Normal‐Driven Spherical Shape Analogies

Abstract

This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape analogy problem, where the analogy relationship is defined on the surface normal. This formulation can deform a 3D shape into different styles within a single framework. One can plug‐and‐play different target styles by providing an exemplar shape or an energy‐based style description (e.g., developable surfaces). Our surface stylization methodology enables Normal Captures as a geometric counterpart to material captures (MatCaps) used in rendering, and the prototypical concept of Spherical Shape Analogies as a geometric counterpart to image analogies in image processing.

Spherical Style Deformation on Single Component Models

“…We compare the deformation result of female face with those obtained using the method of [7]. In the first row of Fig.…”

“…Therefore, other than cubic stylization, more stylizations can be generated. Moreover, based on the same idea, Liu and Jacobson [7] developed an-other method for setting target normal directions, in which the directions were set through a spherical shape analogize to a sphere (the analogy shape), such as spherical parameterization or closest normal method [7].…”

“…To achieve spherical style deformation using the method [7], we use a polyhedron as the style model to approximate the spherical style because the distribution of face normals of a polyhedron approximates the distribution of spherical surface normals. In the section discussing the experimental results, we present the deformation results obtained by the method [7].…”

ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

“…The simplest version of ARAP results from using constant rotations per triangle. This choice has the drawback that bending across edges is not penalized, but it may be useful when other constraints are considered simultaneously [LG15, ZG18, LJ21]. In this case, $$\mathbf {R}$$ is computed in the local step based on the three vertices of a triangle, and divergence is computed in the usual way [PP03, Hir03], considering the columns of the rotation matrices as vector‐valued functions for each of the three coordinates.…”