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Posts tagged as polar

Disc group variation Example disc 2

Disc

Variations that use polar coordinates and swap the ρ and θ values. This converts wedges centered at the origin to half-rings and vice versa.

parplot2d 2

Plotting

These variations are all blurs that plot formulas in two or three dimensions. They allow entering custom formulas, but also come with presets for ease of use.

polarizing tutorial

Polarizing Tutorial

Not a tutorial that divides opinion, one that explains about polarizing technique and background.

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disc

The disc variation is based on polar coordinates, where points are specified by a distance ρ and an angle θ. The basic idea is simple: it just switches ρ and θ (after scaling by π to make things work nicely). This converts wedges centered at the origin to half-rings and vice versa as shown below. The images on the left side are before and on the right side after disc is applied.

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Elliptic

The most commonly used coordinate systems are rectangular coordinates and polar coordinate. But these aren’t the only possibilities. One of the less common coordinate systems is elliptic coordinates. Although their mathematical application is specialized, they can be used in variations to make interesting flames.

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unpolar and foci

The unpolar variation is the opposite of polar2; see the polar description. Whereas polar2 treats the log-polar coordinates of a point as rectangular coordinates, unpolar treats the rectangular coordinates of a point and treats them as log-polar coordinates.

bipolar4

bipolar

The most commonly used coordinate systems are rectangular coordinates and polar coordinates (see polar). But these aren’t the only possibilities. One of the less common coordinate systems is bipolar coordinates. Although their mathematical application is specialized, they can be used in variations to make interesting flames. Rectangular coordinates are based on two families of parallel lines (horizontal and vertical) where each line in the first family intersects each line in the other at a right angle.