NDLI: An interpolation scheme for designing rational rotation-minimizing camera motions

Content Provider	Springer Nature Link
Author	Farouki, Rida T. Giannelli, Carlotta Sestini, Alessandra
Copyright Year	2011
Abstract	When a moving (real or virtual) camera images a stationary object, the use of a rotation-minimizing directed frame (RMDF) to specify the camera orientation along its path yields the least apparent rotation of the image. The construction of such motions, using curves that possess rational RMDFs, is considered herein. In particular, the construction entails interpolation of initial/final camera positions and orientations, together with an initial motion direction. To achieve this, the camera path is described by a rational space curve that has a rational RMDF and interpolates the prescribed data. Numerical experiments are used to illustrate implementation of the method, and sufficient conditions on the two end frame orientations are derived, to ensure the existence of exactly one interpolant. By specifiying a sequence of discrete camera positions/orientations and an initial motion direction, the method can be used to construct general rotation-minimizing camera motions.
Starting Page	63
Ending Page	82
Page Count	20
File Format	PDF
ISSN	10197168
Journal	Advances in Computational Mathematics
Volume Number	38
Issue Number	1
e-ISSN	15729044
Language	English
Publisher	Springer US
Publisher Date	2011-09-23
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Camera orientation Directed frames Rotation-minimizing frames Angular velocity Pythagorean curves Quaternions Interpolation Numeric Computing Calculus of Variations and Optimal Control; Optimization Mathematics Algebra Theory of Computation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves

Hermite Interpolation by Rotation-Invariant Spatial Pythagorean-Hodograph Curves

Rotation-minimizing osculating frames

Rational rotation-minimizing frames—Recent advances and open problems

C1 and C2 interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

An approach to geometric interpolation by Pythagorean-hodograph curves

Corrigendum to “Rational rotation-minimizing frames on polynomial space curves of arbitrary degree” [J. Symbolic Comput. 45 (8) (2010) 844–856]

C 1 Hermite interpolation by Pythagorean hodograph quintics in Minkowski space

An interpolation scheme for designing rational rotation-minimizing camera motions

Similar Documents

Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves

Hermite Interpolation by Rotation-Invariant Spatial Pythagorean-Hodograph Curves

Rotation-minimizing osculating frames

Rational rotation-minimizing frames—Recent advances and open problems

C1 and C2 interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

An approach to geometric interpolation by Pythagorean-hodograph curves

Corrigendum to “Rational rotation-minimizing frames on polynomial space curves of arbitrary degree” [J. Symbolic Comput. 45 (8) (2010) 844–856]

C 1 Hermite interpolation by Pythagorean hodograph quintics in Minkowski space

An interpolation scheme for designing rational rotation-minimizing camera motions