This research is conducted in the summer of 2015 and is possible by the support of various agency, in particular, by the grant of Prof. Angulo Nieves and the New York City Research Initiative.The purpose of this research is to reveal the mathematics and applications of the computer animation techniques of warping and morphing. A warp is a twist or distortion in the form of an object in an image while a morph is the smooth and gradual transformation of an object in one image into the object in another image. Linear algebra makes these computer animation techniques possible; the first phase of this research delves into how those mathematical processes translate into image warps and morphs. Image morphs and morphs were identified as affine transformations of original images. The second part of this study requires the analysis and application of image warping and morphing techniques in an array of fields. The team utilized the computer software, Abrosoft Fantamorph and Morpheus in order to create a series of warps and morphs. This shows an example of the use of technology in undergraduate research. The final phase of this research was to identify what uses NASA can have for these computer animation techniques and what further research can be done to expand our knowledge of warps and morphs. By identifying the mechanics of warps and morph, we can discover how they can assist scientists and organization, such as NASA, to create depictions of objects, ideas, places, and events. Ultimately, studying morphing and warping techniques allows us to find better ways to represent visual datawhether it is images of the ozone hole or maps of the ever-changing weather in a region. The limitations that were found during the study can be used to conduct further research about warps and morphs -such as distorting images using quadratics or varying the rate at which each part of a transformation happens.
Eigenvalues and Eigenvectors are usually taught toward the middle of the semester and this modulo can be implemented right after the topics of diagonalization. Comparing to the other modulo, students will see applications of some advance topics. This also shows one quick application of eigenvalues and eigenvectors in environmental science. There are different types of modeling for the population growth but in this modulo we will introduce the Leslie type's matrix to model population. More appropriately, this modulo belongs to the realm of "population ecology".
This article discusses the integration of computational thinking concepts, including algorithm, coding, abstraction, decomposition, debugging, and pattern recognition, into a Linear Algebra course in a community college in the fall of 2022. Through the implementation of project-based learning (PBL), we aimed to enhance students' understanding of linear algebra topics while familiarizing them with essential computational thinking concepts. A pre-and post-survey assessed the students' familiarity with the concepts. The results indicated a significant improvement in the students' understanding of computational thinking concepts and their application in linear algebra.
System of linear equation arise in various situations and Environmental Science is not an exceptions. This is also one of the first few topics that is covered in any standard linear algebra course. Thus this modulo can be implanted fairly early in the semester just after finishing Gauss-Jordan elimination methods are taught. By implementing this modulo not only students will be motivated to see a real environmental application of linear algebra but also connect theory with application early in the semester while typically application is usually taught toward the end or middle of the semester. Students will start with a warm-up example and will gradually be introduced the various parts of this modulo. Several types of questions are asked throughout this modulo which will guide the students to understand the concepts. At the end of the module, a project is provided as an expansion and extension of this modulo which can be assigned as a short project or as a classroom activity. As a byproduct of this project, student will learn the "Mathematica" software, a very user friendly computer algebra system (CAS).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations鈥揷itations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright 漏 2024 scite LLC. All rights reserved.
Made with 馃挋 for researchers
Part of the Research Solutions Family.