Projective geometry and its applications to computer graphics
Projective geometry and its applications to computer graphics
Computer-Aided Design
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Blend surfaces for set theoretic volume modelling systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Curve Fitting with Conic Splines
ACM Transactions on Graphics (TOG)
Least Square Estimation with Applications to Digital Signal Processing
Least Square Estimation with Applications to Digital Signal Processing
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Curve-fitting with piecewise parametric cubics
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Hermite interpolation of rational space curves using real algebraic surfaces
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Using Geometric Distance Fits for 3-D Object Modeling and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Surface reconstruction with anisotropic density-scaled alpha shapes
Proceedings of the conference on Visualization '98
Interactive curve design using digital French curves
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy
IEEE Transactions on Pattern Analysis and Machine Intelligence
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Constrained fitting in reverse engineering
Computer Aided Geometric Design
Proceedings of the conference on Visualization '01
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Extending Neural Networks for B-Spline Surface Reconstruction
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Adaptive and quality 3D meshing from imaging data
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Approximate implicitization via curve fitting
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment
Journal of Mathematical Imaging and Vision
Topologically Faithful Fitting of Simple Closed Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the complexity of curve fitting algorithms
Journal of Complexity
Functional networks for B-spline surface reconstruction
Future Generation Computer Systems - Special issue: Computer graphics and geometric modeling
Least Squares Fitting of Circles
Journal of Mathematical Imaging and Vision
Approximate algebraic methods for curves and surfaces and their applications
Proceedings of the 21st spring conference on Computer graphics
Using particles to sample and control implicit surfaces
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
ACM SIGGRAPH 2007 papers
Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Front tracking with moving-least-squares surfaces
Journal of Computational Physics
Proceedings of Graphics Interface 2009
Sketch-Based Interfaces and Modeling (SBIM): Sketching piecewise clothoid curves
Computers and Graphics
Reconstruction of Sewer Shaft Profiles from Fisheye-Lens Camera Images
Proceedings of the 31st DAGM Symposium on Pattern Recognition
Feature-based reverse modeling strategies
Computer-Aided Design
Constrained fitting for 2D profile-based reverse modeling
Computer-Aided Design
Estimation of place of articulation during stop closures of vowel-consonant-vowel utterances
IEEE Transactions on Audio, Speech, and Language Processing
Curvature and torsion estimators based on parametric curve fitting
Computers and Graphics
Adaptive scanning in atomic force microscopy
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Functional networks for B-spline surface reconstruction
Future Generation Computer Systems
Error-bounds on curvature estimation
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Faithful recovering of quadric surfaces from 3D range data
3DIM'99 Proceedings of the 2nd international conference on 3-D digital imaging and modeling
Automatic body measurement for mass customization of garments
3DIM'99 Proceedings of the 2nd international conference on 3-D digital imaging and modeling
Approximate implicitization of triangular Bézier surfaces
Proceedings of the 26th Spring Conference on Computer Graphics
Hyper least squares fitting of circles and ellipses
Computational Statistics & Data Analysis
Multi-level partition of unity algebraic point set surfaces
Journal of Computer Science and Technology
Neatening sketched strokes using piecewise French curves
Proceedings of the Eighth Eurographics Symposium on Sketch-Based Interfaces and Modeling
Information Sciences: an International Journal
Technical Section: Quadratic curve and surface fitting via squared distance minimization
Computers and Graphics
A novel parameter decomposition approach to faithful fitting of quadric surfaces
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
On the Solution of the GPS Localization and Circle Fitting Problems
SIAM Journal on Optimization
Growing Least Squares for the Analysis of Manifolds in Scale-Space
Computer Graphics Forum
Sketching piecewise clothoid curves
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
A framework for 3D model reconstruction in reverse engineering
Computers and Industrial Engineering
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Automatic Radial Distortion Estimation from a Single Image
Journal of Mathematical Imaging and Vision
Generalized, basis-independent kinematic surface fitting
Computer-Aided Design
Algorithms for projecting points onto conics
Journal of Computational and Applied Mathematics
A comprehensive process of reverse engineering from 3D meshes to CAD models
Computer-Aided Design
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In the course of developing a system for fitting smooth curves to camera input we have developed several direct (i.e. noniterative) methods for fitting a shape (line, circle, conic, cubic, plane, sphere, quadric, etc.) to a set of points, namely exact fit, simple fit, spherical fit, and blend fit. These methods are all dimension-independent, being just as suitable for 3D surfaces as for the 2D curves they were originally developed for.Exact fit generalizes to arbitrary shapes (in the sense of the term defined in this paper) the well-known determinant method for planar exact fit. Simple fit is a naive reduction of the general overconstrained case to the exact case. Spherical fit takes advantage of a special property of circles and spheres that permits robust fitting; no prior direct circle fitters have been as robust, and there have been no previous sphere fitters. Blend fit finds the best fit to a set of points of a useful generalization of Middleditch-Sears blending curves and surfaces, via a nonpolynomial generalization of planar fit.These methods all require (am+bn)n2 operations for fitting a surface of order n to m points, with a = 2 and b = 1/3 typically, except for spherical fit where b is larger due to the need to extract eigenvectors. All these methods save simple fit achieve a robustness previously attained by direct algorithms only for fitting planes. All admit incremental batched addition and deletion of points at cost an2 per point and bn3 per batch.