A simple geometric model for elastic deformations

By Isaac Chao, Ulrich Pinkall, P. Sanan, Peter Schröder. ACM Transactions on Graphics, 2010

300 citations recorded by the source corpus.

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Nerfies: Deformable Neural Radiance Fields (2020, methodology): “Considering the singular-value decomposition of the Jacobian JT = UΣV , multiple approaches [8, 13] penalize the deviation from the closest rotation as‖JT −R‖2F , where R = VU and‖·‖F is the Frobenius norm.”
Accelerated quadratic proxy for geometric optimization (2016, methodology): “First, note that these energies take the form f (x) = ∑ j E (Tj) |tj |, where EARAP (T ) = 1 2 ‖T −R‖2F , EISO (T ) = 1 2 ( ‖T‖2F + ∥∥T−1∥∥2 F ) , ECONF (T ) = 1 2 (σ1(T )/σd(T )) 2 .”
Efficient elasticity for character skinning with contact and collisions (2011, methodology): “However, [Chao et al. 2010] recently demonstrated the importance of a more accurate approximation to rotational force differentials lacking in warped stiffness approaches.”
Geometry of Logarithmic Strain Measures in Solid Mechanics (2015, background): “The same energy, also called the Biot energy [149], has been recently motivated by applications in digital geometry processing [43].”
Projective dynamics (2014, methodology): “In Figure 12 we compare the performance of our local/global solver to Newton’s method when solving the discretization of Equation 15 for M = SO(3) similar to [Chao et al. 2010].”
A material point method for snow simulation (2013, background): “[Chao et al. 2010] further improve deformable models and in particular show the importance of handling non-linear derivatives correctly.”