Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

Abstract

Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models and subdivision methods require a large number of parameters to model smooth surfaces. NURBS need fewer parameters but have a complicated rational expression and non-uniform shifts in their formulation. We present a new method to construct deformable closed surfaces, which includes exact spheres, by combining the best of two worlds: a smooth, interpolating model with a continuously varying tangent plane and well-defined curvature at every point on the surface.Our formulation is considerably simpler than NURBS and requires fewer parameters than polygon meshes. We demonstrate the generality of our method with applications including intuitive user-interactive shape modeling, continuous surface deformation, shape morphing, reconstruction of shapes from parameterized point clouds, and fast iterative shape optimization for image segmentation. Comparisons with discrete methods and non-interpolating approaches highlight the advantages of our framework.

Biharmonic deformation transfer with automatic key point selection

“…The recent work [8] develops an automatic method to deform meshes of arbitrary shapes to obtain their polycube form. The work [9] proposes a smooth, interpolating representation for shapes with spherical topology, and demonstrates its use for surface deformation. Many practical problems involve shape deformation.…”

Shape Projectors for Landmark-Based Spline Curves

“…The spline-based solution has the additional advantage that the proposed construction can also be applied to curves that are defined by a set of discrete points or landmarks, by simply interpolating them with a linear B-spline. Our framework can be extended to 3-D tensor-product spline surfaces [27] by noting that the inner product between spline surfaces can also be expressed as a matrix-vector multiplication.…”

Procedural Method for Fast Table Mountains Modelling in Virtual Environments

“…This is due to the ease of implementation of procedural methods for generating and rendering synthetic landforms [9,[15][16][17][18]. The main disadvantage of this representation is the inability to replicate models with aspherical topology [19]. Complex models are based on volumetric representation.…”