Scale preserving smoothing of polygons

R L Kashyap1, B J Oommen

  • 1School of Electrical Engineering, Purdue University, West Lafayette, IN 47907.

Related Concept Videos

Scaling01:26

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
Introduction to Scalers01:21

Introduction to Scalers

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts 50 min," or "the gas tank in my car holds 65 L," or "the distance between the two posts is 100 m." A physical quantity that can be specified completely in this manner is called a scalar quantity. The word "scalar" is a synonym for "number." Time, mass, distance, length, volume, temperature, and energy are some examples of scalar quantities.
Scalar...
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

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 with respect to time...