Lectures on minimal surfaces: vol. 1
Lectures on minimal surfaces: vol. 1
Spline conversion for trimmed rational Be´zier- and B-spline surfaces
Computer-Aided Design - Special Issue: Be´zier Techniques
Bézier Surfaces of Minimal Area
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Surface Classification Using Conformal Structures
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Bézier surfaces of minimal area: the Dirichlet approach
Computer Aided Geometric Design
On harmonic and biharmonic Bézier surfaces
Computer Aided Geometric Design
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Periodic surface modeling for computer aided nano design
Computer-Aided Design
A variational level set approach for surface area minimization of triply-periodic surfaces
Journal of Computational Physics
Harmonic volumetric mapping for solid modeling applications
Proceedings of the 2007 ACM symposium on Solid and physical modeling
G2 surface modeling using minimal mean-curvature-variation flow
Computer-Aided Design
Computing general geometric structures on surfaces using Ricci flow
Computer-Aided Design
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Foreword: Discrete Differential Geometry
Computer Aided Geometric Design
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
A general 4th-order PDE method to generate Bézier surfaces from the boundary
Computer Aided Geometric Design
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
CAD tools for aesthetic engineering
Computer-Aided Design
Discrete surfaces in isotropic geometry
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
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In this paper, parametric polynomial minimal surfaces of degree six with isothermal parameter are discussed. We firstly propose the sufficient and necessary condition of a harmonic polynomial parametric surface of degree six being a minimal surface. Then we obtain two kinds of new minimal surfaces from the condition. The new minimal surfaces have similar properties as Enneper's minimal surface, such as symmetry, self-intersection and containing straight lines. A new pair of conjugate minimal surfaces is also discovered in this paper. The new minimal surfaces can be represented by tensor product Bézier surface and triangular Bézier surface, and have several shape parameters. We also employ the new minimal surfaces for form-finding problem in membrane structure and present several modeling examples.