error
 auto v2 =3D v + v; // v2 is vec

 ...and with properties:

 p.x =3D 5; // p is pt, sets p._vals[0]
 v.dx =3D 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 be=
st
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 =3D a =E2=88=A0 b;
assert( a =3D=3D (b =E2=88=93 .1) );
assert( ( a =E2=88=9F b ) =3D=3D ( angle =3D=3D degrees( 90 ) ) );
assert( a =E2=88=A5 b );
auto v =3D a =E2=8B=85 b;


Set c =3D =E2=88=85, d =3D =E2=88=85;

auto union =3D c =E2=88=AA d;
auto intersection =3D c =E2=88=A9 d;

assert( "foo" =E2=88=88 c );
assert( "foo" =E2=88=89 d );
assert( d =E2=88=8C "foo" );
assert( c =E2=88=8B "foo" );

assert( d =E2=8A=82 c );
assert( d =E2=8A=85 c );

assert( =E2=88=8F[1,2,3] =3D=3D =E2=88=91[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_Unico=
de

-- =

Simen
Mar 13 2011
next sibling parent reply Simon <s.d.hammett gmail.com> writes:
On 13/03/2011 14:11, Simen kjaeraas wrote:

 Spacen Jasset <spacenjasset 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.


Convention is to use ^ as cross product and * as dot product.

-- 
My enormous talent is exceeded only by my outrageous laziness.
http://www.ssTk.co.uk
Mar 13 2011
parent reply "Simen kjaeraas" <simen.kjaras gmail.com> writes:
On Sun, 13 Mar 2011 15:43:09 +0100, Simon <s.d.hammett gmail.com> wrote:


 On 13/03/2011 14:11, Simen kjaeraas wrote:

 Spacen Jasset <spacenjasset 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.


 Convention is to use ^ as cross product and * as dot product.


Really? I've never heard of it. Rather, everyone I've talked to about it
has said exactly what I did.

-- 
Simen
Mar 13 2011
parent Simon <s.d.hammett gmail.com> writes:
On 13/03/2011 15:29, Simen kjaeraas wrote:

 On Sun, 13 Mar 2011 15:43:09 +0100, Simon <s.d.hammett gmail.com> wrote:

 Convention is to use ^ as cross product and * as dot product.


 Really? I've never heard of it. Rather, everyone I've talked to about it
 has said exactly what I did.


Openscenegraph uses those conventions and I've seen it used elsewhere as 
well. Not sure where they originated though.

Seeing as dot & cross product are very common, having them as operators 
is really handy.

-- 
My enormous talent is exceeded only by my outrageous laziness.
http://www.ssTk.co.uk
Mar 13 2011
prev sibling parent Caligo <iteronvexor gmail.com> writes:
On Sun, Mar 13, 2011 at 9:11 AM, Simen kjaeraas <simen.kjaras gmail.com>wrote:


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

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


I agree.  It's just better do define 'dot' and 'cross'.  That's how it's
done in Eigen and it works great.
Mar 13 2011