Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

1.0K
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
1.0K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

9.2K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
9.2K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

9.2K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
9.2K
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

248
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
248
Centroid for the Paraboloid of Revolution01:16

Centroid for the Paraboloid of Revolution

836
The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...
836
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

8.9K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
8.9K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Vibrio proteolyticus DCF12.2 postbiotic modulates intestinal metabolic and immune pathways in zebrafish.

Applied microbiology and biotechnology·2026
Same author

Exploring Marine-Derived Polysaccharides Through In Vitro and Zebrafish In Vivo Assays: Initial Trends of A Novel Approach to Drug Screening.

Marine biotechnology (New York, N.Y.)·2025
Same author

Postbiotics of Marine Origin and Their Therapeutic Application.

Marine drugs·2025
Same author

Optical wireless positioning by modulation of the optical source orientation.

Optics express·2025
Same author

Optimizing Extracellular Products from Vibrio proteolyticus for Their Use as Postbiotics in Aquaculture.

Marine biotechnology (New York, N.Y.)·2025
Same author

Dietary Administration of Postbiotics from <i>Vibrio proteolyticus</i> DCF12.2 Enhanced Intestinal Integrity, Microbiota, and Immune Response in Juvenile Gilthead Seabream (<i>Sparus aurata</i>).

Animals : an open access journal from MDPI·2025

Related Experiment Video

Updated: Jan 1, 2026

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads
07:58

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Published on: July 25, 2025

682

Freeform geometrical optics II: from parametric representation to CAD/CAM.

Thibault Grillon, Camilo Valencia-Estrada, Jorge Garcia-Márquez

    Applied Optics
    |December 25, 2019
    PubMed
    Summary
    This summary is machine-generated.

    Freeform optical surfaces enhance image quality and reduce system complexity. A novel vector method enables accurate CAD export of these asymmetric surfaces, ensuring sampling density matches surface irradiance.

    More Related Videos

    Precision Measurements and Parametric Models of Vertebral Endplates
    10:35

    Precision Measurements and Parametric Models of Vertebral Endplates

    Published on: September 17, 2019

    6.8K
    Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging
    07:14

    Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging

    Published on: April 11, 2025

    1.1K

    Related Experiment Videos

    Last Updated: Jan 1, 2026

    Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads
    07:58

    Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

    Published on: July 25, 2025

    682
    Precision Measurements and Parametric Models of Vertebral Endplates
    10:35

    Precision Measurements and Parametric Models of Vertebral Endplates

    Published on: September 17, 2019

    6.8K
    Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging
    07:14

    Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging

    Published on: April 11, 2025

    1.1K

    Area of Science:

    • Optics and Photonics
    • Optical Engineering
    • Computer-Aided Design

    Background:

    • Freeform optical surfaces offer significant advantages in enhancing image quality and reducing component count in optical systems.
    • Unlike conventional optics, freeform surfaces lack symmetry, necessitating advanced mathematical descriptions.
    • Parametric representations, while powerful, can be complex, whereas explicit representations are favored for their compactness and CAD compatibility.

    Purpose of the Study:

    • To demonstrate a method for exporting parametrically represented freeform surfaces to CAD formats without compromising shape accuracy.
    • To introduce a vector method that ensures surface sampling density is proportional to the irradiance distribution.
    • To facilitate the practical application and manufacturing of complex freeform optics.

    Main Methods:

    • Development of a vector-based method for converting parametric freeform surface data.
    • Implementation of algorithms to ensure surface sampling density is irradiance-dependent.
    • Validation of the method through comparison of exported CAD models with original parametric definitions.

    Main Results:

    • The presented vector method successfully exports freeform surfaces to CAD formats with minimal shape deviation.
    • The method achieves a surface sampling density that accurately reflects the irradiance distribution.
    • This ensures that critical areas of the optical surface receive appropriate sampling for analysis and manufacturing.

    Conclusions:

    • Parametrically defined freeform optical surfaces can be accurately represented in CAD formats using the proposed vector method.
    • The irradiance-proportional sampling ensures efficient and accurate data representation for optical design and fabrication.
    • This facilitates the broader adoption of freeform optics in advanced optical systems.