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3D MODELING USING PARTIAL DIFFERENTIAL EQUATIONS...? 3D MODELING USING PARTIAL **DIFFERENTIAL** **EQUATIONS** (PDEs) A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy March 2013 TABLE OF CONTENTS TABLE OF CONTENTS 3 ACKNOWLEDGEMENT 4 ABSTRACT 5 Chapter 3 6 Efficient 3D Data Compression through Parameterization of Free-Form Surface Patches 6 3.1 **Method** 9 3.1.1 Polygon Reduction by Explicit Structured Vertices 9 3.1.2 Sampling and Reconstruction 10 3.1.3 Polynomial Interpolation 14 3.2 RESULTS 15 3.2.1 Data Compression 15 3.22 3D Reconstruction 18 3.2.3 Evaluating the fit 20 ACKNOWLEDGEMENT The successful completion of this study would not have been possible without the involvement of a number of...

41 Pages(10250 words)Essay

Linear Equations...?Linear **Equations**: Linear **equation**, an important concept in algebra was invented by Rane Descartes. Descartes was born in 1596 in France. He studied mathematics from the book of Culvius. Linear algebra was followed by the development of determinants in 1693 and Cramer presented his theory to solve systems of linear **equations** in 1750. Dependent and Independent Variables analysis started developing thereafter. Linear models formation was naturally a next step further for the solution of several real life issues. (A Brief History) Linear **equation** concept gave birth to the dependent and independent variables. Linear **equation** shows a relationship between two...

3 Pages(750 words)Research Paper

Differential Reporting in Australia..."**Differential** accounting standards are required in order to ensure adequate financial reporting for not-for-profits and government entities 0 Introduction:
**Differential** reporting in Australia has long been practiced on the basis of a 'reporting entry' concept. Presently the Australian Accounting Standards Board (AASB) wants to replace the exiting 'reporting entity' concept with a model that the Board thinks will represent a more prescriptive approach. For the proposed change the AASB has taken the 'International Financial Reporting Standard (IFRS) for SME Project' proposed by the International Accounting Standard Board (IASB) as the base model. The AASB has made an Invitation To Comment (ITC) 12 for the...

20 Pages(5000 words)Essay

Differential and Integral Calculus...of Calculus are **Differential** Calculus and Integral Calculus. **Differential** Calculus deals with rates of change while studying or solving a problem and Integral Calculus involves summations of special type. One helps to find the slope of tangent to a curve at a certain point while the other is used to find the area covered by a curve and two points on it.
As the entire natural world is in a constant motion and thus a change, mathematical analysis provides us the means to investigate the process of change, motion and dependence of quantities upon each other.
Consider the motion of a body moving in a straight line whose position is given by a number expressing the distance and direction from a fixed point,...

8 Pages(2000 words)Essay

Solving Equations...Project No. 2: Examination of a Formula Which Yields Prime Numbers Here Here Project No. 2: Examination of a Formula Which Yields Prime Numbers
Introduction
Ever since the glory that was Greece, man’s preoccupation with prime number brought him in countless pursuits. Hence, mathematicians ventured to uncover laws which govern prime number. Euclid was the first to find evidence that there are an infinite number of prime numbers. Meanwhile, Eratosthenes devised a **method** which bears his name, the sieve of Eratosthenes to find all prime numbers to a specified number (Knoebel, Laubenbacher, Lodder & Pengelley, 2007). This project about prime numbers is by far, the most exhilarating academic experience I have worked on.
The...

4 Pages(1000 words)Assignment

Quadratic Equations...Quadratic **Equations** Introduction Raising a pet is not as easy as it looks. To keep a pet one must possess patience and a passion forthe pet that one is raising. Space is vital for the provision of an enabling environment for the rearing of pet. Different pets need different amounts of space for the provision of enough areas for their survival. My pet is a cat, which naturally spends a better part of its day in the house.
This does not make it “a potato couch” and; thus, the need to fence my backyard arises. The backyard is of a rectangular shape with its length, L = 2W- 2 and a width W=13-L. All these measurements are in meters. This area encompasses the whole of my backyard, and it is large enough to provide an ample...

1 Pages(250 words)Assignment

Equations...of 3 and 8 by two separate constants to make one **equation** as follows:
5(3) + (2)(8) = 31 and -7(3) + 1(8) = -13
Step 2: Then write each **equation** as follows:
First **Equation**: 5x + 2y = 31 and Second **Equation**: -7x + y = -13
h. Solve your system of **equations** by the addition/subtraction **method**. Make sure you show the necessary 5 steps. Use the example on page 426 of Mathematics in Our World as a guide.
Using the addition **method**, multiply second **equation** by 2 then subtract the 2 **equations**:
5x + 2y = 31
-14x + 2y = ...

1 Pages(250 words)Assignment

Quadratic equations...Can you think of examples of processes that could be modeled with quadratic **equations**? In the real world, ‘Quadratic **Equations**’ can prove useful in a number of ways as –
(1) Modeling costs for a general store –
In C(x) = -0.03x2 + 57x + 310, for instance, the independent variable ‘x’ may refer to the number of materials bought which a store needs in order to produce sellable items. These materials are worth the variable cost C(x) with fixed cost of $310. Since the parabolic curve opens downward, as characterized by the negative leading coefficient, one manages to determine that a maximum cost is reached when x = -57/[ 2(-0.03) ]. The cost may be predicted to decline once the store decides to...

1 Pages(250 words)Assignment

Differential Treatment...**Differential** Treatment Affiliation **Differential** Treatment It is assumed that the criminal justice does not provide equal treatment to different members of the society. The disparity is mainly created by different social status and ethnic affiliations. The criminal justice system has been criticized for targeting individual from specific minority social and ethnic groups. For instance, Hispanics and African Americans have the majority numbers of convicts. This expectation has influenced the perception of the criminal justice system by minority groups. Most feel that the justice system is influenced by the wealthy and majority groups thus justice may not prevail.
Ways that the criminal justice provides...

3 Pages(750 words)Assignment

Molecular and ionic equations...s Post-Laboratory Assignment Molecular and ionic **equations** Step1 Molecular **equation** Cu(s)+4NHO3 (aq) Cu(NO3)2 (aq)+2NO2 (g)+2H2O (g)
Ironic **equation**
Cu(s)+4H+(aq)+4NO3-(aq) Cu2+(aq)+2NO3-(aq)+ 2N3+(aq)+4O2-(aq)+ 2H2O (g)
Step 2
Molecular **equation**
Cu(NO3)2 (aq)+2NaOH(aq) Cu(OH)2 (s)+2NaNO3 (aq)
Ionic **equation**
Cu2+(aq)+ 2NO3-(aq)+2Na+(aq)+2OH-(aq) Cu2+(aq)+ 2OH-(aq)+2 Na+(aq)+ 2NO3-(aq)
Step 3
Molecular **equation**
Cu(OH)2 (s) CuO(s) +H2O(g)
Ionic **equation**
Cu2+(aq)+ 2OH-(aq) Cu2+(aq)+O2-+ H2O(g)
Step...

1 Pages(250 words)Assignment