About: Polar Equations

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About: Polar Equations Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

Blockland operates using the Cartesian coordinate system. This is a gridlike system much like the tiles on the floor of a bathroom. This system is ideal for certain things, e.g., straight lines, roads, buildings, tiles. It is not as good for other things, such as spirals. Another system, called the Polar coordinate system based on an angle and the distance from the center of a map, is much better suited for this. r=math.cos(2*θ) So, to obtain the values for x and z, we have to multiply r as follows: x = r * math.cos(θ) z = r * math.sin(θ) We now get:

Attributes	Values
rdfs:label	Polar Equations
rdfs:comment	Blockland operates using the Cartesian coordinate system. This is a gridlike system much like the tiles on the floor of a bathroom. This system is ideal for certain things, e.g., straight lines, roads, buildings, tiles. It is not as good for other things, such as spirals. Another system, called the Polar coordinate system based on an angle and the distance from the center of a map, is much better suited for this. r=math.cos(2θ) So, to obtain the values for x and z, we have to multiply r as follows: x = r math.cos(θ) z = r * math.sin(θ) We now get:
dcterms:subject	Scripting
abstract	Blockland operates using the Cartesian coordinate system. This is a gridlike system much like the tiles on the floor of a bathroom. This system is ideal for certain things, e.g., straight lines, roads, buildings, tiles. It is not as good for other things, such as spirals. Another system, called the Polar coordinate system based on an angle and the distance from the center of a map, is much better suited for this. The problem with this is that you need to convert from the Polar system to the Cartesian system, because Blockland operates in the Cartesian system. This is actually easy enough to do, if you have a formula in the Polar system. Let's take the Quadrifolium from Wikipedia. Its polar equation is: r=math.cos(2θ) So, to obtain the values for x and z, we have to multiply r as follows: x = r math.cos(θ) z = r * math.sin(θ) We now get: x=math.cos(2i) math.cos(θ) z=math.cos(2i) math.sin(θ) You will see these formulas again in the script below.

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