This article describes a method for efficiently computing parallel transport of tangent vectors on curved surfaces, or more generally, any vector-valued data manifold. More precisely, it extends vector field defined over region to the rest domain via along shortest geodesics. basic operation enables fast, robust algorithms extrapolating level set velocities, inverting exponential map, geometric medians and Karcher/Fréchet means arbitrary distributions, constructing centroidal Voronoi...

We present a data structure that makes it easy to run large class of algorithms from computational geometry and scientific computing on extremely poor-quality surface meshes. Rather than changing the geometry, as in traditional remeshing, we consider intrinsic triangulations which connect vertices by straight paths along exact input mesh. Our key insight is such triangulation can be encoded implicitly storing direction distance neighboring vertices. The resulting signpost then allows...

Angle-preserving or conformal surface parameterization has proven to be a powerful tool across applications ranging from geometry processing, digital manufacturing, machine learning, yet maps can still suffer severe area distortion. Cone singularities provide way mitigate this distortion, but finding the best configuration of cones is notoriously difficult. This paper develops strategy that globally optimal in sense it minimizes total distortion among all possible cone configurations...

Smooth curves and surfaces can be characterized as minimizers of squared curvature bending energies subject to constraints. In the univariate case with an isometry (length) constraint this leads classic non-linear splines. For surfaces, is too rigid a instead one asks for Willmore (squared mean curvature) energy conformality constraint. We present efficient algorithm (conformally) constrained using triangle meshes arbitrary topology or without boundary. Our conformal class based on discrete...

Given a sequence of poses body we study the motion resulting when is immersed in (possibly) moving, incompressible medium. With given, say, by an animator, governing second-order ordinary differential equations are those rigid with time-dependent inertia acted upon various forces. Some these forces, like lift and drag, depend on surrounding Additionally, must encode effect medium through its added mass. We derive corresponding dynamics which generalize standard equations. All forces based...

We consider motion effected by shape change. Such motions are ubiquitous in nature and the human made environment, ranging from single cells to platform divers jellyfish. The shapes may be immersed various media very viscous air nearly inviscid fluids. In absence of external forces these settings characterized constant momentum. exploit this an algorithm which takes a sequence changing shapes, say, as modeled animator, input produces corresponding world coordinates. Our method is based on...

We introduce a family of boundary conditions and point constraints for conformal immersions that increase the controllability surfaces defined as minimizers variational problems. Our free fix metric on boundary, up to global scale, admit discretization compatible with discrete equivalence. also scale factor, enforcing rigidity geometry in regions interest, describe how presence class encodes knot points spline can be directly manipulated. To control tangent planes, we flux balancing internal...

In both the fields of computer science and medicine there is very strong interest in developing personalized treatment policies for patients who have variable responses to treatments. particular, I aim find an optimal policy which a non-deterministic function patient specific covariate data that maximizes expected survival time or clinical outcome. developed algorithmic framework solve multistage decision problem with varying number stages are subject censoring "rewards" times. specific,...

This paper describes a method for efficiently computing parallel transport of tangent vectors on curved surfaces, or more generally, any vector-valued data manifold. More precisely, it extends vector field defined over region to the rest domain via along shortest geodesics. basic operation enables fast, robust algorithms extrapolating level set velocities, inverting exponential map, geometric medians and Karcher/Fr\'{e}chet means arbitrary distributions, constructing centroidal Voronoi...

The Willmore energy plays a central role in the conformal geometry of surfaces 3-sphere \(S^3\). It also arises as leading term variational problems ranging from black holes, to elasticity, and cell biology. In computational setting discrete version is desired. Ideally it should have same symmetries smooth formulation. Such M\"obius invariant for simplicial was introduced by Bobenko. present paper we provide new geometric interpretation curvature rolling spheres connection analogy where...