<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we revisit the problem of monotonicity preservation of curves and surfaces and we provide some new proofs and open problems. In particular, we prove a new formula for the derivation of rational Bézier curves. We also deal with the rational monotonicity preservation of rational Bézier surfaces and a related conjecture is presented.</p></abstract>

In this paper we revisit the problem of monotonicity preservation of curves and surfaces and we provide some new proofs and open problems. In particular, we prove a new formula for the derivation of rational Bézier curves. We also deal with the rational monotonicity preservation of rational Bézier surfaces and a related conjecture is presented.

Monotonicity preserving representations of curves and surfaces

Universidad de Zaragoza, Escuela Universitaria Politécnica de Teruel

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Monotonicity preserving representations of curves and surfaces"}

In this paper we revisit the problem of monotonicity preservation of curves and surfaces and we provide some new proofs and open problems. In particular, we...

Monotonicity preserving representations of curves and surfaces

Published Online: Nov 03, 2016

Page range: 517 - 528

Received: Sep 11, 2016

Accepted: Nov 03, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00041

Keywords
Monotonicity preservation, axial monotonicity, rational surfaces, rational bilinear patch, shape parameter, shape preservation

© 2016 Jorge Delgado, Juan Manuel Peña, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Monotonicity preserving representations of curves and surfaces

Published Online: Nov 03, 2016

Page range: 517 - 528

Received: Sep 11, 2016

Accepted: Nov 03, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00041

KeywordsMonotonicity preservation, axial monotonicity, rational surfaces, rational bilinear patch, shape parameter, shape preservation

© 2016 Jorge Delgado, Juan Manuel Peña, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Keywords
Monotonicity preservation, axial monotonicity, rational surfaces, rational bilinear patch, shape parameter, shape preservation