Presentation
Closed-form Cauchy Coordinates and Their Derivatives for 2D High-order Cages
DescriptionWe propose closed-form Cauchy coordinates and their derivatives for 2D closed high-order input cages composed of arbitrary-order polynomial curves.
Our coordinates facilitate the transformation of input polynomial curves into output curves of any desired polynomial order.
Central to our derivation is the creative use of the residue theorem with the logarithmic function to obtain the integral of a rational polynomial required for extending the classical 2D Cauchy coordinates to high-order input cages.
Our coordinates enable smooth cage-aware conformal deformations, and the derivatives allow for point-to-point deformation.
Moreover, our derivation can be extended to the input cages with rational polynomial curves.
Through various 2D deformations, we demonstrate how users can intuitively manipulate \Bezier control points to achieve desired deformations easily.
Our coordinates facilitate the transformation of input polynomial curves into output curves of any desired polynomial order.
Central to our derivation is the creative use of the residue theorem with the logarithmic function to obtain the integral of a rational polynomial required for extending the classical 2D Cauchy coordinates to high-order input cages.
Our coordinates enable smooth cage-aware conformal deformations, and the derivatives allow for point-to-point deformation.
Moreover, our derivation can be extended to the input cages with rational polynomial curves.
Through various 2D deformations, we demonstrate how users can intuitively manipulate \Bezier control points to achieve desired deformations easily.
Event Type
Technical Papers
TimeThursday, 18 December 20251:10pm - 1:21pm HKT
LocationMeeting Room S421, Level 4