Hej POV team!

I don't want to mess up your time while heading for 3.5, but yesterday I
stumbled over a little bug in the POVray documentation (Win-Help file
v3.1e, put perhaps elsewhere as well):

 -it says under 'vector functions':

  vcross(A,B) Cross product of A and B. Returns a vector that is the
vector cross product of the two vectors. The resulting vector is
perpendicular to the two original vectors and its length is proportional
to the angle between them. See the animated demo scene VECT2.POV for an
illustration. 
  
 -while it should say:

  vcross(A,B) Cross product of A and B. Returns a vector that is the
vector cross product of the two vectors. The resulting vector is
perpendicular to the two original vectors and its length is equal to the
area of the paralleogram defined by them. See the animated demo scene
VECT2.POV for an illustration. 

and just a proposal for a better formulation:

 -it says under 'float functions':

  vdot(V1,V2) Dot product of V1 and V2. Returns a float value that is
the dot product (sometimes called scalar product of V1 with V2. Formula
is vdot=V1.x*V2.x + V1.y*V2.y + V1.z*V2.z. See the animated demo scene
VECT2.POV for an illustration. 

 -it's completely ok, but it might be better this way:

  vdot(V1,V2) Dot product of V1 and V2. Returns a float value that is
the dot product (sometimes called scalar product) of V1 with V2. It is
directly proportional to the length of the two vectors and the cosine of
the angle between them. Formula is vdot=V1.x*V2.x + V1.y*V2.y +
V1.z*V2.z. See the animated demo scene VECT2.POV for an illustration. 


Uwe.

Post a reply to this message

Uwe Zimmermann <uwe### [at] elekthse> wrote:
:  -it says under 'vector functions':

:   vcross(A,B) Cross product of A and B. Returns a vector that is the
: vector cross product of the two vectors. The resulting vector is
: perpendicular to the two original vectors and its length is proportional
: to the angle between them. See the animated demo scene VECT2.POV for an
: illustration. 
:   
:  -while it should say:

:   vcross(A,B) Cross product of A and B. Returns a vector that is the
: vector cross product of the two vectors. The resulting vector is
: perpendicular to the two original vectors and its length is equal to the
: area of the paralleogram defined by them. See the animated demo scene
: VECT2.POV for an illustration. 

  Your definition is absolutely right, but the original definition is too.
  Cross product can also be formulated as:

  AxB = |A| * |B| * sin(angle(A,B)) * perpendicular_unit_vector(A,B)

  So the length is proportional to the angle between them.
  Perhaps it should have a better wording, though.

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

Post a reply to this message

Nieminen Mika wrote:

>   Your definition is absolutely right, but the original definition is too.
>   Cross product can also be formulated as:
> 
>   AxB = |A| * |B| * sin(angle(A,B)) * perpendicular_unit_vector(A,B)
> 
>   So the length is proportional to the angle between them.
>   Perhaps it should have a better wording, though.

proportionality between the angle and the sine of an angle is only true
for very small angles (if you use radians to define the angle) 
   
    abs(alpha)<0.3   =>  alpha = sin(alpha) +/- 0.5%

I think it's more usefull for those non-mathematicians out there to read
that the length of the cross product of two vectors is proportional to
an area...

Uwe.

Post a reply to this message