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Spellin'n'stuff
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AmiralPatate
AmiralPatate
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It's all convention anyways

The simple answer is to pick a point and two orthogonal directiondirections arbitrarily.

For instance, the center of your capital island is the point of origin, north is towards the North Star and up is towards any perpendicular direction of your choosing. Once you have north and up, you can infer south, down, east and west.

Why so Cartesian?

Cartesian coordinates express a point relative to an origin based on three orthogonal axes. In your case, north, east and up are the three axes.

Now you take these axes, and do something different. North and east form the polar plane. Up is still up and should be perpendicular to your plane.

Now you express coordinates based on: distance to origin, angle on the polar plane (or polar angle, in all 360°), and angle to the up direction (azimuth angle, from -90° straight down to 90° straight up).

You now have a spherical coordinate system.

Why is this better? There are no arbitrary north, south, east, west, up and down direction. There is however an arbitrary plane, which includes an arbitrary 0° polar angle and coincides with the 0° azimuth angle. Remember, it's all convention anyways.

In a 3D space, expressing relative coordinates spherically makes generally more sense than Cartesiannally. You want to know an obstacle inis X meters away in that direction. That it is X,Y,Z meters away from a point of origin that you yourself are U,V,W meters away from doesn't seem quite as useful.

It's all relative anyways

Absolute coordinates (whether Cartesian or spherical, or else) are of little practical use in most cases. In this case, I would advise Cartesian coordinates because it's easier to figure out Cartesian geometry.

Relative coordinates make more sense in practice. We experience the world relative to our point of view. You instinctively know where front/back/left/right/up/down is relative to you. Apply the same logic to the ship. In this case, I would advise spherical coordinates make more sense.

It's all convention anyways

The simple answer is to pick a point and two orthogonal direction arbitrarily.

For instance, the center of your capital island is the point of origin, north is towards the North Star and up is towards any perpendicular direction of your choosing. Once you have north and up, you can infer south, down, east and west.

Why so Cartesian?

Cartesian coordinates express a point relative to an origin based on three orthogonal axes. In your case, north, east and up are the three axes.

Now you take these axes, and do something different. North and east form the polar plane. Up is still up and should be perpendicular to your plane.

Now you express coordinates based on: distance to origin, angle on the polar plane (or polar angle, in all 360°), and angle to the up direction (azimuth angle, from -90° straight down to 90° straight up).

You now have a spherical coordinate system.

Why is this better? There are no arbitrary north, south, east, west, up and down direction. There is however an arbitrary plane, which includes an arbitrary 0° polar angle and coincides with the 0° azimuth angle. Remember, it's all convention anyways.

In a 3D space, expressing relative coordinates spherically makes generally more sense than Cartesiannally. You want to know an obstacle in X meters away in that direction. That it is X,Y,Z meters away from a point of origin that you yourself are U,V,W meters away from doesn't seem quite as useful.

It's all relative anyways

Absolute coordinates (whether Cartesian or spherical, or else) are of little practical use in most cases. In this case, I would advise Cartesian coordinates because it's easier to figure out Cartesian geometry.

Relative coordinates make more sense in practice. We experience the world relative to our point of view. You instinctively know where front/back/left/right/up/down is relative to you. Apply the same logic to the ship. In this case, spherical coordinates make more sense.

It's all convention anyways

The simple answer is to pick a point and two orthogonal directions arbitrarily.

For instance, the center of your capital island is the point of origin, north is towards the North Star and up is towards any perpendicular direction of your choosing. Once you have north and up, you can infer south, down, east and west.

Why so Cartesian?

Cartesian coordinates express a point relative to an origin based on three orthogonal axes. In your case, north, east and up are the three axes.

Now you take these axes, and do something different. North and east form the polar plane. Up is still up and should be perpendicular to your plane.

Now you express coordinates based on: distance to origin, angle on the polar plane (or polar angle, in all 360°), and angle to the up direction (azimuth angle, from -90° straight down to 90° straight up).

You now have a spherical coordinate system.

Why is this better? There are no arbitrary north, south, east, west, up and down direction. There is however an arbitrary plane, which includes an arbitrary 0° polar angle and coincides with the 0° azimuth angle. Remember, it's all convention anyways.

In a 3D space, expressing relative coordinates spherically makes generally more sense than Cartesiannally. You want to know an obstacle is X meters away in that direction. That it is X,Y,Z meters away from a point of origin that you yourself are U,V,W meters away from doesn't seem quite as useful.

It's all relative anyways

Absolute coordinates (whether Cartesian or spherical, or else) are of little practical use in most cases. In this case, I would advise Cartesian coordinates because it's easier to figure out Cartesian geometry.

Relative coordinates make more sense in practice. We experience the world relative to our point of view. You instinctively know where front/back/left/right/up/down is relative to you. Apply the same logic to the ship. In this case, I would advise spherical coordinates.

Source Link
AmiralPatate
AmiralPatate
  • 9k
  • 1
  • 19
  • 44

It's all convention anyways

The simple answer is to pick a point and two orthogonal direction arbitrarily.

For instance, the center of your capital island is the point of origin, north is towards the North Star and up is towards any perpendicular direction of your choosing. Once you have north and up, you can infer south, down, east and west.

Why so Cartesian?

Cartesian coordinates express a point relative to an origin based on three orthogonal axes. In your case, north, east and up are the three axes.

Now you take these axes, and do something different. North and east form the polar plane. Up is still up and should be perpendicular to your plane.

Now you express coordinates based on: distance to origin, angle on the polar plane (or polar angle, in all 360°), and angle to the up direction (azimuth angle, from -90° straight down to 90° straight up).

You now have a spherical coordinate system.

Why is this better? There are no arbitrary north, south, east, west, up and down direction. There is however an arbitrary plane, which includes an arbitrary 0° polar angle and coincides with the 0° azimuth angle. Remember, it's all convention anyways.

In a 3D space, expressing relative coordinates spherically makes generally more sense than Cartesiannally. You want to know an obstacle in X meters away in that direction. That it is X,Y,Z meters away from a point of origin that you yourself are U,V,W meters away from doesn't seem quite as useful.

It's all relative anyways

Absolute coordinates (whether Cartesian or spherical, or else) are of little practical use in most cases. In this case, I would advise Cartesian coordinates because it's easier to figure out Cartesian geometry.

Relative coordinates make more sense in practice. We experience the world relative to our point of view. You instinctively know where front/back/left/right/up/down is relative to you. Apply the same logic to the ship. In this case, spherical coordinates make more sense.