Intersection Tests Research Articles

Optimal Testing of Multiple Hypotheses with Common Effect Direction

We present a theoretical basis for testing related endpoints. Typically, it is known how to construct tests of the individual hypotheses, and the problem is how to combine them into a multiple test procedure that controls the familywise error rate. Using the closure method, we emphasize the role of consonant procedures, from an interpretive as well as a theoretical viewpoint. Suprisingly, even if each intersection test has an optimality property, the overall procedure obtained by applying closure to these tests may be inadmissible. We introduce a new procedure, which is consonant and has a maximin property under the normal model. The results are then applied to PROactive, a clinical trial designed to investigate the effectiveness of a glucose-lowering drug on macrovascular outcomes among patients with type 2 diabetes.

A fast triangle to triangle intersection test for collision detection

AbstractThe triangle‐to‐triangle intersection test is a basic component of all collision detection data structures and algorithms. This paper presents a fast method for testing whether two triangles embedded in three dimensions intersect. Our technique solves the basic sets of linear equations associated with the problem and exploits the strong relations between these sets to speed up their solution. Moreover, unlike previous techniques, with very little additional cost, the exact intersection coordinates can be determined. Finally, our technique uses general principles that can be applied to similar problems such as rectangle‐to‐rectangle intersection tests, and generally to problems where several equation sets are strongly related. We show that our algorithm saves about 20% of the mathematical operations used by the best previous triangle‐to‐triangle intersection algorithm. Our experiments also show that it runs 18.9% faster than the fastest previous algorithm on average for typical scenarios of collision detection (on Pentium 4). Copyright © 2006 John Wiley & Sons, Ltd.

Boolean operations of STL models based on loop detection

For the data processing of rapid prototyping manufacturing, Boolean operation can offer a versatile tool for editing or modifying the STL model, adding the artificial construction, and creating the complex assistant-support structure to meet special technical requests. The topological structure of STL models is built firstly in order to obtain the relationship among the triangular facets of the object. The intersection test between two triangles picked, respectively, from two solids is taken to get the intersection triangle pairs and the intersection segments array, from which the intersection segments loops are detected. The intersection surfaces are divided into several surface patches along the intersection loops. The inclusion prediction is taken by testing the candidate point whether inside or outside the solid region of the solid slice. Detecting the loops for determination of the valid intersection lines greatly increases the efficiency and the reliability of the process.

Intersection test and blossoming perturbation for disk parametric curves and ball parametric surfaces

Errors in curve and surface representation due to inaccuracies in the data are considered and accounted for by introducing disk parametric curves and ball parametric surfaces. Intersection test algorithms and interval extensions using blossoming are discussed for each of the three cases of Bézier curves, tensor product surfaces, and triangular patches. A stability analysis is also performed for each of the three cases. It is shown that under certain restrictions disk Bézier curves and triangular ball Bézier patches are stable with respect to perturbations of the control disks (balls); whereas tensor product ball Bézier surfaces are in general not.

Ray Queries with Wide Object Isolation and the DE-Tree

This article introduces techniques for improving the performance of ray query data structures. The SMI (spatial median plus isolation) algorithm and the DE-tree (dual extent tree) are introduced and used to render all standard procedural database scenes. The ray-tracing experiments suggest that the SMI-created DE-tree features linear space, fast build and search times (on average proportional to NlogN and logN, respectively) and reduced ray-primitive intersection tests. The combined performance is an improvement over existing data structures.

1A1-B06 空気式パラレルマニピュレータを用いた触診シミュレータの開発

Nowadays, the breast cancer, over ahead of stomach one, holds the highest cancer incidence rate among Japanese women. Detection of breast cancer is done by palpation diagnosis, which require doctor to have highly experienced technique. In this study, we develop a palpation simulator which forms a woman's actual breast model holding active controlled variable stiffness property. A pneumatic parallel manipulator is employed as mechanical part of our simulator. In order to display a concrete stiffness feeling to human (doctor), control strategy is proposed where the contact point is detected using an idea of graphical intersection test. A reference stiffness is realized by constructing a compliance control system. By regulating the reference position according to the applied contact force, a palpation motion is executed. The validity of the proposed palpation system are confirmed through some experiments and analysis.

Geocube – GPU accelerated real-time rendering of transparency and translucency

We present a new method based on GPU acceleration for real-time transparency and translucency rendering. Our method computes refraction at both the front and back sides of a transparent object, as well as internal reflection, thus delivering interactive realistic transparency effects on a commodity PC. The real-time performance is made possible by a new acceleration data structure, called geocube, that enables the use of GPU for fast ray-surface intersection testing. In addition, within the same framework, we introduce the novel use of the mip-map for a hierarchical representation of a sequence of key prefiltered environment maps to simulate translucency. By taking ray depth into account and using GPU to interpolate the key filtered maps to produce the desired blurring effects, we achieve real-time realistic translucency rendering of slightly scattering media that allows show-through of background details.

Results to aid applications of ellipsoidal state bounds

Results to assist in the application of the ellipsoidal bounds provided by standard state-bounding algorithms are presented. They include derived bounds on scalar state-dependent quantities and the state values which determine them, tests of intersection and inclusion of ellipsoids, measures of how much an ellipsoid may be changed without altering its inclusion in another, and an ellipsoidal inner bound for the set reachable in the worst case from an ellipsoidal set by ellipsoidally bounded forcing, in a linear system. Approximations are suggested for the most computationally demanding result. Ways in which these results might be employed in aerospace interception problems are discussed to illustrate their utility.

Line Segment Intersection Testing

A method for accurately determining whether two given line segments intersect is presented. This method uses the standard floating-point arithmetic that conforms to IEEE 754 standard. If three or four ending points of the two given line segments are on a same vertical or horizontal line, the intersection testing result is obtained directly. Otherwise, the ending points and their connections are mapped onto a 3×3 grid, and the intersection testing falls into one of the five testing classes. The intersection testing method is based on our method for floating-point dot product summation, whose error bound is 1ulp. Our method does not have the limitation in the method of Gavrilova and Rokne (2000) that the product of two floating-point numbers is calculated by a twice higher precision floating-point arithmetic than that of the multipliers. Furthermore, this method requires less than one-fifth of the running time used by the method of Gavrilova and Rokne (2000), and our new method for calculating the sign of a sum of n floating-point numbers requires less than one-fifteenth of the running time used by ESSA.

Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing

Consider the problem of testing k hypotheses simultaneously. In this article we discuss finite- and large-sample theory of stepdown methods that provide control of the familywise error rate (FWE). To improve on the Bonferroni method or on Holm's stepdown method, Westfall and Young made effective use of resampling to construct stepdown methods that implicitly estimate the dependence structure of the test statistics. However, their methods depend on an assumption known as “subset pivotality.” Our goal here is to construct general stepdown methods that do not require such an assumption. To accomplish this, we take a close look at what makes stepdown procedures work; a key component is a monotonicity requirement of critical values. By imposing monotonicity on estimated critical values (which is not an assumption on the model but rather is an assumption on the method), we show how to construct stepdown tests that can be applied in a stagewise fashion so that at most k tests need to be computed. Moreover, at each stage, an intersection test that controls the usual probability of a type 1 error is calculated, which allows us to draw on an enormous resampling literature as a general means of test construction. In addition, it is possible to carry out this method using the same set of resamples (or subsamples) for each of the intersection tests.

An Efficient Ray-Quadrilateral Intersection Test

We present a new and efficient method to compute the intersection point between a convex planar quadrilateral and a ray. Contrary to the Schlick- Subrenat intersection test, the bilinear coordinates of the intersection point are computed only for rays that hit the quadrilateral. Rays that do not hit the quadrilateral are rejected early. Our method is up to 40% faster compared to the algorithm presented by Schlick and Subrenat. The intersection test we present is based on the Möller-Trumbore ray-triangle intersection algorithm. The new test is at least as fast as two ray-triangle intersection tests, and yields bilinear coordinates with no discontinuities in the isoparametrics. Source code implementing the intersection test is available online.

An Evaluation Framework for Ray-Triangle Intersection Algorithms

We show that comparing geometrical algorithms, in general, is very hard to do in a fair way. Our focus here is on the existing ray-triangle intersection test routines. A set of rules are developed so that a fair comparison can be produced, and this is all implemented in an evaluation framework. If all algorithms are evaluated using different hit rates, on different machines, for different input and output data, and different compilers, then it is impossible to single out one "best" algorithm. However, we provide ranking tables of the algorithms as well as top-five lists for all test computers, which can help a reader pick a good algorithm. Furthermore, a program called a "ray-triangle advisor" is developed that people can use in order to determine which algorithm works best under their particular circumstances. We hope our work can be useful for both developers of new intersection algorithms as well as for users of ray-triangle intersection algorithms.

DEVELOPMENT OF PALPATION SIMULATOR USING PNEUMATIC PARALLEL MANIPULATOR

Nowadays, the breast cancer, over ahead of stomach one, holds the highest cancer incidence rate among Japanese women. Detection of breast cancer is done by palpation diagnosis, which require doctor to have highly experienced technique. In this study, we develop a palpation simulator which forms a woman’s actual breast model holding active controlled variable stiffness property. A pneumatic parallel manipulator is employed as mechanical part of our simulator. In order to display a concrete stiffness feeling to human (doctor), control strategy is proposed where the contact point is detected using an idea of graphical intersection test. A reference stiffness is realized by constructing a compliance control system. By regulating the reference stiffness value according to the contact point, a palpation motion is executed. The validity of the proposed palpation system are confirmed through some experiments and analysis.

Fast 3D Line Segment–Triangle Intersection Test

I present a clean algorithm for determining if a line segment intersects a triangle in three dimensions. The algorithm performs a few binary tests that check if a point of intersection of the line segment and triangle plane is inside the triangle. Then I present some essential optimizations for this algorithm that reduce overall computation complexity. The algorithm does not compute an intersection point. The algorithm is comparable with others, but I believe it is the fastest one when additional memory storage is available.

Hardware-Based Collision and Self-Collision for Rigid and Deformable Surfaces

The interactive requirements of 3D games and physically driven virtual environments add strong constraints to the simulation of natural cloth collisions and self-collisions. In order to achieve interactive rates, we first define smoothness conditions over small patches of deformable surfaces and then resort to image-based collision-detection algorithms that we have developed. Our collision-detection system achieves interactive rates as it accurately tracks collisions and self-interactions of objects consisting of highly deformable surfaces. This method makes use of a novel technique for dynamically generating a hierarchy of cloth bounding boxes in order to perform object-level culling and image-based intersection tests using conventional graphics hardware support. Our results show that, for complex deformable surfaces with an excess of 50,000 triangular elements, we can track collisions at nearly interactive rates.

Image-based collision detection for deformable cloth models

Modeling the natural interaction of cloth and garments with objects in a 3D environment is currently one of the most computationally demanding tasks. These highly deformable materials are subject to a very large number of contact points in the proximity of other moving objects. Furthermore, cloth objects often fold, roll, and drape within themselves, generating a large number of self-collision areas. The interactive requirements of 3D games and physically driven virtual environments make the cloth collisions and self-collision computations more challenging. By exploiting mathematically well-defined smoothness conditions over smaller patches of deformable surfaces and resorting to image-based collision detection tests, we developed an efficient collision detection method that achieves interactive rates while tracking self-interactions in highly deformable surfaces consisting of a large number of elements. The method makes use of a novel technique for dynamically generating a hierarchy of cloth bounding boxes in order to perform object-level culling and image-based intersection tests using conventional graphics hardware support. An efficient backward voxel-based AABB hierarchy method is proposed to handle deformable surfaces which are highly compressed.

Automated left ventricular cardiac MRI segmentation, quantification and visualization using a radial-ray approach

A new segmentation algorithm is proposed that automatically segments the endocardium, epicardium and papillary muscles of the left ventricle (LV) from short-axis cardiac MRI data sets. The algorithm is based on image intensity gradient analysis using higher order derivatives and local parameterisation to obtain reliable segmentation results. User interaction is minimised to just the definition of centre points for the ventricle base, apex and papillary muscles. From the approximate centre of the ventricle on each slice, rays are cast and then scanned to find the extent of the ventricle wall. The segmentation algorithm parameterises three dynamic intersection tests to detect endocardium and epicardium intersections for each emitted ray. A high-resolution mesh describing both surfaces of the myocardium is then constructed from these intersections. Automated segmentation and reconstruction of the papillary muscles allows their exclusion from LV volume calculations and their inclusion in myocardial mass calculations. A software package was developed to evaluate the algorithm, providing DICOM compatibility and user interaction for segmentation corrections. Three-dimensional visualization of the segmentation results is also catered for, as both still and animated meshes, in mono or stereo vision. Currently, the algorithm detects endocardium intersections with great accuracy and the algorithm is robust even on problematic data sets. It also provides accurate reconstruction of the papillary muscles.

Random Field–Union Intersection tests for EEG/MEG imaging

Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same spatiotemporal data: topographic and tomographic. Until now, statistical tests for these two situations have developed separately. This work introduces statistical tests for assessing simultaneously the significance of spatiotemporal event-related potential/event-related field (ERP/ERF) components and that of their sources. The test for detecting a component at a given time instant is provided by a Hotelling's T 2 statistic. This statistic is constructed in such a manner to be invariant to any choice of reference and is based upon a generalized version of the average reference transform of the data. As a consequence, the proposed test is a generalization of the well-known Global Field Power statistic. Consideration of tests at all time instants leads to a multiple comparison problem addressed by the use of Random Field Theory (RFT). The Union-Intersection (UI) principle is the basis for testing hypotheses about the topographic and tomographic distributions of such ERP/ERF components. The performance of the method is illustrated with actual EEG recordings obtained from a visual experiment of pattern reversal stimuli.

RESEARCH REPORT

The purposes of this study were: to compare students' performance on conceptual and algorithmic chemistry problems; to investigate the relationships between learning orientation, formal reasoning, and mental capacity and students' performance on conceptual and algorithmic problems; and to investigate interactions among learning orientation, formal operational reasoning, and mental capacity. Participants were Grade 11 students enrolled in scientific sections of three Lebanese schools. Learning orientation, formal reasoning and mental capacities were measured using the Learning Approach Questionnaire, the Test of Logical Thinking, and the Figural Intersection Test, respectively. Also, students solved conceptual and low M-demand and high M-demand algorithmic chemistry problems. Students' performance on conceptual and algorithmic problems was compared. Regression analyses were used to examine the predictive power of the cognitive variables on each type of chemistry problems. In addition, performance of meaningful and rote learners was compared on all types of problems. Results showed that students performed significantly better on algorithmic than on conceptual problems. Moreover, meaningful learners outperformed rote learners on a test of conceptual problems while no significant differences existed for both levels of algorithmic problems. The three cognitive variables were significant predictors of performance on conceptual chemistry problems but not on algorithmic problems.

Multivariate Quality Control Chart for Autocorrelated Processes

Traditional multivariate statistical process control (SPC) techniques are based on the assumption that the successive observation vectors are independent. In recent years, due to automation of measurement and data collection systems, a process can be sampled at higher rates, which ultimately leads to autocorrelation. Consequently, when the autocorrelation is present in the data, it can have a serious impact on the performance of classical control charts. This paper considers the problem of monitoring the mean vector of a process in which observations can be modelled as a first-order vector autoregressive VAR (1) process. We propose a control chart called Z-chart which is based on the single step finite intersection test (Timm, 1996). An important feature of the proposed method is that it not only detects an out of control status but also helps in identifying variable(s) responsible for the out of control situation. The proposed method is illustrated with the help of suitable illustrations.