Algebraic surfaces

Fundamentals to Geometric Modeling and Meshing

Published in Yongjie Jessica Zhang, Geometric Modeling and Mesh Generation from Scanned Images, 2018

Sometimes, we use intersection of algebraic surfaces to represent lines or curves. Algebraic surfaces are surfaces represented by a polynomial function f(x, y,z). For example, each term of a quadric surface can have degree up to 2. They can represent objects like spheres, disks and cones. These objects intersect each other with lines or curves.

Real-time needle guidance for venipuncture based on optical coherence tomography

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Journal Information

Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2021

Rida T. Farouki, Jack R. Swett, Rachel Ward Rohlen, David B. Smith

The data generated by the OCT probe correspond to a discrete sampling of points on the intersection curve of an indeterminate cylinder with a known cone. The problem is to determine the position, orientation, and radius of the cylinder from these data points. Cylinders and cones1 are special instances of the entire family of algebraic surfaces of degree 2, the quadric surfaces.

Algebraic surfaces

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Fundamentals to Geometric Modeling and Meshing

Real-time needle guidance for venipuncture based on optical coherence tomography