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Related Concept Videos

Polar Coordinates01:24

Polar Coordinates

463
The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance...
463
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

22.2K
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
22.2K
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

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In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
1.1K
Graphs of Polar Equations01:17

Graphs of Polar Equations

377
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...
377
Polar Equations of Conics01:29

Polar Equations of Conics

298
A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can...
298
Spherical Coordinates01:23

Spherical Coordinates

16.7K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
16.7K

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Related Experiment Video

Updated: Mar 12, 2026

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy iPALM
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A Novel Camera Calibration Method Based on Polar Coordinate.

Shaoyan Gai1,2,3, Feipeng Da1, Xu Fang1

  • 1Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, School of Automation, Southeast University, Nanjing 210096, China.

Plos One
|November 1, 2016
PubMed
Summary
This summary is machine-generated.

A new polar coordinate calibration method simplifies camera relationships. This efficient technique achieves high accuracy with fewer points, suitable for multi-camera systems.

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Area of Science:

  • Computer Vision
  • Robotics
  • Geometric Calibration

Background:

  • Camera calibration is crucial for 3D reconstruction and robotic vision.
  • Traditional methods often require numerous calibration points and complex setups.
  • Existing techniques may struggle with multi-camera systems and varying environments.

Purpose of the Study:

  • To introduce a novel camera calibration method utilizing polar coordinates.
  • To simplify the expression of relationships between objects and cameras.
  • To enhance efficiency and accuracy in multi-camera calibration scenarios.

Main Methods:

  • Calibration points are acquired in polar coordinates.
  • Transformation between polar and rectangular coordinates is employed.
  • Objective function optimization is used to determine calibration parameters.

Main Results:

  • The proposed method simplifies the representation of camera-object relationships.
  • It proves effective for multi-camera calibration.
  • Fewer calibration points are required compared to traditional methods.
  • Experimental results confirm high accuracy and convenience.

Conclusions:

  • The polar coordinate-based calibration method is efficient and accurate.
  • It offers a simplified approach for complex multi-camera setups.
  • This method provides a practical solution for convenient camera calibration.