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The role of spatial reasoning in the development of systems in the domain of Artificial Intelligence is increasing. One particular approach, qualitative spatial reasoning, investigates the usage of abstract representation to facilitate the representation of and the reasoning with spatial information.This thesis investigates the usage of intervals along global axes as the under-lying representational and reasoning mechanism for a spatial reasoning system. Aspects that are unique to representing spatial information (flow and multi-dimensionality) are used to provide a method for classifying relations between objects at multiple levels of granularity. The combination of these two mechanisms (intervals and classification) provide the basis for the development of a querying system that allows qualitative queries about object relations in multi-dimensional space to be performed upon the representation.The second issue examined by this thesis is the problem of representing intervals when all the interval relations may not be known precisely. A three part solution is proposed. The first shows how the simplest situation, where all relations are explicit and primitive, can be represented and integrated with the above mentioned querying system. The second situation demonstrates how, for interval relations that are primitive but are not all explicitly known, an effective point based representation may be constructed. Finally, when relations between intervals are disjunctions of possible primitive interval relations, a representation is presented which allows solutions to queries to be constructed from consistent data.Our contribution is two-fold:1. a method of classifying the spatial relations and the means of querying these relations;2. a process of efficiently representing incomplete interval information and the means of efficiently querying this information.The work presented ++ / in this thesis demonstrates the utility of a multi-dimensional qualitative spatial reasoning system based upon intervals. It also demonstrates how an interval representation may be constructed for datasets that have variable levels of information about relationships between intervals represented in the dataset.

Computer-aided architectural design (CAAD) programs represent architectural design at a low level of spatial abstraction. While this representation model allows CAAD programs to capture the precise spatial characteristics of a design, it means that CAAD programs lack the underlying computational apparatus necessary to reason about design at a conceptual level. This thesis is a first step towards building a framework that bridges the gap between the conceptual aspects of a design and its low level CAAD-based spatial representation. Specifically, this thesis presents a new framework, referred to as the Conceptual Requirements Reasoner (CRR), which provides an architect with a framework to validate conceptual design requirements. The CRR will demonstrate how qualitative spatial representation and reasoning techniques can be used as the link between a design's conceptual requirements and its underlying quantitative spatial representation. A museum case study is presented to demonstrate the application of the CRR in a real world design context. It introduces a set of museum design requirements identified in research and shows how these requirements can be validated using the CRR. The results of the case study shows that the CRR is an effective tool for conceptual requirements reasoning.

Collective phenomena are ubiquitous in our every day lives; each day we are likely to observe or take part in a collective. Examples include a traffic jam on the way to work, a flock of birds in the sky or a queue in the shop. These examples include only three types of collective that are considered in this thesis: those phenomena whose individual members can be assigned a physical location in geographic space. However, this criterion is satisfied by many different types of collective. The movement patterns that are exhibited by collectives are one of their most prominent properties; it is often the property that we wish to reason about most. For example, the movement patterns of crowds, traffic or demonstrations. This thesis hypothesises that, given a dataset that comprises the movement data for a group of individuals, the presence of certain collectives can be achieved through an examination of the exhibited movement patterns. To identify the different types of collective that exist, a general taxonomy of collectives is presented. A class of collectives are found to manifest themselves through spatial coherence. Therefore, a set of spatial coherence criteria have been developed that can be applied to a movement dataset to indicate if any individuals within that dataset may be participating in a spatial collective. To indicate the different types of spatial collective that may be extracted, a taxonomy of spatial collectives is also presented.

<p>  </p> <p>Sketching is a valuable skill in engineering for representing information, developing design ideas, and communicating technical and abstract information. Design thinking is supported through sketching as a means of translating between internal and external representations, and creating shared representations of collaborative thinking. Sketching is also an important means of developing spatial abilities which are predictive of success in STEM fields. Computer-based design visualization tools have largely replaced freehand sketching in undergraduate engineering classrooms, but the shift has negatively impacted students’ design thinking and spatial reasoning skills. While many published classroom assessments of engineering and engineering design sketching skill exist, few are linked to theory of mental rotation and mental imagery, and the validity evidence for these instruments is scarce. This dissertation reports the development of a new instrument to assess sketching skills in engineering education based on spatial reasoning skills. </p> <p>The first study is a systematic literature review of engineering education literature on sketching assessment, sketching constructs and metrics were identified across existing tests, as well as cognitive theory which informed their use and wider learning contexts and purposes for sketching assessment. From content analysis after abstract and full paper sorting and review, metrics on accuracy, perspective, line quality, annotations, and aesthetics were found to be most prevalent. Cognitive skills included perceiving the sketch subject, creatively sketching ideas, using metacognition to monitor the sketching process, and communication. Sketching assessment varies by discipline and relies on feedback and scores or grades as well as expert review. </p> <p>From these findings, a new Object Assembly Test of Sketching was developed to evaluate sketching skills on 3-dimensional mental imagery and mental rotation tasks in 1- and 2-point perspective. The second study describes two rounds of pilot testing and revisions to the Object Assembly Test over Fall 2021 and Spring 2022 in two sections of an undergraduate mechanical engineering course. Initial inter-rater reliability values were low and rubric categories had inconsistent performance, and mean scores suggested line quality metrics were more difficult for students than shape quality metrics. Revisions to rubric categories were made after consulting with subject matter experts in engineering design, industrial design, and assessment, and a second round of pilot testing showed improvement in reliability between raters with similar patterns of mean scores. </p> <p>The third study presents reliability and preliminary validity evidence for the Object Assembly Test’s use in undergraduate mechanical engineering design graphics courses. Correlation and repeated-measures ANOVA were used to investigate pre-post score differences before and after sketching classroom learning intervention. A linear relationship between Object Assembly scores and intelligent tutoring software sketching metrics was also modeled for pre-post scores. Inter-rater reliability was improved through two rounds of grading and discussion. Correlations were moderately positive between scores and metrics, with more complex exercises negatively related to Speed. Post-test scores were significantly higher than pre-test scores but did not interact significantly with skill. Linear regression results showed some significant prediction of Precision and Smoothness by shape quality metrics, and a clear speed-accuracy tradeoff with negative prediction of Speed by nearly all sketching skills. </p> <p>We anticipate future use for this instrument where instructors and researchers may implement the sketching exercises and rubric in engineering classrooms alongside 3-dimensional drawing software. The Object Assembly Test can provide students with opportunities to practice perspective sketching before using computer design tools, as well as apply mental imagery and mental rotation cognition when manipulating complex solid shapes for sketching. Ongoing validation studies with this instrument will expand to a more diverse test-taking population and develop a theoretical model of mental rotation and mental imagery skills to inform object assembly sketching. </p>

When animals explore a new environment, they do not acquire a precise map of the places visited. In fact, research has shown that learning is a recurring process. Over time, new information helps the animal to update their perception of the locations it has visited. Yet, they are still able to use the fuzzy and often incomplete representation to find their way home. This process has been termed the cognitive mapping process. The work presented in this thesis uses a mobile robot equipped with sonar sensors to investigate the nature of such a process. Specifically, what is the information that is fundamental and prevalent in spatial navigation? Initially, the robot is instructed to compute a “cognitive map” of its environment. Since a robot is not a cognitive agent, it cannot, by definition, compute a cognitive map. Hence the robot is used as a test bed for understanding the cognitive mapping process. Yeap’s (1988) theory of cognitive mapping forms the foundation for computing the robot’s representation of the places it has visited. He argued that a network of local spaces is computed early in the cognitive mapping process. Yeap coined these local spaces as Absolute Space Representations (ASRs). However, ASR is not just a process of partitioning the environment into smaller local regions. The ASRs describe the bounded space that one is in, how one could leave that space (exits) and how the exits serves to link the ASRs to form a network that serves as the cognitive map (see Jefferies (1999)). Like the animal’s cognitive map, ASRs are not precise geometrical maps of the environment but rather, provide a rough shape or feel of the space the robot is currently in. Once the robot computes its “cognitive map”, it is then, like foraging and hoarding animals, instructed to find its way home. To do so, the robot uses two crucial pieces of information: distance between exits of ASRs and relative orientation of adjacent ASRs. A simple animal-like strategy was implemented for the robot to locate home. Results from the experiments demonstrated the robot’s ability to determine its location within the visited environment along its journey. This task was performed without the use of an accurate map. From these results and reviews of various findings related to cognitive mapping for various animals, we deduce that: Different animals have different sensing capabilities. They live in different environments and therefore face unique challenges. Consequently, they evolve to have different navigational strategies. However, we believe two crucial pieces of information are inherent in all animals and form the fundamentals of navigation: distance and orientation. Higher level animals may encode and may even prefer richer information to enhance the animal’s cognitive map. Nonetheless, distance and orientation will always be computed as a core process of cognitive mapping. We believe this insight will help future research to better understand the complex nature of cognitive mapping.

A symbolic image database system is a system in which a large amount of image data and their related information are represented by both symbolic images and physical images. How to perceive spatial relationships among the components in a symbolic image is an important criterion to find a match between the symbolic image of the scene object and the one being store as a modal in the symbolic image database. Spatial reasoning techniques have been applied to pictorial database, in particular those using 2D strings as an index representation have been successful. In this thesis, we extend the existing three levels of type-i similarity to more levels to aid similarity retrieval more precisely. There are 13 spatial operators which were introduced by Lee and Hsu to completely represent spatial relationships in 1D space. But, they just combined the 13 spatial relationships on x- and y-axis to represent the spatial relationships in 2D space by 13 times 13 = 169 spatial relationships. However, the 169 spatial relationships are still not sufficient to show all kinds of spatial relationships between any two objects in 2D space. For example, the directional relationships, like North or South West, exist in 2D space and is difficult to be deducted from those 13 spatial operators. Thus, we add the nine directional relationships to the 169 spatial relationships in 2D space. In this way, we can distinguish up to 289 spatial relationships in 2D space. Moreover, in our proposed strategy, we also take care of the problem caused by the MBRs. In most of the previous approaches for iconic indexing, for simplifying the concerns, they apply the MBRs of two objects to define the spatial relationship between them. The topological relationships, however, between objects can be quite different from the spatial relationship of their respective $MBR$s. Therefore, sometimes, it is hard to correctly describe the spatial relationship of the objects in terms of the relationships between their corresponding MBRs. To improve this drawback resulted from MBRs, we adopting the concept of topological relationships in our proposed strategy. Good access methods for large image databases are important for efficient retrieval. The signature files can be viewed as a preselection searching filter to prune off the unsatisfied images. In order to solve the ambiguity of the MBRs and to present the spatial relationships in two dimensional space completely, we propose a hybrid approach-based signature extraction method for similarity retrieval. From our simulation study, we show that our approach can provide a higher rate of a correct match and requires a smaller storage cost than Lee et al.'s 2D B-based signature approach. In some case, the correct match rate based on our proposed strategy can be up to 42.18%, while it is just 16.66% in Lee et al.'s strategy. Moreover, the worst case of the storage cost required in our proposed strategy is 1686 bits. But, it always needs 2015 bits in Lee et al.'s strategy.

When animals explore a new environment, they do not acquire a precise map of the places visited. In fact, research has shown that learning is a recurring process. Over time, new information helps the animal to update their perception of the locations it has visited. Yet, they are still able to use the fuzzy and often incomplete representation to find their way home. This process has been termed the cognitive mapping process. The work presented in this thesis uses a mobile robot equipped with sonar sensors to investigate the nature of such a process. Specifically, what is the information that is fundamental and prevalent in spatial navigation? Initially, the robot is instructed to compute a “cognitive map” of its environment. Since a robot is not a cognitive agent, it cannot, by definition, compute a cognitive map. Hence the robot is used as a test bed for understanding the cognitive mapping process. Yeap’s (1988) theory of cognitive mapping forms the foundation for computing the robot’s representation of the places it has visited. He argued that a network of local spaces is computed early in the cognitive mapping process. Yeap coined these local spaces as Absolute Space Representations (ASRs). However, ASR is not just a process of partitioning the environment into smaller local regions. The ASRs describe the bounded space that one is in, how one could leave that space (exits) and how the exits serves to link the ASRs to form a network that serves as the cognitive map (see Jefferies (1999)). Like the animal’s cognitive map, ASRs are not precise geometrical maps of the environment but rather, provide a rough shape or feel of the space the robot is currently in. Once the robot computes its “cognitive map”, it is then, like foraging and hoarding animals, instructed to find its way home. To do so, the robot uses two crucial pieces of information: distance between exits of ASRs and relative orientation of adjacent ASRs. A simple animal-like strategy was implemented for the robot to locate home. Results from the experiments demonstrated the robot’s ability to determine its location within the visited environment along its journey. This task was performed without the use of an accurate map. From these results and reviews of various findings related to cognitive mapping for various animals, we deduce that: Different animals have different sensing capabilities. They live in different environments and therefore face unique challenges. Consequently, they evolve to have different navigational strategies. However, we believe two crucial pieces of information are inherent in all animals and form the fundamentals of navigation: distance and orientation. Higher level animals may encode and may even prefer richer information to enhance the animal’s cognitive map. Nonetheless, distance and orientation will always be computed as a core process of cognitive mapping. We believe this insight will help future research to better understand the complex nature of cognitive mapping.

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The purpose of this study is to describe the effect of a curriculum rich in spatial reasoning activities and experiences on the ability of my fifth grade students to spatially reason. The study was conducted to examine 1) the effects of my practice of incorporating spatial reasoning lessons and activities in my fifth-grade mathematics classroom on the students' ability to spatially reason and 2) the effects of my practice of incorporating spatial reasoning lessons and activities on my students' ability to problem solve. Data were collected over a ten-week period through the use of student interviews, anecdotal records, photos of student work, student journals, pre- and posttests and a post-study survey. In this study, students demonstrated a statistically significant increase on all pre- and posttests. The student interviews, anecdotal records, photos of student work, and student journals all revealed spatial reasoning was used in mathematics problem solving. The study suggests that spatial reasoning can be taught and spatial reasoning skills can be used in problem solving.