Abstract
It is in many cases practical to compose a continuous surface out of some low-degree Bézier surface patches having C1 (first-order parametric) continuity between the adjacent patches. The paper presents a relatively simple geometric construction of the position of the control points in the neighbourhood of the common boundary curve to ensure the required \@mathrm C^1 continuity. The construction is based on the well-known criteria of the continuous joints of the Bézier surface patches and on a straightforward geometric similarity.
Highlights
Nowadays the freeform surfaces are already popular not just in industrial design and among the computer-aided architectural design (CAAD) systems
The Bézier surfaces are preferred in many cases, due to their advantageous properties
With the increased number of knots, the equation describing the curve becomes more complicated, consisting of more terms, the degree of the curve is increased, it is often preferable to describe more complicated shapes by connecting several Bézier curves of lower degree together, while using the property of the curve that the sides of its control polygon at the end points are tangential to the curve at its end points
Summary
Nowadays the freeform surfaces are already popular not just in industrial design and among the computer-aided architectural design (CAAD) systems. The parametric vector of the Bézier curve with the given control points or knots will be: LII
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
