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<DIV><FONT size=2 face=Arial>Hi Philippe,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>From an engineering standpoint, angles for arcs are
very rarely quoted. Another alternative is to fix the current implementation so
that Point2 does not have to lie on the arc and is used only for the arc plane
and angle and note the limitation about collinear Point1 & Point2. Then put
the new API in vtkArcSource2. But you have probably considered
this.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>The API change will not affect me but thought
it courteous to respond to your invitation for comments.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>John.</FONT></DIV></DIV>
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style="BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: 0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B>
<A title=philippe.pebay@kitware.com
href="mailto:philippe.pebay@kitware.com">Philippe Pebay</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=jcplatt@dsl.pipex.com
href="mailto:jcplatt@dsl.pipex.com">John Platt</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, December 01, 2011 8:03
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [vtk-developers] Ill-posed
problem in vtkArcSource</DIV>
<DIV><BR></DIV>Hello John<BR><BR>Thanks for the reply. In the current
implementation, Point2 is also used to specify the angle, as you described (in
addition to specifying a plane). I think this is a problem because it lets the
user specify an Point2 that does not belong to the arc, and the output will in
this case not be an arc. <BR><BR>The problem that I see with requiring the
normal only in the degenerate cases is that the user might not know this; or,
a program using the arc source might be asked to work in all cases, including
flat and null angles, which means that one would either have to rewrite the
code to use the new interface (thus making useless anyway the old API), or,
test thevalue of the angle to use the new API in some cases only, which would
create unnecessary code complexity.<BR><BR>I think that we are going to go
ahead with a new, consistent and generic API. Will some of you own code be
potentially affected by this?<BR><BR>Thank you<BR>Philippe<BR> <BR>
<DIV class=gmail_quote>On Wed, Nov 30, 2011 at 1:08 AM, John Platt <SPAN
dir=ltr><<A href="mailto:jcplatt@dsl.pipex.com"
target=_blank>jcplatt@dsl.pipex.com</A>></SPAN> wrote:<BR>
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class=gmail_quote><U></U>
<DIV bgcolor="#ffffff">
<DIV><FONT size=2 face=Arial>Hi Philippe,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>I presume Point1 (projected onto the arc
plane) is retained to specify the radius and start of the arc. Point2
could be used instead of the angle to determine the turn of the arc (not
radius to avoid the inconsistency you mentioned). You could then say that
the normal was only required when Point1 & Point2 are collinear and
defaults to (0,0,1). Just a thought.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>John.</FONT></DIV>
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style="BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: 0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
<DIV>
<DIV></DIV>
<DIV>
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV style="FONT: 10pt arial; BACKGROUND: #e4e4e4"><B>From:</B> <A
title=philippe.pebay@kitware.com href="mailto:philippe.pebay@kitware.com"
target=_blank>Philippe Pebay</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=vtk-developers@vtk.org
href="mailto:vtk-developers@vtk.org" target=_blank>VTK Developers</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, November 29, 2011 8:58
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [vtk-developers] Ill-posed
problem in vtkArcSource</DIV>
<DIV><BR></DIV>Hello all,<BR><BR>A couple of weeks ago, I noticed that
vtkArcSource was yielding incorrect outputs for flat [mod pi] angles,
i.e., when the Center, Point1 and Point2 point instance variables were
aligned.<BR><BR>I thought it was a simple bug which would be readily
fixed. I finally found time to return to it today, only to notice that the
cause of the problem is to be found in the following lines:<BR><BR>
double v1[3] = { this->Point1[0] -
this->Center[0],<BR>
this->Point1[1] -
this->Center[1],<BR>
this->Point1[2] - this->Center[2] };<BR> double v2[3] = {
this->Point2[0] -
this->Center[0],<BR>
this->Point2[1] -
this->Center[1],<BR>
this->Point2[2] - this->Center[2] };<BR> double normal[3],
perpendicular[3];<BR> vtkMath::Cross( v1, v2, normal );<BR>
vtkMath::Cross( normal, v1, perpendicular );<BR> vtkMath::Normalize(
perpendicular );<BR><BR>Specifically, the source of the problem is the
utilization of the cross (vector) product to find the normal between v1
and v2, the coordinate vectors of Point1 and Point2 with respect to the
center of the arc: when they are aligned with the centers, v1 and v2
become co-linear, and as a result the cross product vanishes within
machine precision, hence causing the rest of the algorithm to fall apart
(cf. 1st attached image).<BR><BR>As I was thinking of a fix (by checking
for nullity of the cross product within some tolerance, and then creating
an ad-hoc normal vector), I realized that in this particular case, the
problem was in fact ill-posed: indeed, if Center, Point1, and Point2 are
aligned, with the two latter points being equidistant from the former,
then there is an infinity of arcs satisfying the specification. In other
words, the current API of vtkArcSource does not allow for a unique
specification of flat [mod pi] angles, because in this case there is not
one particular arc to be chosen and drawn. There is, therefore, no
possible fix with the current API.<BR><BR>In addition to this issue, the
current API poses the (already known) problem that it is possible to
specify an over-constrained and inconsistent input, when Point1 and Point2
are not equidistant from the center, causing the algorithm to draw an arc
attached to a segment reaching out to the former point (cf. 2nd attached
image).<BR><BR>At this point, I would therefore suggest that the API be
changed to allow for another, consistent and generic specification of an
arc: namely, it would have :<BR>- a center [unchanged from current
API]<BR>- a normal (providing the orientation for the rotation as well as
the plane)<BR>- an angle<BR>- an angular resolution [unchanged from
current API]<BR>With those in hand, the gist of the algorithm creating the
arc itself would remain unchanged. This new API would solve both problems.
<BR clear=all><BR>Currently, only a couple of classes in VTK proper appear
to be using vtkArcSource. It would thus be easy to upgrade VTK to the new
arc source. For other applications we could leave the current instance
variables available until we decide to deprecate the current approach
altogether. As the arc-drawing algorithm would remain essentially
unchanged, a test checking which of the two arc specifications is to be
used (the older one, for backwards compatibility, being the default for
the time being) would suffice to make approaches cohabit for a
while.<BR><BR>I reported an issue in the bug tracker, but thought that an
e-mail to the list would probably elicit more discussion.<BR><BR>Looking
forward to your comments,<BR>Thank you,<BR>Philippe<BR><BR><BR>--
<BR><FONT color=#888888>Philippe Pébay<BR>Directeur de la Visualisation et
du Calcul Haute Performance<BR>Kitware SAS<BR>20 rue de la
Villette<BR>69328 Lyon cedex 03, France<BR><A value="+33426685003">+33
(0)4.26.68.50.03</A><BR><A href="http://www.kitware.fr/"
target=_blank>http://www.kitware.fr</A></FONT><BR></DIV></DIV>
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<P></P></BLOCKQUOTE></DIV></BLOCKQUOTE></DIV><BR><BR clear=all><BR>--
<BR><FONT color=#888888>Philippe Pébay<BR>Directeur de la Visualisation et du
Calcul Haute Performance<BR>Kitware SAS<BR>20 rue de la Villette<BR>69328 Lyon
cedex 03, France<BR><A value="+33426685003">+33 (0)4.26.68.50.03</A><BR><A
href="http://www.kitware.fr/"
target=_blank>http://www.kitware.fr</A></FONT><BR></BLOCKQUOTE></BODY></HTML>