An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Interpolation with developable Be´zier patches
Computer Aided Geometric Design
Developable (1, n)-Be´zier surfaces
Computer Aided Geometric Design
A simple algorithm for designing developable Bézier surfaces
Computer Aided Geometric Design
Degree elevation and developable Bézier surfaces
Computer Aided Geometric Design
Developability-preserved free-form deformation of assembled patches
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Computer aided geometric design of strip using developable Bézier patches
Computers in Industry
| Hi-index | 0.00 |
This paper studies geometric design of developable composite Bezier surfaces from two boundary curves. The number of degrees of freedom (DOF) is characterized for the surface design by deriving and counting the developability constraints imposed on the surface control points. With a first boundary curve freely chosen, (2m+3), (m+4), and five DOFs are available for a second boundary curve of a developable composite Bezier surface that is G^0, G^1, and G^2, respectively, and consists of m consecutive patches, regardless of the surface degree. There remain five and (7-2m) DOFs for the surface with C^1 and C^2 continuity. Allowing the end control points to superimpose produces Degenerated triangular patches with four and three DOFs left, when the end ruling vanishes on one and both sides, respectively. Examples are illustrated to demonstrate various design methods for each continuity condition. The construction of a yacht hull with a patterned sheet of paper unrolled from 3D developable surfaces validates practicality of these methods in complex shape design. This work serves as a theoretical foundation for applications of developable composite Bezier surfaces in product design and manufacturing.