Hypothesizing undetected and occluded three-dimensional features using predicate logic based spatial reasoning

2005 ◽  
Author(s):  
M. Magee ◽  
M. Nathan
Keyword(s):  
Spatial Reasoning ◽  
Predicate Logic ◽  
Three Dimensional

Modelling spatial reasoning systems with shape algebras and formal logic

1997 ◽  
Vol 11 (4) ◽  
pp. 273-285 ◽  
Author(s):  
Scott C. Chase
Keyword(s):  
Spatial Reasoning ◽  
Predicate Logic ◽  
Spatial Relations ◽  
Large Set ◽  
First Order ◽  
Reasoning Systems ◽  
Geometric Objects ◽  
Small Set ◽  
Definition Of ◽  
High Level

AbstractThe combination of the paradigms of shape algebras and predicate logic representations, used in a new method for describing designs, is presented. First-order predicate logic provides a natural, intuitive way of representing shapes and spatial relations in the development of complete computer systems for reasoning about designs. Shape algebraic formalisms have advantages over more traditional representations of geometric objects. Here we illustrate the definition of a large set of high-level design relations from a small set of simple structures and spatial relations, with examples from the domains of geographic information systems and architecture.

Bringing Dynamic Geometry to Three Dimensions

2015 ◽  
pp. 68-99
Author(s):  
Nicholas H. Wasserman
Keyword(s):  
Teaching And Learning ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Dynamic Geometry ◽  
State Standards ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Common ◽  
K 12

Contemporary technologies have impacted the teaching and learning of mathematics in significant ways, particularly through the incorporation of dynamic software and applets. Interactive geometry software such as Geometers Sketchpad (GSP) and GeoGebra has transformed students' ability to interact with the geometry of plane figures, helping visualize and verify conjectures. Similar to what GSP and GeoGebra have done for two-dimensional geometry in mathematics education, SketchUp™ has the potential to do for aspects of three-dimensional geometry. This chapter provides example cases, aligned with the Common Core State Standards in mathematics, for how the dynamic and unique features of SketchUp™ can be integrated into the K-12 mathematics classroom to support and aid students' spatial reasoning and knowledge of three-dimensional figures.

Proportional Reasoning with a Pyramid

2011 ◽  
Vol 16 (9) ◽  
pp. 544-549
Author(s):  
Ami Mamolo ◽  
Margaret Sinclair ◽  
Walter J. Whiteley
Keyword(s):  
Spatial Reasoning ◽  
Proportional Reasoning ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model

A three-dimensional model and geometry software can help develop students' spatial reasoning and visualization skills.

Intelligent critiquing and tutoring of spatial reasoning skills

1996 ◽  
Vol 10 (3) ◽  
pp. 235-249 ◽  
Author(s):  
Ole Jakob Mengshoel ◽  
Sanjeev Chauhan ◽  
Yong Se Kim
Keyword(s):  
Engineering Students ◽  
Spatial Reasoning ◽  
Graph Matching ◽  
Three Dimensional ◽  
Partial Solution ◽  
Instructional Software ◽  
Preliminary Evaluation ◽  
Software System ◽  
Solid Objects ◽  
3D Solid

AbstractThe ability to reason spatially is an important skill required for engineers, particularly in engineering design and construction. One aspect of spatial reasoning is visualizing and constructing three-dimensional (3D) solid objects from two-dimensional (2D) projections. To assist in teaching this to engineering students, an instructional software system is being developed at the University of Illinois. This instructional software system is comprised of the Visual Sweeper and the Visual Teacher. The Visual Sweeper is a geometric framework for solving missing view problems. In missing view problems, students create 3D solid objects from two 2D projections by applying operations inverse to orthographic projection. The Visual Teacher, which is the focus of this article, is an intelligent critiquing and tutoring module that gives feedback to the student regarding partial solutions to missing view problems. The Visual Teacher is comprised of a Recognizer and a Critiquer. The Recognizer identifies which solution solid the student's partial solution is closest to. Based on the solution solid and a student's partial solution, the Criti-quer gives critique and advice to the student. The Recognizer is based on an algorithm for bipartite graph matching, while the Critiquer uses a rule-based approach. This paper describes the Visual Teacher, gives examples of how it can be used, presents preliminary evaluation results, and discusses the system's assumptions and limitations.

What counts as the evidence for three-dimensional and four-dimensional spatial representations?

2013 ◽  
Vol 36 (5) ◽  
pp. 567-568 ◽  
Author(s):  
Ranxiao Frances Wang ◽  
Whitney N. Street
Keyword(s):  
Reference Frames ◽  
Spatial Reasoning ◽  
Three Dimensional ◽  
Sufficient Evidence ◽  
Spatial Representations ◽  
Chance Performance ◽  
Systematic Biases ◽  
Reasoning Tasks

AbstractThe dimension of spatial representations can be assessed by above-chance performance in novel shortcut or spatial reasoning tasks independent of accuracy levels, systematic biases, mosaic/segmentation across space, separate coding of individual dimensions, and reference frames. Based on this criterion, humans and some other animals exhibited sufficient evidence for the existence of three-dimensional and/or four-dimensional spatial representations.

Using Origami to Promote Geometric Communication

2003 ◽  
Vol 9 (4) ◽  
pp. 222-229
Author(s):  
Rebecca R. Robichaux ◽  
Paulette R. Rodrigue
Keyword(s):  
Geometric Modeling ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Middle School Mathematics ◽  
Mathematics Lesson ◽  
Mathematical Arguments ◽  
Spatial Sense ◽  
Teaching Geometry ◽  
Geometric Concepts

Rigami has been used frequently in teaching geometry to promote the development of spatial sense; to make multicultural connections with mathematical ideas; and to provide students with a visual representation of such geometric concepts as shape, properties of shapes, congruence, similarity, and symmetry. Such activities meet the Geometry Standard (NCTM 2000), which states that students should be engaged in activities that allow them to “analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships” and to “use visualization, spatial reasoning, and geometric modeling to solve problems” (p. 41). This article begins with an explanation of the importance of communication in the mathematics classroom and then describes a middle school mathematics lesson that uses origami to meet both the Geometry Standard as well as the Communication Standard.

Activities for Students: Connecting Spatial Reasoning Ideas in Mathematics and Chemistry

2013 ◽  
Vol 107 (3) ◽  
pp. 220-224
Author(s):  
Sonali Raje ◽  
Michael Krach ◽  
Gail Kaplan
Keyword(s):  
Dimensional Analysis ◽  
Spatial Reasoning ◽  
Three Dimensional ◽  
Student Activity

Stereochemistry and three-dimensional analysis constitute significant parts of this student activity.

An Examination of the Convergent Validity of the ICAR16 and WAIS-IV

2020 ◽  
Vol 38 (8) ◽  
pp. 1052-1059 ◽  
Author(s):  
Stephanie R. Young ◽  
Timothy Z. Keith
Keyword(s):  
Convergent Validity ◽  
Spatial Reasoning ◽  
Three Dimensional ◽  
Number Series ◽  
Convenience Sample ◽  
Visual Spatial ◽  
Confirmatory Factor ◽  
Fluid Reasoning ◽  
The Matrix ◽  
Matrix Reasoning

The construct validity of the International Cognitive Ability Resource (ICAR) has yet to be investigated using a gold-standard individually administered intelligence battery. The present study used a convenience sample of 97 students to examine the respective relations between the ICAR16 and overall intelligence ( g) and the Cattell–Horn–Carroll broad abilities measured by the WAIS-IV. Large correlations were observed between the observed overall scores (rICAR16, full-scale IQ = .81, p < .001) and the CFA-estimated general factors ( r = .94, p < .001). Evidence from confirmatory factor models suggests that the ICAR letter–number Series task measures fluid reasoning, while the matrix reasoning, verbal reasoning, and three-dimensional reasoning tasks measure visual–spatial reasoning (Gv). Findings support the ICAR16 as a valid brief measure of nonverbal intelligence; however, replications in larger samples are needed.

scholarly journals Spatial Reasoning Based on 3D-ICSRM Model

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Yongshan Liu ◽  
Xiang Gong ◽  
Dehan Kong
Keyword(s):  
Spatial Reasoning ◽  
Three Dimensional ◽  
Spatial Relationship ◽  
Three Dimensional Objects ◽  
Proposed Model ◽  
Relationship Model ◽  
Composite Models ◽  
Differentiation Degree ◽  
And Performance ◽  
Reasoning Algorithm

The existing spatial relationship composite models have defects in both cognitive habits and differentiation degree when describing the spatial relationship between the three dimensional objects. These defects can cause inaccuracy in the process of spatial reasoning. In order to solve this problem, this paper proposes a Three-Dimensional Improved Composite Spatial Relationship Model (3D-ICSRM). Then a high-precision spatial relationship reasoning algorithm is presented based on this model, which combines qualitative and quantitative analyses. Finally, both the correctness and performance advantages of spatial reasoning algorithm are verified by experiments based on this proposed model.

scholarly journals Parametric Creative Design of Building Free-forms Roofed with Transformed Shells Introducing Architect’s and Civil Engineer’s Responsible Artistic Concepts

Buildings ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 58 ◽  
Author(s):  
Jacek Abramczyk ◽  
Aleksandra Prokopska
Keyword(s):  
Spatial Reasoning ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mutual Position ◽  
Software Applications ◽  
Single Structure ◽  
Interdisciplinary Problems ◽  
Engineering Models ◽  
Parametric Description ◽  
Effective Design

The article concerns a parametric description of unconventional building forms roofed with folded sheeting transformed elastically into shells. The description supports the designer in the search for attractive forms and a rational use of materials. The adoption of strictly defined sets of initial parameters determines the diversification of the designed architectural free-forms. An impact of selected proportions between these parameters on these forms is illustrated by an example of a single structure. Folded elevations and a segmented shell roof make each such structure internally coherent and externally sensitive. The mutual position and proportions of the shape of all elements, such as the roof, eaves, and façades, along with regular patterns in the same structure, determine this consistency of its form and sensitivity to harmonious incorporation into the natural or built environments. The study is a new insight into shaping free-forms of buildings in which the modern and ecological materials determine the important shape and mechanical limitations of these forms. With a skillful approach, the materials allow their extensive use in buildings. However, various interdisciplinary problems related to architectural shaping of free-forms and static and strength work thin-walled shell sheeting roofs must be solved. For effective design it is necessary to use relevant software applications, where spatial reasoning is crucial for ordering the three-dimensional space by means of simplified engineering models.

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