5 ms·

Much better curves for editing are k-curves (see http://faculty.cs.tamu.edu/schaefer/research/kcurves.pdf http://faculty.cs.tamu.edu/schaefer/research/kcurves.p

Much better curves for editing are k-curves (see http://faculty.cs.tamu.edu/schaefer/research/kcurves.pdf http://faculty.cs.tamu.edu/schaefer/research/kcurves.pdf) which are starting to pop up in all new Adobe tools also.

jacobolus 7y ago
Just be warned that what Adobe ships in their software is completely different than what they describe in their paper or patent.
- raphlinus 7y ago
  Indeed. The biquadratics aren't particularly smooth, and don't support inflections naturally. See https://raphlinus.github.io/curves/2018/12/21/new-spline.html https://raphlinus.github.io/curves/2018/12/21/new-spline.htm... for more on this.
  - delhanty 7y ago
    Are you able to expand on that statement a little? Your blog post is interesting as always. But I can't seem to find a reference to biquadratic in either the post or the linked Adobe paper.
    - jacobolus 7y ago
      > Our curves consist of one quadratic curve, with control points [...] per interpolated point p_i So what happens is each segment between two knots (in the paper) is made of 2 pieces of parametric quadratic polynomials (i.e. parabolas). Each knot is at the vertex of the same parabola to each side, which can be broken at the vertex into two parts, each of which belongs to one of the adjacent segments. The solver in the paper makes sure that at the joint between two parabolas, the absolute magnitude of curvature matches. This means there aren’t really any smooth inflection points and you always get a discrete jump in curvature at an inflection. This looks bad, so in practice Adobe implemented something different in their software.
      - delhanty 7y ago
        Aha! That makes perfect sense thank you. So the name biquadratic is analogous to biarc. Although the usage here is slightly different to a biarc because it's the same parabola each side of the vertex. The choice of the name biquadratic is possible unfortunate because it is already taken for an existing class of algebraic space curves [0] >Biquadratics are algebraic curves of degree four that are the intersection between two quadrics that do not share a common line (in which case the curve would be of degree three). then >See also Cartesian ovals, Booth curves (including the lemniscate of Bernoulli), the Külp quartic, the Dürer shell curve, the bicorn, that are planar projections of biquadratics. which was the source of my confusion as I had assumed that raphlinus's reference was to planar projections of these classical quartic curves. [0] https://www.mathcurve.com/courbes3d.gb/biquadratic/biquadratic.shtml https://www.mathcurve.com/courbes3d.gb/biquadratic/biquadrat...
pixelpoet 7y ago
Spotted Schaefer in the URL, definitely going to read it. He codeveloped a supremely elegant way of doing subdivision surfaces: https://pdfs.semanticscholar.org/7dca/9a9d6b7da89b9bcaf146d8a79c392e117daf.pdf https://pdfs.semanticscholar.org/7dca/9a9d6b7da89b9bcaf146d8...
splittingTimes 7y ago
Since there are some papers posted in the replies here, do you guys have any recommendantions on what are some journals that should be read by people working in the field of 3D graphics and CAD/CAM software development to stay ahead of the curve?
- deleted 7y ago
  [deleted]
- delhanty 7y ago
  Hesitate to link anything from Elsevier, but IIRC the two standard industry 3D CAD/CAM journals are: ● Computer-Aided Design - more applications and commercial stuff https://www.journals.elsevier.com/computer-aided-design https://www.journals.elsevier.com/computer-aided-design ● Computer Aided Geometric Design - mainly geometric algorithms for curves and surfaces https://www.journals.elsevier.com/computer-aided-geometric-design https://www.journals.elsevier.com/computer-aided-geometric-d...

jacobolus 7y ago

Just be warned that what Adobe ships in their software is completely different than what they describe in their paper or patent.

raphlinus 7y ago
Indeed. The biquadratics aren't particularly smooth, and don't support inflections naturally. See https://raphlinus.github.io/curves/2018/12/21/new-spline.html https://raphlinus.github.io/curves/2018/12/21/new-spline.htm... for more on this.
- delhanty 7y ago
  Are you able to expand on that statement a little? Your blog post is interesting as always. But I can't seem to find a reference to biquadratic in either the post or the linked Adobe paper.
  - jacobolus 7y ago
    > Our curves consist of one quadratic curve, with control points [...] per interpolated point p_i So what happens is each segment between two knots (in the paper) is made of 2 pieces of parametric quadratic polynomials (i.e. parabolas). Each knot is at the vertex of the same parabola to each side, which can be broken at the vertex into two parts, each of which belongs to one of the adjacent segments. The solver in the paper makes sure that at the joint between two parabolas, the absolute magnitude of curvature matches. This means there aren’t really any smooth inflection points and you always get a discrete jump in curvature at an inflection. This looks bad, so in practice Adobe implemented something different in their software.
    - delhanty 7y ago
      Aha! That makes perfect sense thank you. So the name biquadratic is analogous to biarc. Although the usage here is slightly different to a biarc because it's the same parabola each side of the vertex. The choice of the name biquadratic is possible unfortunate because it is already taken for an existing class of algebraic space curves [0] >Biquadratics are algebraic curves of degree four that are the intersection between two quadrics that do not share a common line (in which case the curve would be of degree three). then >See also Cartesian ovals, Booth curves (including the lemniscate of Bernoulli), the Külp quartic, the Dürer shell curve, the bicorn, that are planar projections of biquadratics. which was the source of my confusion as I had assumed that raphlinus's reference was to planar projections of these classical quartic curves. [0] https://www.mathcurve.com/courbes3d.gb/biquadratic/biquadratic.shtml https://www.mathcurve.com/courbes3d.gb/biquadratic/biquadrat...

pixelpoet 7y ago

Spotted Schaefer in the URL, definitely going to read it. He codeveloped a supremely elegant way of doing subdivision surfaces: https://pdfs.semanticscholar.org/7dca/9a9d6b7da89b9bcaf146d8a79c392e117daf.pdf https://pdfs.semanticscholar.org/7dca/9a9d6b7da89b9bcaf146d8...

splittingTimes 7y ago

Since there are some papers posted in the replies here, do you guys have any recommendantions on what are some journals that should be read by people working in the field of 3D graphics and CAD/CAM software development to stay ahead of the curve?

deleted 7y ago
[deleted]
delhanty 7y ago
Hesitate to link anything from Elsevier, but IIRC the two standard industry 3D CAD/CAM journals are: ● Computer-Aided Design - more applications and commercial stuff https://www.journals.elsevier.com/computer-aided-design https://www.journals.elsevier.com/computer-aided-design ● Computer Aided Geometric Design - mainly geometric algorithms for curves and surfaces https://www.journals.elsevier.com/computer-aided-geometric-design https://www.journals.elsevier.com/computer-aided-geometric-d...