Bounded distortion harmonic shape interpolation

Chien, Edward; Chen, Renjie; Weber, Ofir

doi:10.1145/2897824.2925926

Cited by 21 publications

(27 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Chen et al [11] extended their method by supporting the wider class of quasi-conformal mappings, in order to provide interpolations with a bounded amount of conformal distortion. Chien et al [12] improved [11] presenting an algorithm two orders of magnitude faster. Moreover, the method from Chien et al is meshless, thus provides results with increased smoothness.…”

Section: D Shape Interpolationmentioning

confidence: 99%

“…Our system simulates the depth between the different body parts of the characters by moving them in the scene according to the position of the viewer. It exploits 3 different techniques: billboarding [1], parallax scrolling [6] and 2D shape interpolation [12]. As shown in figure 2, the system requires as input a character split in different body parts.…”

Section: D Characters In a 3d Environmentmentioning

confidence: 99%

“…There are several methods that solve this problem. For our system, we chose to rely on Bounded Distortion Harmonic (BDH) Shape Interpolation [12]. This method produce "provably good" [26] harmonic mappings -they are smooth, locally injective and have bounded conformal isometric distortion -such that its geometric distortion is bounded by the input mapping's one.…”

Section: D Characters In a 3d Environmentmentioning

confidence: 99%

See 2 more Smart Citations

Repurpose 2D Character Animations for a VR Environment Using BDH Shape Interpolation

Barbieri

Cawthorne

Xiao

et al. 2017

Next Generation Computer Animation Techniques

View full text Add to dashboard Cite

Fig. 1. Two examples of 2D characters placed in a 3D environment using our framework.Abstract. Virtual Reality technology has spread rapidly in recent years. However, its growth risks ending soon due to the absence of quality content, except for few exceptions. We present an original framework that allows artists to use 2D characters and animations in a 3D Virtual Reality environment, in order to give an easier access to the production of content for the platform. In traditional platforms, 2D animation represents a more economic and immediate alternative to 3D. The challenge in adapting 2D characters to a 3D environment is to interpret the missing depth information. A 2D character is actually flat, so there is not any depth information, and every body part is at the same level of the others. We exploit mesh interpolation, billboarding and parallax scrolling to simulate the depth between each body segment of the character. We have developed a prototype of the system, and extensive tests with a 2D animation production show the effectiveness of our framework.

show abstract

Section: D Shape Interpolationmentioning

confidence: 99%

Section: D Characters In a 3d Environmentmentioning

confidence: 99%

Section: D Characters In a 3d Environmentmentioning

confidence: 99%

See 1 more Smart Citation

Repurpose 2D Character Animations for a VR Environment Using BDH Shape Interpolation

Barbieri

Cawthorne

Xiao

et al. 2017

Next Generation Computer Animation Techniques

View full text Add to dashboard Cite

show abstract

“…This theory has been widely applied in surface parameterization, shape deformation, shape registration, etc. Recently, Chien et al present an improved method with bounded distortion property based on harmonic mappings [CCW16]. However, these methods have different aims and they do not consider shape interpolation problem.…”

Section: Related Workmentioning

confidence: 99%

“…in the past decade [GY03, KSS06, SM06, BCGB08, SSP08,JZDG09,ZLYG09,LWT * 10]. In this paper, we extend the bounded distortion interpolation in [CWKBC13] and [CCW16] by applying Teichmüller maps. In [WG10], the authors introduce a differential shape representation for conformal maps, using so-called "conformal factors" and "angular factors" to control the intermediate shapes.…”

Section: Related Workmentioning

confidence: 99%

Planar Shape Interpolation Based On Teichmüller Mapping

Nian

Chen

2016

Computer Graphics Forum

View full text Add to dashboard Cite

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 t = 0 t = 0.333 t = 0.666 t = 1 Figure 1: Interpolation between a horse and a dinosaur. From left to right: source (t = 0), intermediate shapes (t = 0.333 and t = 0.666),target (t = 1), and the conformal distortion graph which depicts the normalized conformal distortion for 1000 most distorted triangles along the time variable t. As it can be seen from the texture image that circles in the source shape gradually become ellipses in the intermediate shapes, and that the conformal distortion of the map is almost linear with respect to t. Abstract Shape interpolation is a classical problem in computer graphics and has been widely investigated inthe past two decades. Ideal shape interpolation should be natural and smooth which have good properties such as affine and conformal reproduction, bounded distortion, no fold-overs, etc. In this paper, we present a new approach for planar shape interpolation based on Teichmüller maps -a special type of maps in the class of quasi-conformal maps. The algorithm consists of two steps. In the first step, a Teichmüller map is computed from the source shape to the target shape, and then the Beltrami coefficient is interpolated such that the conformal distortion is linear with respect to the time variable. In the second step, the intermediate shape is reconstructed by solving the Beltrami equation locally over each triangle and then stitching the mapped triangles by conformal transformations. The new approach preserves all the good properties mentioned above and produces more natural and more uniform intermediate shapes than the start-of-the-art methods. Especially, the conformal distortion changes linearly with respect to the time variable. Experiment results show that our method can produce appealing results regardless of interpolating between the same or different objects.interpolation which includes the interpolation of the interior of the domain. In this paper, we only deal with shape blending of 2D domains. Figure 1 illustrates an example.Given a source shape and a target shape, the ultimate goal of shape blending is to generate a sequence of intermediate shapes with some good properties, such as intersection free (no foldovers), bounded distortion, affine reproduction and smoothness. Different methods differ by the quantities they choose to interpolate. However, most methods can't satisfy all the above properties, especially bounded distortion property and intersection free. Recent-

show abstract

Content-aware image resizing using quasi-conformal mapping

Kang

Chen

2017

Vis Comput

View full text Add to dashboard Cite

Bounded distortion harmonic shape interpolation

Cited by 21 publications

References 24 publications

Repurpose 2D Character Animations for a VR Environment Using BDH Shape Interpolation

Repurpose 2D Character Animations for a VR Environment Using BDH Shape Interpolation

Planar Shape Interpolation Based On Teichmüller Mapping

Content-aware image resizing using quasi-conformal mapping

Contact Info

Product

Resources

About