comp.graphics.algorithms Google Group

Re: Testing for circle overlapping a pie slice.

newsgroup.spamfil...@virtualinfinity.net (Daniel Pitts) — Tue, 05 Jan 2010 07:53:35 UT

Well, pie slice is most accurate, but my requirements are a little less
strict. My actual need is to find the closest circle to the vertex
which is within the bounded rays.
I'll want to improve the speed eventually, but I think in order to do
that, I'll need to implement a spacial index of my circles.

Re: Testing for circle overlapping a pie slice.

dnospamebe...@usemydomain.com (Dave Eberly) — Tue, 05 Jan 2010 05:55:07 UT

Your subject line says "pie slice", which I interpreted to mean a
sector of a circle (a finite region). Your description here indicates
that you mean the region bounded between two rays (an infinite
region), which is easier to handle (with the algorithm you mention).

Re: Testing for circle overlapping a pie slice.

newsgroup.spamfil...@virtualinfinity.net (Daniel Pitts) — Tue, 05 Jan 2010 05:09:42 UT

Hmm, looking a little more at the document, it looks like I might be
better off using the method describe there. The only problem is the
algorithm expects the cone to be defined in terms of an axis and theta,
but I've defined it as two separate angles.
Actually, now that I think about it, I probably can refactor my code

Re: surface interpolation?

n...@here.com (Kaba) — Mon, 04 Jan 2010 23:40:53 UT

Hi Dave,
Could you post a link to such a paper (or papers)?
For my own interest:)

Re: Testing for circle overlapping a pie slice.

newsgroup.spamfil...@virtualinfinity.net (Daniel Pitts) — Mon, 04 Jan 2010 22:59:44 UT

I actually came up with a solution to this. I test if the center of the
circle is within the angles OR if either ray intersects the circle. This
gives me the results I need.

Re: surface interpolation?

dnospamebe...@usemydomain.com (Dave Eberly) — Mon, 04 Jan 2010 22:01:56 UT

You say you know the order? Then you have a triangle mesh, right? This
meets your C0-continuity criterion. I am missing something in your posts,
because this would easy enough that you would not be posting about it :)
If you have a triangle mesh and you want instead C1 continuity, there are
tricks you can do with Bezier triangle patches (your quads would be split

Re: surface interpolation?

rui.mac...@gmail.com (Rui Maciel) — Mon, 04 Jan 2010 19:37:44 UT

The points aren't positioned following any set of rules. They just respect their
relative placement among each other and the surface that they generate isn't
heavily distorted. It's just like I start off with a set of points which fully
describe a regular polyhedron but the nodes may be moved a bit off their original

Re: surface interpolation?

rui.mac...@gmail.com (Rui Maciel) — Mon, 04 Jan 2010 19:22:52 UT

Kaba wrote:
Yes, I'm aiming for a set of independent polynomial patches.
In my case it's only important to ensure C0 continuity.
Thanks for the link, Kaba. After a quick browse I believe that that isn't
necessarily what I had in mind. What I'm looking for should be simpler than the
process described in the paper, as I only need to generate a surface from a small

Re: surface interpolation?

david_f_kni...@yahoo.com (david_f_knight) — Mon, 04 Jan 2010 19:03:15 UT

It seems to me there's a terminology problem here. If you have true
control points, then you already have everything you need to solve
your problem. There is no such thing as generic control points; all
control points are specific to their particular algorithm. On the
other hand, if all you have is data points on a surface, then there

ISA 2010: submissions until 25 January 2010

natty2...@gmail.com (natty2006@gmail.com) — Mon, 04 Jan 2010 16:24:13 UT

Apologies for cross-postings. Please send to interested colleagues and
students
-- CALL FOR PAPERS - Deadline for submissions: 25 January 2010 --
IADIS INTERNATIONAL CONFERENCE INTELLIGENT SYSTEMS AND AGENTS 2010
Freiburg, Germany, 29 - 31 July 2010
([link])
part of the IADIS Multi Conference on Computer Science and Information

Re: Testing for circle overlapping a pie slice.

dnospamebe...@usemydomain.com (Dave Eberly) — Mon, 04 Jan 2010 14:42:29 UT

This is similar to the 3D problem of testing for intersection of a sphere
and a cone:
[link]
Test whether the circle is "outside" either line forming the pie slice (a 2D
one-sided cone). If it is, then there is no intersection. If it is not,

Testing for circle overlapping a pie slice.

newsgroup.spamfil...@virtualinfinity.net (Daniel Pitts) — Mon, 04 Jan 2010 05:08:54 UT

Another 2d problem...
Given a circle (point + radius), and a pie slice (centered at origin +
start/stop angle), is there an easy test for whether the circle
intersects with the pie slice?
boolean intersects(AngelBracket bracket, Vector center, double radius) {
return /* true if circle is in the angle bracket */;

Re: surface interpolation?

dnospamebe...@usemydomain.com (Dave Eberly) — Mon, 04 Jan 2010 02:52:59 UT

What else do you know about the points? For example, is a "distorted face"
generated by moving the originally planar points in the direction
perpendicular to the plane? Are the points grouped by face? Are your faces
essentially triangles? Do you know adjacency information about the points
on a distorted face? Any such information will help avoid the generic case

Re: surface interpolation?

n...@here.com (Kaba) — Sun, 03 Jan 2010 22:22:17 UT

(I am writing this after reading your answer to Dave)
When you mention Lagrance polynomials it seems that you are expecting to
represent the surfaces either using a single polynomial patch or a set
of independent polynomial patches.
Out of these two the first one is often a bad idea since surfaces are

Re: surface interpolation?

rui.mac...@gmail.com (Rui Maciel) — Sun, 03 Jan 2010 17:51:49 UT

The points are used to define arbitrary surfaces, each of a very specific format.
To be more precise, each set of points are used to define surfaces of polyhedrons,
such as tetrahedrons and hexahedrons, which may have distorted faces.
<snip/>
Sounds interesting. Is there any online doc which touches that subject that I can