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Automatically Controlled Morphing of 2D Shapes with Textures

Authors: Alexander Tereshin https://orcid.org/0000-0002-8218-0222, Valery Adzhiev https://orcid.org/0000-0002-8447-7089, Oleg Fryazinov, Felix Marrington-Reeve, and Alexander PaskoAuthors Info & Affiliations
https://doi.org/10.1137/19M1241581
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Abstract

This paper deals with 2D image transformations from a perspective of a 3D heterogeneous shape modeling and computer animation. Shape and image morphing techniques have attracted a lot of attention in artistic design, computer animation, and interactive and streaming applications. We present a novel method for morphing between two topologically arbitrary 2D shapes with sophisticated textures (raster color attributes) using a metamorphosis technique called space-time blending (STB) coupled with space-time transfinite interpolation. The method allows for a smooth transition between source and target objects by generating in-between shapes and associated textures without setting any correspondences between boundary points or features. The method requires no preprocessing and can be applied in 2D animation when position and topology of source and target objects are significantly different. With the conversion of given 2D shapes to signed distance fields, we have detected a number of problems with directly applying STB to them. We propose a set of novel and mathematically substantiated techniques, providing automatic control of the morphing process with STB and an algorithm of applying those techniques in combination. We illustrate our method with applications in 2D animation and interactive applications.

MSC codes

  1. metamorphosis
  2. transfinite color interpolation
  3. space-time bounded blending
  4. signed distance fields

MSC codes

  1. 65S05
  2. 51N20
  3. 68R01

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Supplementary Material

Index of Supplementary Materials

Title of paper: Automatically Controlled Morphing of 2D Shapes with Textures

Authors: Alexander Tereshin, Valery Adzhiev, Oleg Fryazinov, Felix Marrington-Reeve and Alexander Pasko

File: SupplementaryMaterials1.pdf

Type: PDF

Contents: This file contains the interval estimation for the coefficient a0.

File: figure5.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 5.

File: figure8.mpg

Type: Animation

Contents: figure8.mpg -- Animated sequence of frames represented in Figure 8.

File: figure10a.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 10(a).

File: figure10b.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 10(b).

File: figure10c.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 10(c).

File: figure11a.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 11(a).

File: figure11b.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 11(b).

File: figure11c.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 11(c).

File: figure12.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 12.

File: figure13.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 13.

File: figure15.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 15.

File: figure16.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 16.

File: figure17a.mpg

Type: Animation

Contents: Animated sequemce of frames represented in Figure 17(a).

File: figure17b.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 17(b).

File: figure17c.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 17(c).

File: figure17d.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 17(d).

File: figure18.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 18.

File: figure19.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 19.

File: figure20.mpg

Type: Animation

Contents: Animated sequence of frames represented in Figure 20.

File: space-time-blending_example.mpg

Type: Animation

Contents: Additional animated sequence of frames.

File: application_example.mpg

Type: Animation

Contents: Application example animation.

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Information & Authors

Information

Published In

cover image SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Volume 13 • Issue 1 • January 2020
Pages: 78 - 107
DOI: 10.1137/19M1241581
ISSN (online): 1936-4954

Copyright

© 2020, Society for Industrial and Applied Mathematics.

History

Submitted: 7 February 2019
Accepted: 24 October 2019
Published online: 4 February 2020

MSC codes

  1. metamorphosis
  2. transfinite color interpolation
  3. space-time bounded blending
  4. signed distance fields

MSC codes

  1. 65S05
  2. 51N20
  3. 68R01

Authors

Affiliations

Felix Marrington-Reeve
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