CHAPTER 6 (1) VECTOR VISUALIZATION. OUTLINE Vector datasets are samplings of vector fields over discrete spatial domains Visualizing Vector A number of.

Slides:

Advertisements

Similar presentations

3 Vectors in Physics 3-1 Scalars versus Vectors

Advertisements

Data Visualization Lecture 9

Vector Field Visualization Jian Huang, CS 594, Spring 2002 This set of slides reference slides developed by Prof. Torsten Moeller, at CS, Simon Fraser.

Yingcai Xiao Chapter 6 Fundamental Algorithms. Types of Visualization Transformation Types 1.Data (Attribute Transformation) 2.Topology (Topological Transformation)

Visualization Data Representation Ray Gasser SCV Visualization Workshop – Fall 2008.

1 Higher Dimensional Vector Field Visualization: A Survey Zhenmin Peng, Robert S. Laramee Department of Computer Science Swansea University, Wales UK

Image Space Based Visualization of Unsteady Flow on Surfaces Robert Laramee Bruno Jobard Helwig Hauser Presenter: Bob Armstrong 24 January 2007.

Introduction to Volume Visualization Mengxia Zhu Fall 2007.

Chapter 7 Bits of Vector Calculus. (1) Vector Magnitude and Direction Consider the vector to the right. We could determine the magnitude by determining.

9.7 Divergence and Curl Vector Fields: F(x,y)= P(x,y) i + Q(x,y) j F(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k Example 1 : Graph the 2-dim vector field.

PHY 1151 Principles of Physics I

IS&T Scientific Visualization Tutorial - Summer 2010 Scientific Visualization Tutorial.

ITUppsala universitet Data representation and fundamental algorithms Filip Malmberg

Flow Visualization Overview

Scalar and Vector Fields

Interactive Visualization of Volumetric Data on Consumer PC Hardware: Introduction Daniel Weiskopf Graphics Hardware Trends Faster development than Moore’s.

Scalars and Vectors. Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude – A numerical value.

3-2 Vectors and Scalars  Is a number with units. It can be positive or negative. Example: distance, mass, speed, Temperature… Chapter 3 Vectors  Scalar.

Andrea Brambilla 1 Øyvind Andreassen 2,3 Helwig Hauser 1 Integrated Multi-aspect Visualization of 3D Fluid Flows 1 University of Bergen, Norway 2 Norwegian.

Lei Zhang and Guoning Chen, Department of Computer Science, University of Houston Robert S. Laramee, Swansea University David Thompson and Adrian Sescu,

CDS 301 Fall, 2009 Vector Visualization Chap. 6 October 7, 2009 Jie Zhang Copyright ©

Scientific Visualization Module 6 Volumetric Algorithms (adapted by S.V. Moore – slides deleted, modified, and added) prof. dr. Alexandru (Alex) Telea.

Curl and Divergence.

Robert S. Laramee 1 1 Flow Like You've Never Seen It Robert S. Laramee Visual and Interactive Computing.

Starter If you are in a large field, what two pieces of information are required for you to locate an object in that field?

A Survey on Visualization of Time-Dependent Vector Fields by Texture-based Methods Henry “Dan” Derbes MSIM 842 ODU Main Campus.

DESCRIBING MOTION: Kinematics in One Dimension CHAPTER 2.

2D Flow Visualization streamline, pathline, hedges, spotnoise 郭翰琦陈珩.

Taylor Rassmann.  Optical flow is still being attained from the UCF50 dataset.  On action 35 out of 50  Currently at 900 GB of data.

Vector Visualization Mengxia Zhu. Vector Data A vector is an object with direction and length v = (v x,v y,v z ) A vector field is a field which associates.

Vector Field Visualization

Design and Implementation of Geometric and Texture-Based Flow Visualization Techniques Robert S. Laramee Markus Hadwiger Helwig Hauser.

1 Feature Extraction and Visualization of Flow Fields State-of-the-Art Report Feature Extraction and Visualization of Flow Fields Frits.

Data Visualization Fall 2015.

CHAPTER 3: VECTORS NHAA/IMK/UNIMAP.

CHAPTER 5 CONTOURING. 5.3 CONTOURING Fig 5.7. Relationship between color banding and contouring Contour line (isoline): the same scalar value, or isovalue.

Scalar-Vector Interaction in Animating but non-alive Fields …… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Special Vector Calculus.

Vectors in Two Dimensions. VECTOR REPRESENTATION A vector represents those physical quantities such as velocity that have both a magnitude and a direction.

SCALAR VISUALIZATION. OUTLINE Visualizing scalar data A number of the most popular scalar visualization techniques Color mapping Contouring Height plots.

Direction Makes a Difference Quantities that describe magnitude but DO NOT include direction are called scalar quantities or just scalars. (distance, speed,

CHAPTER 14 Vector Calculus Slide 2 © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 14.1VECTOR FIELDS 14.2LINE INTEGRALS.

Vectors and Scalars. Edexcel Statements A scalar quantity is a quantity that has magnitude only and has no direction in space Examples of Scalar Quantities:

2/24/2016 A.Aruna/Assistant professor/IT/SNSCE 1.

Plots of Fluid Flow Data Profile plots- A profile plot indicates how the value of a scalar (or vector can be plotted but only the magnitude) property varies.

CDS 301 Fall, 2008 Domain-Modeling Techniques Chap. 8 November 04, 2008 Jie Zhang Copyright ©

How Far? distance: –symbol: d –units: meters displacement: –symbol: –units: meters How far an object has traveled Is a “vector” quantity How far an.

Scientific Visualization Module 4 Vector Visualization (adapted – some slides modified or omitted) prof. dr. Alexandru (Alex) Telea

The vector measure of rotation around a point

67 x 89 = ? 67 x

Robert S. Laramee 1 Visualization Lecture Flow visualization, An Introduction.

Vectors and Scalars.  A scalar is a number which expresses quantity. Scalars  may or may not have units associated with them.  Examples: mass, volume,

Motion of a Fluid Particle (Kinematics)

Motion of a Fluid Particle (Kinematics)

Simplified Representation of Vector Fields

VTK: The Visualization Toolkit

Partial Derivative - Definition

Physics Section 3.1 Represent quantities using vectors

Chapter 5(1) Color MaPPING

Chapter 5(1) Color MaPPING

EEE 161 Applied Electromagnetics

Using Flow Textures to Visualize Unsteady Vector Fields

Vector Field Visualization

Domain-Modeling Techniques

Introduction and Mathematical Concepts

Introduction and Mathematical Concepts

Vector Field Visualization

Scalar and vector quantities

Fig. 3 CFD simulations. CFD simulations. (A to R) Details of water flow around Tribrachidium oriented at 0° to the current. Model with original height.

Presentation transcript:

CHAPTER 6 (1) VECTOR VISUALIZATION

OUTLINE Vector datasets are samplings of vector fields over discrete spatial domains Visualizing Vector A number of the popular visualization methods for vector datasets Vector glyphs Vector color coding Displacement plots Stream objects Texture-based vector visualization The simplified representation of vector fields

OUTLINE Vector Visualization: Application: Computational Fluid Dynamics (CFD) 6.1 Mathematical operators to analyze vector fields 6.2 Vector glyphs 6.3 Scalar Visualization techniques to depict vector fields 6.4 Displacement plot technique 6.5 Stream objects 6.6 Use of textures 6.7 Strategies for simplified representation of vector datasets

6.1 DIVERGENCE ( 发散度 ) AND VORTICITY ( 旋度 ) The Divergence of v=(v x,v y,v z ) is the scalar quantity Vorticity (curl or rotor of v )

6.1 DIVERGENCE AND VORTICITY Fig 6.1. Divergence and curl in 2D. (a) Divergence construction. (b) Source point. (c) Sink point. (d) Rotor construction. (e) High-vorticity field. Source point: Positive; Spread Sink point: Negative; Sucked.

6.1 DIVERGENCE AND VORTICITY Fig 6.2 (a) Divergence of a 2D vector field (b) Absolute value of vorticity of a 2D vector field

6.1 DIVERGENCE AND VORTICITY Fig 6.3 Vorticity of a 2D fluid flow field. Note the alternation between vortices with opposite spinning directions. (Courtesy of I. Barosan, Eindhoven University, Netherlands.)

6.2 VECTOR GLYPHS Vector Glyphs Simplest, fastest, most popular technique for visualizing vector fields Associate a vector glyph, or vector icon, with every sample point of the vector dataset A sign conveys properties of the represented vector, such as direction, orientation, and magnitude Many variations of framework Lines (convey direction) 3D cone (convey direction + orientation) Arrow (convey direction + orientation)

6.2 VECTOR GLYPHS Figure 6.4. Hedgehog visualization of a 2D magnetohydrodynamic velocity field. (Data courtesy of Prof. Martin Rumpf, University of Bonn, Germany.)

6.2 VECTOR GLYPHS Figure 6.5. Different glyph types. (a) Cones. (b) Arrows.

6.2 VECTOR GLYPHS VECTOR GLYPH EXAMPLES Trade-off The power of expression of glyph Number of attributes they can encode Minimal screen size The difference between scalar and vector visualization --- in sampling terms Subsampling problem Random sampling

6.2 VECTOR GLYPHS VECTOR GLYPH EXAMPLES Figure 6.6. Visual interpolation of vector glyphs. (a) Small data variations are easily interpolated. (b) Large data variations create more problems.

6.2 VECTOR GLYPHS VECTOR GLYPH EXAMPLES Figure 6.7. (a) Vector glyphs on a dataset regularly subsampled on a rotated sample grid. (b) Subsampling artifacts are alleviated by random sampling. Both visualization display 1200 glyphs.

6.2 VECTOR GLYPHS VECTOR GLYPH EXAMPLES Figure 6.8. Glyph-based visualization of a 3D vector field. (Data courtesy of Prof. Martin Rumpf, University of Bonn, Germany.) 3D glyph  Occlusion problem Sparse sampling Draw the glyph transparently Monochrome: easier to interpret

6.2 VECTOR GLYPHS VECTOR GLYPH EXAMPLES Figure 6.9. Glyph-based vector visualization on a 3D velocity isosurface.