A Linear Variational System for Modelling From Curves

We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we...

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Bibliographic Details
Published in:Computer graphics forum Vol. 30; no. 6; pp. 1850 - 1861
Main Authors: Andrews, James, Joshi, Pushkar, Carr, Nathan
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.09.2011
Subjects:
3-D graphics
Analysis
and object representations
Cauchy constraint
Control systems
curve-based modelling
Dynamical systems
Editing
I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Curve
I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling—Curve, surface, solid, and object representations
Image processing systems
Laplace transforms
Laplacian framework
linear
Modelling
Nonlinear dynamics
solid
Studies
surface
Three dimensional
Three dimensional models
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve‐based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.
Bibliography:istex:82C81D7B6044447BBDBCF92CF28F008AC62D8C00
ArticleID:CGF1966
ark:/67375/WNG-CQDG07FC-S
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2011.01966.x