## barycentric coordinates for quads

graphics

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• 1. partial thinning?
Hi! I wonder if it is possible to thin an volumetric object while loading only parts of it into memory? I.e. an 3D voxel object is diveded into several parts along the z-axis. To get the correct medial surface/axis of the whole object while thinning one single part only at a time, one must somehow preserve the important voxels at the "border crossing" to the next (and the previous) part. But how shall I know which voxels are important? Is it possible to thin an object this way at all? All my ideas to solve this problem are not working correctly and I couldn't find anything in the internet, that someone had found a solution for it (are at least tried to solve it). Any suggestions? Regards, Holger
• 2. Parallel 3D thinning algorithm from Tsao and Fu
Hi! Because I couldn't find the complete paper, I've got some problems implementing this algorithm. From what I know, one subcycle of the algorithm contains the following steps: 1. get all border voxels of direction d 2. for all candidates: - check if the voxel is simple -> yes, continue - check if the voxel is final -> no, continue - check if the "checking plane condition" is fullfilled -> yes, continue -> mark the voxel as deletable 3. delete all marked voxels My problem is the "simple point condition". How can I check this via a small 3x3x3 neighborhood? I found some hints about the number of connected components in a 3x3x3 neighborhood. So a point is simple, if the number of connected components for the foreground and the background are both exactly one. But I don't have a clue how to count the connected components and I could hardly find useful information. Thanks for help. Holger
• 3. Finding random points within a close bezier path
I have a bezier path, and I would like to randomly distribute an object within the path bounds via determine random points that lie within the path perimeter. I don't need anything extremely accurate, as long as I can get roughly within the area. These paths consist of 3 to several dozen of bezier curve segments. In some cases I may have a compound shape made up of several paths, but I'm not worried about that at this point. After some research, I have no leads as to how this might be done. Any help would be appreciated.
• 4. Finding random points within a closed bezier path
[NOTE: I posted this yesterday but I believe there was a bug in the system.] I have a closed path which consists of 3 to several dozen cubic bezier curve segments. I would like to determine a group of points which lie inside this path. I would prefer an efficient over accurate method. After some research, I haven't found any clues as to how to do this. Any help would be greatly appreciated. Thanks.
• 5. LeftEdgeScan
I am currently reading about scan conversion (of triangles in particular) and the leftedgescan algorithm. I understand why it works on the left edge, but can't make it work on the remaining two edges. How do you scan convert the remaining two edges after the left edge has been converted?

### barycentric coordinates for quads

```Hi everyone, some of you know how fill a quads in 2D using barycentric
coordinates?At the present, I'm splitting the quads into 2 triangles,
but that way is inefficient because I have to iterate over the second
bounding box which repeats pixel that were filled previously (by
example, to fill the 2nd triangle I traversed the 1st triangle that
belongs at bounding box formed by 2nd triangle)
Thanks

esmitt
```

### barycentric coordinates for quads

```Hi everyone, some of you know how fill a quads in 2D using barycentric
coordinates?At the present, I'm splitting the quads into 2 triangles,
but that way is inefficient because I have to iterate over the second
bounding box which repeats pixel that were filled previously (by
example, to fill the 2nd triangle I traversed the 1st triangle that
belongs at bounding box formed by 2nd triangle)
Thanks

esmitt
```

### Re: barycentric coordinates for quads

```Am 01.07.2010 00:50, schrieb esmitt:

I think we all know that that's a bad idea, so don't worry about its
implementation too much.

You appear completely confused about the terms you're using.  What makes
you think that filling using barycentric coordinates would require a
bounding box?

And while we're at it: what makes you think barycentrics are a useful
tool for a polygon into pixels?  They have nothing to do with pixels!
```

### Re: barycentric coordinates for quads

```Thanks for your answer.

On Jun 30, 6:55m, Hans-Bernhard Brer < XXXX@XXXXX.COM >

I know that a scanline solution better but for now, I need to use
barycentric coordinates.
Well, when I talk about bounding box is just like a delimiter for my
splitted triangle and iterate over each pixels and decides if (x,y) is
inside..nothing else

I'm using it to make another algorithms

```

### Re: barycentric coordinates for quads

```Am 01.07.2010 01:51, schrieb esmitt:

How did you arrive at the conclusion that you "need" them?  I have to
ask again, because they make no sense whatsoever for the job at hand.

And what would be keeping you from iterating over the bounding box of
the entire quad, and just evaluating

if (pixel_inside_triangle1(x,y) || pixel_inside_triangle2(x,y))

Well, if you're going to loop over pixels in bounding boxes, that
effectively _is_ a scanline algorithm anyway --- so what's keeping you
from using a proper one?
```

```Hi everyone, some of you know how fill a quads in 2D using barycentric
coordinates?At the present, I'm splitting the quads into 2 triangles,
but that way is inefficient because I have to iterate over the second
bounding box which repeats pixel that were filled previously (by
example, to fill the 2nd triangle I traversed the 1st triangle that
belongs at bounding box formed by 2nd triangle)
Thanks

esmitt
```

```Hi,

just curious if there's a neat way to get the barycentric coordinates
(or similar) of the current fragment in a GLSL shader?

Only way I could think of it was to render each triangle individually,
but that's not too good for performance...

- Asbjn
```

```Hello all,
I have points P1, P2 lying in a triangle A, B, C. I'm able to compute
barycentric coordinates of P1 and P2. Is it possible to interpolate
somehow the barycentric coordinates to obtain points which lie on the
line segment P1P2? Of course, I could interpolate linearly between P1
and P2, but I would like to interpolate bar. coordinates instead. Is
that possible?

Thanks.

Jindra
```

```Hi all,

I have a point in barycentric coordinates within a triangle,
I know its vertex (in world coordinates).

It is possible to turn the barycentric coordinates
to the world space?

Thanks in advance !!
```

```Hi there,

Assume one point is within a cuboid,
The point should be represented by a linear combination of all vertices
of the coboid.
Could someone tell me how to calculate the weight for those vertices?
or any reference paper?

I only know the same case within a convex polygon and a tetrahedron..
subdivide the cuboid into several tetrahedra?

Thanks very much : )

Best Regards,
Brian

```