Isometric shape interpolation

Baek, Seung-Yeob; Lim, Jeonghun; Lee, Kunwoo

doi:10.1016/j.cag.2014.09.025

Cited by 21 publications

(6 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first item of the equation penalizes the deviation of the embedding to edge vectors solved in Subsection :

\begin{matrix} true \\ right E_{E V} (false{v_{i}, i \in I false}) & = & left \sum_{(g, j, i) \in F} false[{false∥ v_{g} - v_{j} - {bolde}_{g j} false∥}^{2} \\ left + {∥ v_{j} - v_{i} - e_{j i} ∥}^{2} + {∥ v_{i} - v_{g} - e_{i g} ∥}^{2}], \end{matrix}

where

{bolde}_{g j} = - l_{g j} u, {bolde}_{j i} = l_{j i} false(prefixcos β boldu - prefixsin β boldv false), {bolde}_{i g} = l_{i g} false(prefixcos α boldu + prefixsin α boldv false)

and α and β are, respectively, two angles of the triangle as shown in Figure [BLL15]. It is easy to cope with degenerate cases based on the analysis depicted in Figure .…”

Section: Las and Shape Reconstructionmentioning

confidence: 99%

“…Based on the notion, they proposed a fast as-isometric-as-possible interpolation framework. Baek et al [BLL15] introduced isometry-invariant intrinsic coordinates (IICs) to code the transformation between orthogonal frames on adjacent triangles for multiple shape interpolation. In essence, IICs play the role of connection maps.…”

Section: Connection Mapsmentioning

confidence: 99%

“…Slightly different from the multi‐scale geometry interpolation [WDAH10], Baek et al . [BLL15] employed the edge length and supplementary dihedral angle as two ingredients of the isometry‐invariant intrinsic coordinates (IICs) of edges to code the geometry of intermediate frames. The third entry of the IIC is an angle used to align the first edge of two adjacent triangles.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, only a

2 n_{E}

‐parameters sequence is required to represent a pose, where

n_{E}

is the edge number of the mesh. In addition, geometric shape can be recovered from this kind of quantities in a relatively efficient manner as demonstrated in [WDAH10, WLT12] and [BLL15]. Our contributions are summarized as follows: A new blend shape representation is proposed based on the sparse localized decomposition of variation of edge lengths and dihedral angles.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Articulated‐Motion‐Aware Sparse Localized Decomposition

Wang

Zeng

et al. 2016

Computer Graphics Forum

View full text Add to dashboard Cite

Compactly representing time‐varying geometries is an important issue in dynamic geometry processing. This paper proposes a framework of sparse localized decomposition for given animated meshes by analyzing the variation of edge lengths and dihedral angles (LAs) of the meshes. It first computes the length and dihedral angle of each edge for poses and then evaluates the difference (residuals) between the LAs of an arbitrary pose and their counterparts in a reference one. Performing sparse localized decomposition on the residuals yields a set of components which can perfectly capture local motion of articulations. It supports intuitive articulation motion editing through manipulating the blending coefficients of these components. To robustly reconstruct poses from altered LAs, we devise a connection‐map‐based algorithm which consists of two steps of linear optimization. A variety of experiments show that our decomposition is truly localized with respect to rotational motions and outperforms state‐of‐the‐art approaches in precisely capturing local articulated motion.

show abstract

“…The first item of the equation penalizes the deviation of the embedding to edge vectors solved in Subsection :

\begin{matrix} true \\ right E_{E V} (false{v_{i}, i \in I false}) & = & left \sum_{(g, j, i) \in F} false[{false∥ v_{g} - v_{j} - {bolde}_{g j} false∥}^{2} \\ left + {∥ v_{j} - v_{i} - e_{j i} ∥}^{2} + {∥ v_{i} - v_{g} - e_{i g} ∥}^{2}], \end{matrix}

where

{bolde}_{g j} = - l_{g j} u, {bolde}_{j i} = l_{j i} false(prefixcos β boldu - prefixsin β boldv false), {bolde}_{i g} = l_{i g} false(prefixcos α boldu + prefixsin α boldv false)

and α and β are, respectively, two angles of the triangle as shown in Figure [BLL15]. It is easy to cope with degenerate cases based on the analysis depicted in Figure .…”

Section: Las and Shape Reconstructionmentioning

confidence: 99%

Section: Connection Mapsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Furthermore, only a

2 n_{E}

‐parameters sequence is required to represent a pose, where

n_{E}

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Articulated‐Motion‐Aware Sparse Localized Decomposition

Wang

Zeng

et al. 2016

Computer Graphics Forum

View full text Add to dashboard Cite

show abstract

“…This method, however, only preserves the boundary and the interior of the input shapes may still be distorted. Then, as-rigid-as-possible [37,38] and as-isometric-as-possible [37,39] interpolation methods were proposed. The former uses rigid motion and compatible triangulation to improve the effect of interpolation, and the latter uses an isometry-invariant intrinsic coordinate system to simplify nonlinear isometric interpolation into a simple linear algebraic problem to achieve an effective isometric interpolation.…”

Section: Related Workmentioning

confidence: 99%

A morphing approach for continuous generalization of linear map features

Gao

Chen

2020

PLoS ONE

View full text Add to dashboard Cite

With the development of web maps, people are no longer satisfied with fixed and limited scale map services but want to obtain personalized and arbitrary scale map data. Continuous map generalization technology can be used to generate arbitrary scale map data. This paper proposes a morphing method for continuously generalizing linear map features using shape context matching and hierarchical interpolation (SCM-HI). More specifically, shape characteristics are quantitatively described by shape context on which shape similarity is measured based on a chi-square method; then, two levels of interpolation, skeleton and detail interpolations, are employed to generate the geometry of intermediate curves. The main contributions of our approach include (1) exploiting both the geometry and spatial structure of a vector curve in shape matching by using shape context, and (2) preserving both the main shape structure as-rigid-as-possible and local geometric details as gradual and smooth as possible for intermediate curves by hierarchical interpolation. Experiments show that our method generates plausible morphing effects and can thus serve as a robust approach for continuous generalization of linear map features.

show abstract