Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Graphical Representation of Inequalities

Graphical Representation of Inequalities

The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all points...

Graphs of Functions

Graphs of Functions

Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...

Vector Algebra: Graphical Method

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...

Graphs of Polar Equations

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...

Guidelines for Sketching a Curve

Guidelines for Sketching a Curve

Curve sketching is a systematic method for understanding the overall behavior of a function by analyzing its key mathematical features. A function defines a curve on the coordinate plane, where the horizontal axis represents the input variable and the vertical axis represents the output. The process begins by determining the domain, which specifies the set of input values for which the function is defined and establishes the horizontal extent of the graph.Intercepts with the horizontal and...

Graphs of Equations in Two Variables

Graphs of Equations in Two Variables

An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

[Vitreous body substitutes: current solutions and future perspectives].

Die Ophthalmologie·2026

Same author

Stress modulates gastric interoception depending on eating traits and emotion regulation: evidence from the magic table.

Scientific reports·2026

Same author

Embodied memory for emotional faces: Effects of cardiac cycle phases and post-learning stress on identity and expression memory.

Biological psychology·2026

Same author

Efficiency Pitfalls of Explainable AI in Clinical Diagnostic and Treatment Human-AI Workflows.

Human factors·2026

Same author

Drug strategies for the treatment and prevention of proliferative vitreoretinopathy: an overview of innovative treatment concepts.

International ophthalmology·2026

Same author

Understanding the Charles Bonnet syndrome: An updated review.

Brain research bulletin·2025

Search research articles

Related Experiment Video

Updated: May 13, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Pointed drawings of planar graphs.

Oswin Aichholzer¹, Günter Rote, André Schulz

¹Institute for Software Technology, Graz University of Technology, Austria.

Computational Geometry : Theory and Applications

|March 9, 2013

Summary

This study presents algorithms for drawing planar graphs without crossings, ensuring all vertex angles exceed π. These methods utilize biarcs or parabolic arcs for vertex angle constraints in graph visualization.

Keywords:

Angular resolution Planar drawings Pointed pseudotriangulations

More Related Videos

Analyzing Dendritic Morphology in Columns and Layers

Analyzing Dendritic Morphology in Columns and Layers

Published on: March 23, 2017

Related Experiment Videos

Last Updated: May 13, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Analyzing Dendritic Morphology in Columns and Layers

Analyzing Dendritic Morphology in Columns and Layers

Published on: March 23, 2017

Area of Science:

Computational Geometry
Graph Theory
Computer Graphics

Background:

Standard plane straight-line drawings of graphs may not satisfy the condition that every vertex angle is greater than π.
Achieving specific angle constraints in graph drawings is crucial for various applications.

Purpose of the Study:

To develop algorithms for constructing crossing-free planar graph drawings where all vertex angles are greater than π.
To investigate the use of different curve types (biarcs, Bézier curves, circular arcs) for achieving these angle constraints.

Main Methods:

Algorithms are presented for constructing drawings using tangent-continuous biarcs.
Algorithms are developed for constructing drawings using quadratic Bézier curves (parabolic arcs).
The methods accommodate predefined vertex positions from existing straight-line drawings.

Main Results:

Demonstrated that crossing-free planar graphs can be drawn with vertex angles greater than π using biarcs or parabolic arcs, even with fixed vertex positions.
Showcased that arbitrary vertex placement allows for drawings with circular arcs while maintaining the angle property.

Conclusions:

The study provides effective algorithms for generating angle-constrained planar graph drawings.
The findings expand the possibilities for visually appealing and functionally constrained graph representations in computer graphics and computational geometry.