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Related Concept Videos

Vectors01:30

Vectors

Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...
Cartesian Vector Notation01:28

Cartesian Vector Notation

Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.
Vector Components in the Cartesian Coordinate System01:29

Vector Components in the Cartesian Coordinate System

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...

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Automatic Identification of Dendritic Branches and their Orientation
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Automatic Identification of Dendritic Branches and their Orientation

Published on: September 17, 2021

A Subdivision-Based Representation for Vector Image Editing.

Zicheng Liao1, Hugues Hoppe, David Forsyth

  • 1Department of Computer Science, University of Illinois at Urbana-Champaign, 201 N. Goodwin Ave., Urbana, IL 61801, USA. liao17@illinois.ed

IEEE Transactions on Visualization and Computer Graphics
|March 7, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new vector graphics representation using subdivision surfaces, enhancing editability and detail control for artists and designers. This flexible framework improves vector image processing and stylization for high-quality results.

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Area of Science:

  • Computer Graphics
  • Image Processing
  • Geometric Modeling

Background:

  • Vector graphics offer scalability and editability, crucial for interactive design.
  • Existing vector representations may lack flexibility for advanced editing and detail control.

Purpose of the Study:

  • Introduce a novel vector image representation for enhanced editability and user interaction.
  • Develop a unified framework supporting diverse vector graphics operations.
  • Enable control over the level of detail in vectorized images.

Main Methods:

  • Utilized piecewise smooth subdivision surfaces for a unified vector image framework.
  • Designed a feature-oriented vector image pyramid for multi-level abstraction.
  • Implemented GPU-accelerated subdivision for efficient rasterization.

Main Results:

  • The new representation supports shape editing, color editing, and image stylization.
  • Achieved high visual quality and superior support for editing operations compared to existing methods.
  • The feature-oriented pyramid effectively controls abstraction levels.

Conclusions:

  • The proposed subdivision surface-based representation offers a flexible and powerful approach to vector graphics.
  • This framework facilitates novel vector graphics creation through reuse and alteration of vectorized content.
  • The system provides efficient rasterization and advanced editing capabilities for artists and designers.