Balancing Rotation Minimizing Frames with Additional Objectives
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
When moving along 3D curves, one may require local coordinate frames for visited points, such as for animating virtual cameras, controlling robotic motion, or constructing sweep surfaces. Often, consecutive coordinate frames should be similar, avoiding sharp twists. Previous work achieved this goal by using various methods to approximate rotation minimizing frames (RMFs) with respect to a curve's tangent. In this work, we use Householder transformations to construct preliminary tangentaligned coordinate frames and then optimize these initial frames under the constraint that they remain tangent-aligned. This optimization minimizes the weighted sum of squared distances between selected vectors within the new frames and fixed vectors outside them (such as the axes of previous frames). By selecting different vectors for this objective function, we reproduce existing RMF approximation methods and modify them to consider additional objectives beyond rotation minimization. We also provide some example computer graphics use cases for this new frame tracking.
Description
CCS Concepts: Computing methodologies -> Shape modeling; Procedural animation; Mathematics of computing -> Mathematical optimization
@article{10.1111:cgf.14979,
journal = {Computer Graphics Forum},
title = {{Balancing Rotation Minimizing Frames with Additional Objectives}},
author = {Mossman, Christopher and Bartels, Richard H. and Samavati, Faramarz F.},
year = {2023},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14979}
}