2,986 research outputs found
Physically Interacting With Four Dimensions
Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009People have long been fascinated with understanding the fourth
dimension. While making pictures of 4D objects by projecting them to 3D can help reveal basic geometric features, 3D graphics images by themselves are of limited value. For example, just as 2D shadows of 3D curves may have lines crossing one another in the shadow, 3D graphics projections of smooth 4D topological surfaces can be interrupted where one surface intersects another.
The research presented here creates physically realistic models for
simple interactions with objects and materials in a virtual 4D world.
We provide methods for the construction, multimodal exploration, and interactive manipulation of a wide variety of 4D objects. One basic achievement of this research is to exploit the free motion of a
computer-based haptic probe to support a continuous motion that
follows the \emph{local continuity\/} of a 4D surface, allowing collision-free exploration in the 3D projection. In 3D, this interactive probe follows the full local continuity of the surface as though we were in fact \emph{physically touching\/} the actual static 4D object.
Our next contribution is to support dynamic 4D objects that can move, deform, and collide with other objects as well as with themselves. By combining graphics, haptics, and collision-sensing physical modeling, we can thus enhance our 4D visualization experience. Since we cannot actually place interaction devices in 4D, we develop fluid methods for interacting with a 4D object in its 3D shadow image using adapted reduced-dimension 3D tools for manipulating objects embedded in 4D. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D interactive or haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the real-world experience accessible to human beings
Optimizing the Use of Matlab GUI Attributes in the Creation of Calculus Learning Media: An Effort to Measure Students' Innovative Attitudes
Calculus learning requires a high level of visualization in instilling concepts optimally to students. Therefore, the purpose of this study is to look at students' innovative attitudes in developing matlab GUI-based learning media in solving calculus problems and see the influence of the ability to use matlab GUI attributes on the level of innovation of the students in developing learning media. In the early stages, the students developed media according to the given topic. In the second stage, the product was assessed in terms of its validity. The students' innovative attitudes were assessed by a team of experts using questionnaires with 5-point Likert scale. From the 16 media successfully developed, validation results were obtained with an average score of 3.83 which means "valid". Meanwhile, from the assessment of innovative attitudes, the students’ attitudes are in the category of "innovative" with an average score of 3.61. In addition, the results of the regression tests revealed that the innovative attitudes are influenced by the ability to use the matlab GUI attributes by 84.2%. The rest is influenced by other factors with similarities: . Lastly, the results of the assessment showed that the media belonged to the category of "very effective" (score 81.2%).
Model Choice and Diagnostics for Linear Mixed-Effects Models Using Statistics on Street Corners
The complexity of linear mixed-effects (LME) models means that traditional
diagnostics are rendered less effective. This is due to a breakdown of
asymptotic results, boundary issues, and visible patterns in residual plots
that are introduced by the model fitting process. Some of these issues are well
known and adjustments have been proposed. Working with LME models typically
requires that the analyst keeps track of all the special circumstances that may
arise. In this paper we illustrate a simpler but generally applicable approach
to diagnosing LME models. We explain how to use new visual inference methods
for these purposes. The approach provides a unified framework for diagnosing
LME fits and for model selection. We illustrate the use of this approach on
several commonly available data sets. A large-scale Amazon Turk study was used
to validate the methods. R code is provided for the analyses.Comment: 52 pages, 15 figures, 3 table
From approximating to interpolatory non-stationary subdivision schemes with the same generation properties
In this paper we describe a general, computationally feasible strategy to
deduce a family of interpolatory non-stationary subdivision schemes from a
symmetric non-stationary, non-interpolatory one satisfying quite mild
assumptions. To achieve this result we extend our previous work [C.Conti,
L.Gemignani, L.Romani, Linear Algebra Appl. 431 (2009), no. 10, 1971-1987] to
full generality by removing additional assumptions on the input symbols. For
the so obtained interpolatory schemes we prove that they are capable of
reproducing the same exponential polynomial space as the one generated by the
original approximating scheme. Moreover, we specialize the computational
methods for the case of symbols obtained by shifted non-stationary affine
combinations of exponential B-splines, that are at the basis of most
non-stationary subdivision schemes. In this case we find that the associated
family of interpolatory symbols can be determined to satisfy a suitable set of
generalized interpolating conditions at the set of the zeros (with reversed
signs) of the input symbol. Finally, we discuss some computational examples by
showing that the proposed approach can yield novel smooth non-stationary
interpolatory subdivision schemes possessing very interesting reproduction
properties
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