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Related Experiment Video

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Dissection, MicroCT Scanning and Morphometric Analyses of the Baculum

Dissection, MicroCT Scanning and Morphometric Analyses of the Baculum

Published on: March 19, 2017

Ball-morph: definition, implementation, and comparative evaluation.

Brian Whited¹, Jaroslaw Jarek Rossignac

¹Walt Disney Animation Studios, 500 S. Buena Vista Street, Burbank, CA 91521-4850, USA. brian.whited@disney.com

IEEE Transactions on Visualization and Computer Graphics

|April 9, 2011

Summary

We introduce b-compatibility for planar curves and propose three symmetric ball morphing techniques. The linear ball-morph minimizes travel distance, while the circular ball-morph minimizes distortion between curves.

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Area of Science:

Computer Graphics
Computational Geometry
Differential Geometry

Background:

Curve morphing is essential in computer graphics and geometric modeling.
Existing morphing techniques often lack symmetry or introduce significant distortion.
The concept of b-compatibility for curves is introduced to ensure well-behaved morphs.

Purpose of the Study:

To define b-compatibility for planar curves.
To propose and construct three novel symmetric ball morphing techniques.
To compare these novel morphs against existing methods using various cost metrics.

Main Methods:

Definition of b-compatibility for planar curves.
Development of three ball morphing techniques based on automatic ball-map correspondence.
Derivation of linear, circular, and parabolic vertex trajectories.
Comparative analysis using six cost measures: travel-distance, distortion, stretch, local acceleration, average squared mean curvature, and maximum squared mean curvature.

Main Results:

The proposed ball morphs are symmetric and meet input curves at a right angle (circular and parabolic).
The linear ball-morph demonstrates the shortest travel-distance across tested scenarios.
The circular ball-morph exhibits the least distortion among the evaluated methods.
Performance comparison highlights the dependence of results on specific input curve characteristics.

Conclusions:

The proposed ball morphing techniques offer a symmetric and controllable approach to curve interpolation.
The linear and circular ball-morphs provide distinct advantages in minimizing travel-distance and distortion, respectively.
The choice of morphing technique should consider the specific application requirements and input curve properties.