Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Computer Engineering Expert

Surface Flattening using Discrete Harmonic Map, Morphing, and Texture Mapping.

1. Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary)

1.1. Map the boundary loop onto a unit rectangle using chord-length parameterization:

a) Pick a random starting point B0, trace the boundary loop L, compute its total length |L|;

b) Starting from B0, find vertices B1, B2, B3 on L, such that the lengths of the boundary paths from B0 to B1, B2, and B3 , are (or just passed) |L|/4, |L|/2, and 3|L|/4, respectively;

c) Map B0, B1, B2, and B3, to (0,0), (1,0), (1,1), and (0,1) respectively, map curve segments (B0, B1), (B1, B2), (B2, B3), (B3, B0) to four boundaries of the unit square accordingly using chord-length parameterization. This fixes the boundary mapping: all boundary vertices are mapped.

1.2. For every interior vertex, map it to the weighted average center of its one-rings. The weight is the harmonic weight, i.e., the cotangent weight defined on the original mesh.

Initially, map all interior vertices to (0.5,0.5), then use one of the following two ways to find the solution:

A easier but slower way:

Iteratively move the mapping position of each vertex:

Uik+1 = (Uik+(Σj≡n(i) wij ujk j≡n(i) wij )/2,

Here u denotes the coordinates on the plane, and we use k and k+1 to indicate the position before and after the (k+1)-th iteration.

You may need to do a few thousand iterations until you see the movement is small.

A faster way:

Assemble the coefficient matrix and solve the linear system (check slides)

2. Use your keyboard to control a linear interpolation between the original mesh and its planar target shape

a. Each vertex vi has its original 3D coordinates pi and 2D coordinates ui, its current position is xi = (1-t) pi+t ui

b. Use “-“ and “+” to decrease/increase the value of t, which should be restricted to [0,1]

3. Do a texture mapping using your computed coordinates.

Computer Engineering, Engineering

  • Category:- Computer Engineering
  • Reference No.:- M91809

Have any Question? 


Related Questions in Computer Engineering

1 what is security and information security what is the

1. What is security and information security? What is the difference? 2. It has been stated that security is a continuous process; what are the states in this process? 3. What are the differences between symmetric and as ...

Design and implement an algorithm that will efficiently

Design and implement an algorithm that will efficiently search a given text for a particular keyword or pattern and record the number of times the keyword or pattern is found. Design a main program that calls the procedu ...

In the second lab we use ftp to transfer some files we use

In the second lab, we use FTP to transfer some files. We use Wireshark to capture some packets. We show that FTP uses two separate connections: a control connection and a data-transfer connection. The data connection is ...

When you send an email message in html format you should

When you send an email message in HTML format, you should also send it in text format for all but one of the following reasons. Which one is it? Some people have their mail clients set to show only text The message may n ...

1 assume there is a server with the domain name

1. Assume there is a server with the domain name www.common.com. a. Show an HTTP request that needs to retrieve the document /usr/users/doc. The client accepts MIME version 1, GIF or JPEG images, but the document should ...

Need help writing a paper700- to 1050-word paper that will

Need help writing a paper 700- to 1,050-word paper that will be used as your reference manual in which you address the following: Define HIE Explain the purpose and use of HIE. Explain the 3 key forms of HIE. Explain how ...

1 the example describing skey stated that for md4 and md5

1. The example describing S/Key stated that "for MD4 and MD5, dictionary attacks are not a threat provided the seeds are chosen randomly." Why? How realistic is this assumption? 2. Why should a time-based authentication ...

The next day at sls found everyone in technical support

The next day at SLS found everyone in technical support busy restoring computer systems to their former state and installing new virus and worm control software. Amy found herself learning how to install desktop computer ...

In the game of life a blinker is a period 2 oscillator can

In the Game of Life, a blinker is a period 2 oscillator. Can you find another period 2 oscillator? How about a period 3 oscillator? A period 15 oscillator? Save your configurations as buttons in the Life model in the Net ...

Question 11 corporate culture has been said to be the

Question 1: 1. Corporate culture has been said to be the toughest component of a business to change. Do you agree or disagree with this statement and why? 2. Define the five types of power according to French and Raven's ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro