Offset Triangular Mesh Using the Multiple Normal Vectors of a Vertex Su-Jin Kim1, Dong-Yoon Lee2 and Min-Yang Yang3
1

Korea Advanced Institute of Science and Technology, sujinkim@kaist.ac.kr 2 Korea Advanced Institute of Science and Technology, yunny@kaist.ac.kr 3 Korea Advanced Institute of Science and Technology, myyang@kaist.ac.kr

ABSTRACT This paper introduces and illustrates the results of a new method for offsetting triangular mesh by moving all vertices along the multiple normal vectors of a vertex. The multiple normal vectors of a vertex are set the same as the normal vectors of the faces surrounding the vertex, while the two vectors with the smallest difference are joined repeatedly until the difference is smaller than allowance. Offsetting with the multiple normal vectors of a vertex does not create a gap or overlap at the smooth edges, thereby making the mesh size uniform and the computation time short. In addition, this offsetting method is accurate at the sharp edges because the vertices are moved to the normal directions of faces and joined by the blend surface. The method is also useful for rapid prototyping and tool path generation if the triangular mesh is tessellated part of the solid models with curved surfaces and sharp edges. The suggested method and previous methods are implemented on a PC using C++ and illustrated using an OpenGL library. Keywords: Offset, Triangular mesh, Multiple normal vectors

1. INTRODUCTION Offsets are widely used in tool path generation for numerical control machining, rapid prototyping, hollow or shelled model generation, and access space representations in robotics. In a numerical control machining area, 2D and 3D offsets are particularly important and useful for gouge-free and collision-free tool paths [1,2]. In 2D milling, a contour is offset by the size of the cutter radius, and invalid loops are removed for a gouge-free tool path [1]. In 3D milling, a gouge can be removed by computing the cutter...

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Cloning vector:
A cloning vector is a small piece of DNA, taken from a virus, a plasmid, or the cell of a higher organism, that can be stably maintained in an organism, and into which a foreign DNA fragment can be inserted for cloning purposes.( Genome Dictionary. Retrieved 2012-10-18.)
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Express each of the following vectors in terms of and
(a)
(b)
(c)
(Total 4 marks)
2. The vectors , are unit vectors along the x-axis and y-axis respectively.
The vectors = – + and = 3 + 5 are given.
(a) Find + 2 in terms of and .
A vector has the same direction as + 2 , and has a magnitude of 26.
(b) Find in terms of and .
(Total 4 marks)
3. The circle shown has centre O and radius 6. is the vector , is the vector and is the vector .
(a) Verify that A, B and C lie on the circle.
(3)
(b) Find the vector .
(2)
(c) Using an appropriate scalar product, or otherwise, find the cosine of angle .
(3)
(d) Find the area of triangle ABC, giving your answer in the form a , where a ∈ .
(4)
(Total 12 marks)
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(a) Find the vectors and .
(b) Find the angle between the diagonals of the quadrilateral OABC.
(Total 4 marks)
5. Find a vector equation of the line passing through (–1, 4) and (3, –1). Give your answer in the form r = p + td, where t ∈ R
(Total 4 marks)
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...the completion of the project.
NAME: PARTH KHANDURI
NAME:SHEFALI JAIN
ROLL NO: 10102171
ROLL NO: 10102216
CONTENTS
CHAPTER 1: INTRODUCTION
1.1 Background
1.2 Motivation
1.3 Outline
CHAPTER 2: COLOR SPACE
2.1 Introduction
2.2 Color Image Models
2.2.1 RGB Model
2.2.2 rgb Model
CHAPTER 3: COLOR SIMILARITY MEASURE
3.1 Introduction
3.2 Euclidean Distance
3.3 RGB
CHAPTER 4: COLOR IMAGE EDGE DETECTION
4.1 Introduction
4.2 Edge detection
4.3 Edge detection in color image
4.4 Techniques used
CHAPTER 5: DIFFERENTIAL OPERATORS
5.1 Sobel operator
5.2 Formulation
5.3 Thresholding and linking
CHAPTER 6: VECTOR ORDER STATISTIC OPERATOR
6.1 Introduction
6.2 Edge detectors
6.2.1 Vector range edge detector
6.2.2 Minimum vector range edge detector
6.2.3 Vector dispersion edge detector
6.2.4 Minimum vector dispersion edge detector
CHAPTER 7: PROJECT IMPLEMENTATION
7.1 Input image
7.2 On applying sobel operator
7.3 On applying VR edge detector
7.4 On applying MVR edge detector
7.5 On applying VD edge detector
7.6 On applying MVD edge detector
CHAPTER 8: RESULTS AND CONCLUSIONS
8.1 Results
8.2 Conclusion
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D
APPENDIX E
APPENDIX F
REFRENCES
CHAPTER 1
INTRODUCTION
1.1 Introduction
When humans are asked to describe a picture, they generally give a list of objects within the
picture as well as their...

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Tufts University
August 19, 2012
ii
This work is subject to copyright. It may be copied for non-commercial purposes.
Preface
The present volume is a sequel to my earlier book, Calculus Deconstructed: A Second Course in First-Year Calculus, published by the Mathematical Association in 2009. I have used versions of this pair of books for severel years in the Honors Calculus course at Tufts, a two-semester “boot camp” intended for mathematically inclined freshmen who have been exposed to calculus in high school. The ﬁrst semester of this course, using the earlier book, covers single-variable calculus, while the second semester, using the present text, covers multivariate calculus. However, the present book is designed to be able to stand alone as a text in multivariate calculus. The treatment here continues the basic stance of its predecessor, combining hands-on drill in techniques of calculation with rigorous mathematical arguments. However, there are some diﬀerences in emphasis. On one hand, the present text assumes a higher level of mathematical sophistication on the part of the reader: there is no explicit guidance in the rhetorical practices of mathematicians, and the theorem-proof format is followed a little more brusquely than before. On the other hand, the material being developed here is unfamiliar territory, for the intended...

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HDI Regression Using Health, Education &Income
3/21/2012
Department Of Business Economics
Jasmine Kaur(598)
Kshama (577)
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ABSTRACT
In this project we have employed tools of empirical econometric analysis to examine the relationship between the Human Development Index and the indicators of Human Development.
Table of contents
Topics | Page no: |
1.Abstract | (i) |
2. Literature Review | |
3. Theory 3.1 Data 3.2 Dummy Variable 3.3 Regression3.4 Interpretation | |
4. Hypothesis testing | |
LITERATURE REVIEW
Human development plays a fundamental role and remains the most important factor in Economic growth and development in countries of the world. The Human Development Index (HDI), first introduced in the 1990 Human Development Report (UNDP: 1990), was in response to the need for a measure that could better represent human achievements in several basic capabilities. This a composite statistic used to rank countries by level of “human development” and to separate countries into developed (high development), developing (middle development), and underdevelopment (low development) categories. The statistic is computed using data on Life Expectancy, Education and Per Capita GDP, each as an indicator of Standard of Living. Human Development is...

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Easyjet has always had a one-way ticketing policy. The airline has only one price in the market for any one flight at any one time. The lowest fare is offered into the market first and then prices rise as the departure draws closer and the seats are sold. This ticketing philosophy is transparent to consumers. There is a “value for money” offering, which is easily understood by consumers. By offering only one price in the market, the consumer is confident that “shopping around” using other channels or making greater ticketing restrictions will not reap the reward of lower fares. As the airline educates their consumers that the cheapest fares are sold first, consumers checking prices are more likely to purchase straightaway as they will have confidence that lower prices are not likely to appear later. The airline only sells tickets on a one-way basis and therefore if a passenger wants a return ticket they must buy two one-way tickets. The advantage of this for passengers is that they can book short stay trips without having to pay flexible return ticket prices. For business travellers the availability of flexible tickets is usually considered important. If a business meeting runs over the traveller...

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