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

Course conclusionnbspnbspplease respond to the followingyou

"Course Conclusion"   Please respond to the following: You have just completed 10 weeks of an introduction to networking course. Imagine you have been asked to create a one-day training course that highlights the importa ...

1 some have described social engineering as being

1. Some have described social engineering as being perpetuated by our internal fears. Discuss those fears. 2. What is the role of software security testing in the process of finding solutions to system vulnerabilities?

Individual visual logic calculationsselect two calculation

Individual: Visual Logic: Calculations? Select two calculation tasks that a program could perform that could be used by a small business. Each task must include the following: • Inputting a value • Performing a calculati ...

1 design and implement a function that reverses the order

1. Design and implement a function that reverses the order of the items in a queue. Your solution may only use the operations defined by the Queue ADT, but you are free to use other data structures if necessary 2. Implem ...

Capture network traffic while accessing a website with your

Capture network traffic while accessing a website with your web browser. In Wireshark, go to Statistics > HTTP > Packet Counter >Create Stat. How many Response Packets did you capture? What types of Response Packets and ...

In this exercise we want to analyze some variants of key

In this exercise, we want to analyze some variants of key derivation. In practice, one masterkey kMK is exchanged in a secure way (e.g. certificate-based DHKE) between the involved parties. Afterwards, the session keys a ...

Task descriptionproject animationusing adobe after effects

TASK DESCRIPTION Project: Animation Using Adobe After Effects students are to create an animation. LEARNING OUTCOMES - Produce documents and present work in multimedia formats appropriate for the intended audience. - App ...

Q1 identify and provide definitions of the major components

Q1: Identify and provide definitions of the major components of object oriented database modeling? Q2: Identify tools used to develop object oriented data model? Q3: Define its differences between object oriented data mo ...

Assignment topicnbspthere are nearly a dozen core concepts

Assignment Topic: There are nearly a dozen core concepts or principles that SCRUM is founded upon, which are listed in the "SCRUM Orientation" PowerPoint presentation. Choose three or more of those principles. Research e ...

Assignmentyou have been recently hired to assist with

Assignment You have been recently hired to assist with purchasing computer forensics tools and resources for a major corporation. Using the concepts that you learned in chapters nine through twelve recommend specific too ...

  • 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

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

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen