About coordinate systems
Coordinate systems are an important concept in computer graphics, as they are used to specify the position and orientation of objects in a virtual space. A coordinate system is a system of numbers, symbols, and axes that is used to describe the position of a point or object in space.
There are several different types of coordinate systems that are commonly used in computer graphics, including the cartesian, polar, and spherical coordinate systems.
The most commonly used coordinate system in computer graphics is the Cartesian coordinate system, which is named after the mathematician René Descartes. In this system, a point in space is defined by two or three numbers: its x-coordinate, y-coordinate. The x-coordinate specifies the point's position along the x-axis, the y-coordinate specifies the point's position along the y-axis. In 3D graphics a 3rd z-coordinate is used.
The polar coordinate system is another commonly used coordinate system in computer graphics. In this system, a point in space is defined by two numbers: its radius and angle. The radius specifies the distance of the point from the origin, and the angle specifies the direction of the point from the origin.
To convert from Cartesian to polar coordinates, you need to first determine the radius of the point. This can be done using the Pythagorean theorem, which states that the square of the radius is equal to the sum of the squares of the x-coordinate and the y-coordinate. In other words, the radius is the square root of the sum of the squares of the x-coordinate and the y-coordinate.
Once the radius has been determined, the angle can be calculated using the arc tangent function. This function takes the y-coordinate and the x-coordinate as inputs and returns the angle in radians. The angle can then be converted to degrees if desired.
For example, to convert the point (3,4) from Cartesian to polar coordinates, first determine the radius using the Pythagorean theorem:
radius = sqrt(3^2 + 4^2) = 5
Next, use the arc tangent function to determine the angle:
angle = atan2(4/3) = 53.13 degrees
Therefore, the polar coordinates of the point (3,4) are (5,53.13).
Majority of projects on codeguppy.com are using the Cartesian system of coordinates for 2D graphics. There are however a few projects that use the polar system of coordinates. Please feel free to explore the Polar category.
Regardless of the specific coordinate system used, all of these systems serve the same basic purpose: to provide a way of describing the position and orientation of objects in a virtual space.
By using coordinate systems, computer graphics programs can represent and manipulate objects in a virtual space in a precise and consistent way.
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