# Approximate implicitization using linear algebra

arXiv: https://arxiv.org/abs/1605.08638 · HTML: https://mlsanity.com/paper/1605.08638/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2016.

## Built on by (most cited first, 3 of 3)

- [Fit4CAD: A point cloud benchmark for fitting simple geometric primitives in CAD objects](https://mlsanity.com/paper/2105.06858/) (2021)
- [Fitting and recognition of geometric primitives in segmented 3D point clouds using a localized voting procedure](https://mlsanity.com/paper/2205.15426/) (2022)
- [Adaptive Approximate Implicitization of Planar Parametric Curves via Weak Gradient Constraints](https://mlsanity.com/paper/2302.11767/) (2023)

## Abstract (arXiv)

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating point implementation in computer aided geometric design (CAGD) systems. We unify the approaches under the names of commonly known polynomial basis functions, and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.