Jung-Hong Chuang

On local implicit approximation and its applications

A method is proposed for computing an implicit approximant at a point to a parametric curve or surface. The method works for both polynomially and rationally parameterized curves and surfaces and achieves an order of contact that can be prescribed. In the case of nonsingular curve points, the approximant must be irreducible, but in the surface case additional safeguards are incorporated into the algorithm to ensure irreducibility. The method also yields meaningful results at most singularities. In principle, the method is capable of exact implicitization and has a theoretical relationship with certain resultant-based elimination methods.

Variable-radius blending by constrained spine generation

Radius blends, very important in geometric and solid modeling, can be seen as the trimmed envelope of a rolling sphere or a sweeping circle with a constant or variable radius that centers on a spine curve and touches the surfaces to be blended along the linkage curves. Usually, in variable-radius blending, the radius is difficult to specify, and the spine curve is hard to trace. We propose several geometric constraints to specify the variable radius, which we then translate to a nonlinear system to represent the spine curve exactly. This is finally traced numerically in a high-dimensional space. We also propose a paradigm that implements the constraints while tracing along the spine curve in 3D space. We represent the result in parametric form.

Variable-radius blending of parametric surfaces

The radius blend is a popular surface blending because of its geometric simplicity. A radius blend can be seen as the envelope of a rolling sphere or sweeping circle that centers on a spine curve and touches the surface to be blended along the linkage curves. For a given pair of base surfaces in parametric form, a reference curve, and a radius function of the rolling sphere, we present an exact representation for the variable-radius spine curve and propose a marching procedure. We describe methods that use the derived spine curve and linkage curves to compute a parametric form of the variable-radius sphearical and circular blends.

Real-Time Translucent Rendering Using GPU-based Texture Space Importance Sampling

We present a novel approach for real‐time rendering of translucent surfaces. The computation of subsurface scattering is performed by first converting the integration over the 3D model surface into an integration over a 2D texture space and then applying importance sampling based on the irradiance stored in the texture. Such a conversion leads to a feasible GPU implementation and makes real‐time frame rate possible. Our implementation shows that plausible images can be rendered in real time for complex translucent models with dynamic light and material properties. For objects with more apparent local effect, our approach generally requires more samples that may downgrade the frame rate. To deal with this case, we decompose the integration into two parts, one for local effect and the other for global effect, which are evaluated by the combination of available methods [DS03, MKB* 03a] and our texture space importance sampling, respectively. Such a hybrid scheme is able to steadily render the translucent effect in real time with a fixed amount of samples.

User-assisted mesh simplification

During the last decade, many simplification methods have been proposed to generate multi-resolution meshes for real-time applications. Practitioners have found that these methods alone usually fail to produce satisfactory result when models of very low polygon count are desired. This is due to the fact that the existing methods take no semantic or functional metric into account, and moreover, each error metric has its own strength and weakness. In this paper, we propose a user-assisted mesh simplification framework that allows users to improve the quality of simplified meshes derived by any error metric. The framework consists of two stages. The first stage employs a weighting scheme that allows users to refine a unsatisfactory region to achieve a user-specified resolution. The second stage is a local refinement scheme aiming to provide a user-guided fine-tune to recover local sharp features. The proposed weighting scheme differs from the previous approaches in that the weights are used to directly reorder the edge collapsing sequence rather than weighting the collapsing cost. Such a direct reordering mechanism ensures a predictable increase of resolution in the selected region, and is both error-metric and resolution independent.

Texture Adaptation for Progressive Meshes

Level‐of‐detail modeling is a vital representation for real‐time applications. To support texture mapping progressive meshes (PM), we usually allow the whole PM sequence to share a common texture map. Although such a common texture map can be derived by using appropriate mesh parameterizations that consider the minimization of geometry stretch, texture stretch, or even the texture deviation introduced by edge collapses, we have found that even with a well parameterized texture map, the texture mapped PM still reveals apparent texture distortion due to geometry changes and the nature of linear interpolation used by texture mapping hardware. In this paper, we propose a novel, simple, and efficient approach that adapts texture content for each edge collapse, aiming to eliminate texture distortion. A texture adaptation and its inverse are local and incremental operations that can be fully supported by texture mapping hardware, the render‐to‐texture feature, and the fragment shader. Once the necessary correspondence in the partition of texture space is built during the course of PM construction, the texture adaptation or its inverse can be applied on the fly before rendering the simplified or refined model with texture map. We also propose the mechanism of indexing mapping to reduce blurred artifacts due to under‐sampling that might be introduced by texture adaptation.

Consistent parametrization by quinary subdivision for remeshing and mesh metamorphosis

The vertex correspondence establishment among multiple objects is a versatile operation in computer graphics and geometry processing. We propose a systematic method called recursive quinary subdivision to efficiently find a dissection for a meshed object of genus-zero with little user input. The process can be easily extended to multiple objects, taking into account the alignment of extra feature points for applications such as mesh metamorphosis, to derive a common dissection. Based on the dissection and the parameterization associated with each resulting patch, uniform or adaptive remeshing can be performed to yield a set of semi-regular meshes. Moveover, geometric details can be easily resampled and stored as normal maps. We demonstrate the mesh metamorphosis application between two or more objects based on the vertex correspondence established by the common dissection and parameterization.

Computing caustic effects by backward beam tracing

Caustic effects produced by the transport of light from specular surfaces to diffuse surfaces are a common type of optical effect that cannot be modeled by ray tracing. We propose a two-pass algorithm to model caustic effects efficiently and reliably. In the proposed method, information on transmitted light beams is collected in a tree structure, which is used to compute the intensity efficiently. The method does not require the polygonization of diffuse surfaces and can easily be combined with any rendering algorithm.

Physically based cosmetic rendering

Simulating realistic makeup effects is one of the important research issues in the 3D facial animation and cosmetic industry. Existing approaches based on image processing techniques, such as warping and blending, have been mostly applied to transfer ones makeup to anothers. Although these approaches are intuitive and need only makeup images, they have some drawbacks, for example, distorted shapes and fixed viewing and lighting conditions. In this paper, we propose an integrated approach, which combines the Kubelka–Munk model and a screen‐space skin rendering approach, to simulate 3D makeup effects. The Kubelka–Munk model is used to compute total transmittance when light passes through cosmetic layers, whereas the screen‐space translucent rendering approach simulates the subsurface scattering effects inside human skin. The parameters of Kubelka–Munk model are obtained by measuring the optical properties of different cosmetic materials, such as foundations, blushes, and lipsticks. Our results demonstrate that the proposed approach is able to render realistic cosmetic effects on human facial models, and different cosmetic materials and styles can be flexibly applied and simulated in real time. Copyright

Efficient generation of isosurfaces in volume rendering

Abstract An efficient method for extracting isosurfaces from volume data is proposed. The method utilizes a modified branch-on-need octree to bypass regions of no current interest. In addition, during the generation of triangle meshes neighboring triangles are merged according to certain criteria. Methods are also given to significantly reduce the space required for octrees. The method is more efficient and generates far fewer triangles than the marching cube algorithm. The performance of the proposed method is compared with that of several existing methods.