On Monday, January 27, 2025 at 07:09:21 AM EST, John David via Discuss discuss@lists.openscad.org wrote:
As mentioned elsewhere, I like Gerald Farin's books on CAGD and his NURBS books.
Dianne Hansford also has several books on the subjects. Even though these books
are typically more advanced than something focusing on Bézier curves only, they make
sure to address many of the more esoteric properties, as well as the basics.
Thanks again for mentioning those --- I have them on my "Want to Read" list in Goodreads, and was able to find at least one on thriftbooks.com --- next up is finding the time to read through everything and then see how it applies in my project.
William
On Sunday, January 26, 2025 at 10:56:45 PM EST, Adrian Mariano via Discuss discuss@lists.openscad.org wrote:
Well, you don't say what you want to do with conic sections.
I'm trying to model a specific toolpath and the 3D result.
I've never heard of anybody making much of of them in CAD modeling other than for simple things like roundings.
This use-case is a lot more complex.
It could be because the computations get annoying. Beziers have simple computations.
That sounds right --- when I had a commercial tool calculate the toolpaths for a test 2" x 1" x 1" design it took about 20 minutes and resulted in a ~127MB file.
William
Also take a look at abebooks.com. I can see several of the books on sale
used for $10 to $20 a pop. Yea, the books, particularly Farin's book on
curves and surfaces, is a tough read. If you get deep into this, see if
you can find an extra tutorial on "blossoms" which is a mathematical
notation he started using which simplifies the algorithms by abstracting
into arbitrary dimensionality.
On Mon, Jan 27, 2025 at 11:04 AM William F. Adams via Discuss <
discuss@lists.openscad.org> wrote:
On Monday, January 27, 2025 at 07:09:21 AM EST, John David via Discuss <
discuss@lists.openscad.org> wrote:
As mentioned elsewhere, I like Gerald Farin's books on CAGD and his NURBS
books.
Dianne Hansford also has several books on the subjects. Even though
these books
are typically more advanced than something focusing on Bézier curves
only, they make
sure to address many of the more esoteric properties, as well as the
basics.
Thanks again for mentioning those --- I have them on my "Want to Read"
list in Goodreads, and was able to find at least one on thriftbooks.com
--- next up is finding the time to read through everything and then see how
it applies in my project.
William
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