Joo-Haeng Lee

B-spline curve fitting based on adaptive curve refinement using dominant points

In this paper, we present a new approach of B-spline curve fitting to a set of ordered points, which is motivated by an insight that properly selected points called dominant points can play an important role in producing better curve approximation. The proposed approach takes four main steps: parameterization, dominant point selection, knot placement, and least-squares minimization. The approach is substantially different from the conventional approaches in knot placement and dominant point selection. In the knot placement, the knots are determined by averaging the parameter values of the dominant points, which basically transforms B-spline curve fitting into the problem of dominant point selection. We describe the properties of the knot placement including the property of local modification useful for adaptive curve refinement. We also present an algorithm for dominant point selection based on the adaptive refinement paradigm. The approach adaptively refines a B-spline curve by selecting fewer dominant points at flat regions but more at complex regions. For the same number of control points, the proposed approach can generate a B-spline curve with less deviation than the conventional approaches. When adopted in error-bounded curve approximation, it can generate a B-spline curve with far fewer control points while satisfying the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

A cellular topology-based approach to generating progressive solid models from feature-centric models

Abstract Progressive mesh representation and generation have become one of the most important issues in network-based computer graphics. However, current researches are mostly focused on triangular mesh models. On the other hand, solid models are widely used in industry and are applied to advanced applications such as product design and virtual assembly. Moreover, as the demand to share and transmit these solid models over the network is emerging, how to effectively stream the solid models has been considered as one of the major research issues. In this paper, we present a cellular topology-based approach to generating progressive solid models (PSM) from feature-based models. The proposed approach introduces a new scheme for storing and transmitting solid models over the network. The cellular topology (CT) approach makes it possible to effectively generate PSMs and to efficiently transmit the models over the network with compact model size. Thus, an arbitrary solid model SM designed by a set of design features is stored as a much coarser solid model SM 0 together with a sequence of n detail records that indicate how to incrementally refine SM 0 exactly back into the original solid model SM=SM n .

Direct manipulation of generalized cylinders based on B-spline motion

We present a direct manipulation technique that allows interactive control of the shape of generalized cylinders. We interpret the generalized cylinder as the sweep surface of a planar cross-sectional B-spline curve under B-spline motion. The generated surface is a NURBS surface that interpolates a given sequence of crosssectional curves along a skeleton curve. Directly manipulating a surface point on the generalized cylinder modifies the crosssectional shape and its motion and deforms the generalized cylinder to interpolate the exact point location specified by the user. The surface is deformed by a target tracking procedure.

Polygonal boundary approximation for a 2D general sweep based on envelope and boolean operations

This paper presents an algorithm that approximates (using polygons) the boundary of a general sweep for an arbitrary 2D curved object (possibly with holes). Based on set-theoretic properties of the general sweep, our algorithm generates the polygonal sweep boundary incrementally, where envelope approximations and union operations are repeatedly applied to intermediate boundaries of the sweep and consecutive instances of the moving object at sampled locations of the motion. For approximation, each instance of the object is polygonized along the motion, where the object may experience dynamic shape transformation with topological changes such as creating and /or destroying internal holes. The incremental nature of the proposed algorithm makes the boundary construction of a general sweep useful for applications in interactive shape design, collision detection, and mechanical part design. Our algorithm generates a precise approximation of the boundary of a general sweep with real-time performance in computing unsweeps, Minkowski sums and differences, and constant radius offsets. Some experimental results are also given in this paper.

Modeling generalized cylinders using direction map representation

For generalized cylinders (GC) defined by contours of discrete curves, we propose two algorithms to generate GC surfaces (1) in polygonal meshes and (2) in developable surface patches of the cylindrical type. To solve the contour blending problem of generalized cylinder, the presented algorithms have adopted the algorithms and properties of linear interpolation by direction map (LIDM) that interpolate geometric shapes based on direction map merging and group scaling operations. Moreover, we propose an algorithm to develop generated developable surface patches on a plane. Proposed algorithms are fast to compute and easy to implement.

Thread-Based BRDF Rendering on GPU

Rendering BRDF surfaces have been intensively studied to produce physically plausible appearance of surface materials. Illumination at a surface point is formulated as an integral of a BRDF producted with incident radiance over the hemi-sphere domain. One popular method to compute the integral is Monte Carlo integration which estimates it with a sum of the integrand evaluated at stochastically sampled rays. Although its simple nature is practically attractive, it has a serious drawback of noise artifacts in 3D rendering. In this paper, we propose a novel noise-free Monte Carlo rendering algorithm running on a GPU in real-time. The main contribution is a new importance sampling scheme providing consistent sample rays over surfaces. For each evenly spaced latitude angle of eye ray, denoted by

Error-bounded B-spline curve approximation based on dominant point selection

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FRC based augment reality for aiding cooperative activities

, incident rays are sampled with a PDF derived from the target BRDF lobe. We use a force-based update method to make sample rays consistent between consecutive

A note on hybrid control of robotic spatial augmented reality

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New Geometric Interpretation and Analytic Solution for Quadrilateral Reconstruction

s. Finally, corresponding sample rays are linearly connected to form a smooth curve, called a {\it sample thread}. In rendering, the sample rays for a surface point are obtained as thread points specified by