**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

>

> 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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