Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
Algebraic geometry for computer-aided geometric design
IEEE Computer Graphics and Applications
Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Advanced animation and rendering techniques
Advanced animation and rendering techniques
Interpolation and approximation of curves and surfaces using Po´lya polynomials
CVGIP: Graphical Models and Image Processing
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Curve fitting with Be´zier cubics
Graphical Models and Image Processing
Adaptive subdivision and the length and energy of Be´zier curves
Computational Geometry: Theory and Applications
The uniqueness of Be´zier control points
Computer Aided Geometric Design
A shape controlled fitting method for Be´zier curves
Computer Aided Geometric Design
On the derivatives of second and third degree rational Bézier curves
Computer Aided Geometric Design
Approximate implicitization using monoid curves and surfaces
Graphical Models and Image Processing
Tutorial: Time-Multiplexed Stereoscopic Computer Graphics
IEEE Computer Graphics and Applications
Data Reduction Using Cubic Rational B-Splines
IEEE Computer Graphics and Applications
Approximation by Interval Bezier Curves
IEEE Computer Graphics and Applications
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D reconstruction from drawings with straight and curved edges
SIGGRAPH Asia 2013 Technical Briefs
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This article introduces a new curve reconstruction method based on recovering the control points of parametric cubic curves. The method developed here has two stages: finding the 3D control points of parametric curves and reconstruction of free curves. The 3D control points of curves are computed from 2D image sequences by using projective reconstruction of the 3D control points and the bundle adjustment algorithm. The relationships among parametric curves, such as Hermite curves, Bézier curves and B-spline curves, are established so that a curve of any model can be achieved for best fitting. Some experiments are performed to show the performance and effectiveness of the algorithm.The method is based on the slope following and learning algorithm, which provides an efficient way of finding the 3D control points of any type of cubic Bézier curves. This method, which is an extension of our previous work on recovering control points of 2D Bézier curves, can automatically fit a set of data points with piecewise geometrically continuous cubic parametric curves. The experimental results demonstrate that our method is a fast and efficient way of recovering 3D control points of parametric curves, matching free curves and shape reforming.