Min-Ho Kyung

Nonlinear kinematic tolerance analysis of planar mechanical systems

This paper presents a nonlinear kinematic tolerance analysis algorithm for planar mechanical systems comprised of higher kinematic pairs. The part profiles consist of line and circle segments. Each part translates along a planar axis or rotates around an orthogonal axis. The part shapes and motion axes are parameterized by a vector of tolerance parameters with range limits. A system is analyzed in two steps. The first step constructs generalized configuration spaces, called contact zones, that bound the worst-case kinematic variation of the pairs over the tolerance parameter range. The zones specify the variation of the pairs at every contact configuration and reveal failure modes, such as jamming, due to changes in kinematic function. The second step bounds the worst-case system variation at selected configurations by composing the zones. Case studies show that the algorithm is effective, fast, and more accurate than a prior algorithm that constructs and composes linear approximations of contact zones.

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

Controlled linear perturbation

\theta

Noiseless GPU rendering of isotropic BRDF surfaces

, 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

Robust polyhedral Minkowski sums with GPU implementation

\theta

Robust parameter synthesis for planar higher pair mechanical systems

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

GPU Algorithm for Outer Boundaries of a Triangle Set

\theta

Relighting 3D Scenes with a Continuously Moving Camera

. Since the threads provide sample rays consistently varying on the surface, the estimation variance manifesting image noise is minimized. A thread set is precomputed for each BRDF before rendering so that no sampling overhead is imposed on the GPU. According to our experiments, about 100 threads are sufficient for most measured BRDFs to achieve a plausible quality, which enables the interactive performance.

Parallel mesh simplification using embedded tree collapsing

We present an algorithmic solution to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric predicates, which can cause combinatorial errors in the algorithm output. We make approximate computation accurate by performing small input perturbations, which we compute using differential calculus. This strategy supports fast, accurate Minkowski sum computation. The only prior robust implementation uses a less efficient algorithm, requires exact algebraic computation, and is far slower based on our extensive testing.

Thread-based BRDF rendering on GPU

Illumination at a surface point is formulated as an integral of a BRDF using the incident radiance over the hemisphere domain. A popular method to compute the integral is Monte Carlo integration, in which the surface illumination is computed as the sum of the integrand evaluated with stochastically sampled rays. Although its simple nature is practically attractive, it incurs the serious drawback of noise artifacts due to estimator variance. In this paper, we propose a novel noiseless Monte Carlo rendering algorithm running in real time on a GPU. The main contribution is a novel importance sampling scheme, which constructs spatially continuous sample rays over a surface. For each evenly spaced polar angle of the eye ray, denoted by θ, incident rays are sampled with a PDF (probability density function) derived from a target BRDF lobe. We develop a force-based update method to create a sequence of consistent ray sets along θ’s. Finally, corresponding rays in the sequence of ray sets are linearly connected to form a continuous ray curve, referred to as a sample thread. When rendering, illumination at a surface point is computed with rays, each of which is given as a point on a sample thread. Because a thread provides a sample ray that continuously varies on a surface, the random variance of the illumination, causing visual noise during the Monte Carlo rendering process, is eliminated. A thread set is precomputed for each BRDF to free the GPU from the burden of sampling during real-time rendering. According to extensive experiments, approximately 100 threads are sufficient for most measured BRDFs with acceptable rendering quality for interactive applications.