# comp.graphics.algorithms

## Subject: Re: Offset curves on a 3D surface for area coverage planning

4805455@gmail.com wrote:
>
> Hello. I am looking into existing algorithms for computing offset
> curves on a 3D surface. The intent is to use this algorithm to compute
> a planned path on a 3D surface that completely covers the surface. The
> input will be the 3D surface data and an initial curve over the surface
> to guide the shape of the remaining, offset curves. One application
> might be removing material on a mild 3D surface such as cutting grass
> on some hills. I have seen some work on 2D as it relates to milling,
> but not much on 3D.

Then isn't much resemblance to the actual task of computer controlled
cutting grass on a rolling hill and computer controlled 3d milling
machines. In the case of mowing the grass, the surface is defined by the
constraint that the wheels of the mower have to be in contact always
(gravity). The surface probably will never be defined other than
something generally well behaved within a certain set of boundaries.
Therefore the motion can simply be mapped in 2d projected from above
(GPS for instance is used in agriculture).
For a 3-axis milling machine There is generally a CAM program that
computes a toolpath based on numerous constraints that the operator
chooses to impose. In the end the toolpath is still either project from
above or calculated as a series of constant z level operations (starting
from the top down). This eventually becomes a series of blocks fed to
the CNC where each block informs the machine how much to move each axis.
For 3-axis machining of 3d surfaces this is almost always simply one
linear move for each block. So the toolpath can be a humongous string of
linear 3d moves.

> I do seem to see a lot of computer graphics
> pictures with what looks like what I need, such as the the gargoyle
> found lower down on the following page
> . (Not looking for geodesics
> though). The whole subject is wide open for me:
>
> 1. What is the best way to represent the surface?

For CNC The cutterline surface is almost always a polygon mesh. The
cutterline surface is a surface derived from a defined CAD surface that
is intended to be cut. For instance if the tool is defined as having a
spherical shape (ball end mill) then the cutterline surface is simply an
offset from the surface to be cut (will be more complicated if you want
gouge protection). The CAD surface is most often NURBS.

> 2. What is the best way to represent a curve on the surface?

For CNC 3d milling a series of connected straight lines. In theory there
are better representations but you won't be able find anyone using them
anywhere.

> 3. How has anyone done this algorithm in 3D already?

For CNC The trick is to develop the cutter-line surface. If you succeed
at that, mapping a toolpath projected from above or at constant z level
is not difficult.

-jim

> 4. Are there any good books on this subject?
> 5. Any leads at all?
>
> Thanks a lot.
>
> Sincerely,
>
> Jim

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