Hongbo Fu

Handle-aware isolines for scalable shape editing

Handle-based mesh deformation is essentially a nonlinear problem. To allow scalability, the original deformation problem can be approximately represented by a compact set of control variables. We show the direct relation between the locations of handles on the mesh and the local rigidity under deformation, and introduce the notion of handle-aware rigidity. Then, we present a reduced model whose control variables are intelligently distributed across the surface, respecting the rigidity information and the geometry. Specifically, for each handle, the control variables are the transformations of the isolines of a harmonic scalar field representing the deformation propagation from that handle. The isolines constitute a virtual skeletal structure similar to the bones in skinning deformation, thus correctly capturing the low-frequency shape deformation. To interpolate the transformations from the isolines to the original mesh, we design a method which is local, linear and geometry-dependent. This novel interpolation scheme and the transformation-based reduced domain allow each iteration of the nonlinear solver to be fully computed over the reduced domain. This makes the per-iteration cost dependent on only the number of isolines and enables compelling deformation of highly detailed shapes at interactive rates. In addition, we show how the handle-driven isolines provide an efficient means for deformation transfer without full shape correspondence.

Effective Derivation of Similarity Transformations for Implicit Laplacian Mesh Editing

Laplacian coordinates as a local shape descriptor have been employed in mesh editing. As they are encoded in the global coordinate system, they need to be transformed locally to reflect the changed local features of the deformed surface. We present a novel implicit Laplacian editing framework which is linear and effectively captures local rotation information during editing. Directly representing rotation with respect to vertex positions in 3D space leads to a nonlinear system. Instead, we first compute the affine transformations implicitly defined for all the Laplacian coordinates by solving a large sparse linear system, and then extract the rotation and uniform scaling information from each solved affine transformation. Unlike existing differential‐based mesh editing techniques, our method produces visually pleasing deformation results under large angle rotations or big‐scale translations of handles. Additionally, to demonstrate the advantage of our editing framework, we introduce a new intuitive editing technique, called configuration‐independent merging, which produces the same merging result independent of the relative position, orientation, scale of input meshes.

Sketching hairstyles

This paper presents an intuitive sketching interface for interactive hairstyle design, made possible by an efficient numerical updating scheme. The user portrays the global shape of a desired hairstyle through a few 3D style curves which are manipulated by interactively sketching freeform strokes. Our approach is based on a vector field representation which is obtained by solving a sparse linear system with the style curves acting as boundary constraints. The key observation is that the specific sparseness pattern of the linear system enables an efficient incremental numerical updating scheme. This gives rise to a sketching interface that provides interactive visual feedback to the user. Interesting hairstyles can be easily created in minutes.

Spherical Piecewise Constant Basis Functions for All-Frequency Precomputed Radiance Transfer

This paper presents a novel basis function, called spherical piecewise constant basis function (SPCBF), for precomputed radiance transfer. SPCBFs have several desirable properties: rotatability, ability to represent all-frequency signals, and support for efficient multiple product. By smartly partitioning the illumination sphere into a set of subregions and associating each subregion with an SPCBF valued 1 inside the region and 0 elsewhere, we precompute the light coefficients using the resulting SPCBFs. Efficient rotation of the light representation in SPCBFs is achieved by rotating the domain of SPCBFs. During runtime rendering, we approximate the BRDF and visibility coefficients using the set of SPCBFs for light, possibly rotated, through fast lookup of summed-area table (SAT) and visibility distance table (VDT), respectively. SPCBFs enable new effects such as object rotation in all-frequency rendering of dynamic scenes and on-the-fly BRDF editing under rotating environment lighting. With graphics hardware acceleration, our method achieves real-time frame rates.

Topology-free cut-and-paste editing over meshes

Existing cut-and-paste editing methods over meshes are inapplicable to regions with non-zero genus. To overcome this drawback, we propose a novel method in this paper. Firstly, a base surface passing through the boundary vertices of the selected region is constructed using the boundary triangulation technique. Considering the connectivity between the neighboring vertices, a new detail encoding technique is then presented based on surface parameterization. Finally, the detail representation is transferred onto the target surface via the base surface. This strategy of creating a base surface as a detail carrier allows us to paste features of non-zero genus onto the target surface. By taking the physical relationship of adjacent vertices into account, our detail encoding method produces more natural and less distorted results. Therefore, our elegant method not only can eliminate the dependence on the topology of the selected feature, but also reduces the distortion effectively during pasting.

Optimal boundaries for Poisson mesh merging

Existing Poisson mesh editing techniques mainly focus on designing schemes to propagate deformation from a given boundary condition to a region of interest. Although solving the Poisson system in the least-squares sense distributes the distortion errors over the entire region of interest, large deformation in the boundary condition might still lead to severely distorted results. We propose to optimize the boundary condition (the merging boundary) for Poisson mesh merging. The user needs only to casually mark a source region and a target region. Our algorithm automatically searches for an optimal boundary condition within the marked regions such that the change of the found boundary during merging is minimal in terms of similarity transformation. Experimental results demonstrate that our merging tool is easy to use and produces visually better merging results than unoptimized techniques.

Hierarchical aggregation for efficient shape extraction

This paper presents an efficient framework which supports both automatic and interactive shape extraction from surfaces. Unlike most of the existing hierarchical shape extraction methods, which are based on computationally expensive top-down algorithms, our framework employs a fast bottom-up hierarchical method with multiscale aggregation. We introduce a geometric similarity measure, which operates at multiple scales and guarantees that a hierarchy of high-level features are automatically found through local adaptive aggregation. We also show that the aggregation process allows easy incorporation of user-specified constraints, enabling users to interactively extract features of interest. Both our automatic and the interactive shape extraction methods do not require explicit connectivity information, and thus are applicable to unorganized point sets. Additionally, with the hierarchical feature representation, we design a simple and effective method to perform partial shape matching, allowing efficient search of self-similar features across the entire surface. Experiments show that our methods robustly extract visually meaningful features and are significantly faster than related methods.