Just a comment on the diagram that is trying to illustrate a projection from a sphere. Rather that what is illustrated, imagine a light source at the center of the sphere. The shadow of the polygon "projected" onto a flat piece of paper outside of the sphere is in essence a type of projection. To me the diagram is implying a projection is like a reflected surface which is an incorrect way to visualize what is happening.

Also, at least in the ESRI world, georeferencing is not applying points to a sphere. Georeferencing is assigning a known planar (projected) coordinate system to either a raster or vector dataset that has originated from either a scanning or digitizing operation in which a 'local' coordinate system was first applied. "Local" in this case simply means the coordinates were made up with no reference to a real world coordinate system. That is, a map may have originally been hand digitized where the person decided the lower left coordinate of the map had an XY value of (0,0). Georeferencing is the process of assigning a set of real world (projected) coordinates to the original. If this process is applied to a photograph or scanned map then the georeferencing process will often warp the original image to fit within the set of reference points that have been assigned real world planar coordinates. This "georeference warping" is not the same as the distortions created when projecting from a sphere onto a plane. "Georeference warping" is all about correcting distortions produced by either the camera or scanner. When projecting a feature from a spherical surface to a planar surface there is always a distortion created in distance, area, scale, and bearing. You choose a projection to minimize one or more of these distortions, depending on the intended purpose of the map.

As to the strings on a ball illustration, rather than strings I would use pencils of various lengths that start from a point on the sphere and end on a flat piece of paper. The outer ends of the pencils represent the projected points. In a sense, changing the geographic coordinate system (datum for this discussion) is analogous to rotating the sphere on one more axis to a new position. The concept works only for isolated areas on the earth. That is for NAD27 to WGS84 it applies pretty well to the 48 contiguous states of the USA but not for Canada or Alaska. For those areas you have to correct the NAD 27 datum first and then make the NAD7 to WGS84 move. Whereas for NAD83 to WGS84 the concept works for most of North America.

Just a comment on the diagram that is trying to illustrate a projection from a sphere. Rather that what is illustrated, imagine a light source at the center of the sphere. The shadow of the polygon "projected" onto a flat piece of paper outside of the sphere is in essence a type of projection. To me the diagram is implying a projection is like a reflected surface which is an incorrect way to visualize what is happening.

Also, at least in the ESRI world, georeferencing is not applying points to a sphere. Georeferencing is assigning a known planar (projected) coordinate system to either a raster or vector dataset that has originated from either a scanning or digitizing operation in which a 'local' coordinate system was first applied. "Local" in this case simply means the coordinates were made up with no reference to a real world coordinate system. That is, a map may have originally been hand digitized where the person decided the lower left coordinate of the map had an XY value of (0,0). Georeferencing is the process of assigning a set of real world (projected) coordinates to the original. If this process is applied to a photograph or scanned map then the georeferencing process will often warp the original image to fit within the set of reference points that have been assigned real world planar coordinates. This "georeference warping" is not the same as the distortions created when projecting from a sphere onto a plane. "Georeference warping" is all about correcting distortions produced by either the camera or scanner. When projecting a feature from a spherical surface to a planar surface there is always a distortion created in distance, area, scale, and bearing. You choose a projection to minimize one or more of these distortions, depending on the intended purpose of the map.

As to the strings on a ball illustration and changing the datum, rather than strings I would use pencils of various lengths that start from a point on the sphere and end on a flat piece of paper. The outer ends of the pencils represent the projected points. In a sense, changing the geographic coordinate system (datum for this discussion) is analogous to rotating the sphere on one more axis to a new position. The concept works only for isolated areas on the earth. That is for NAD27 to WGS84 it applies pretty well to the 48 contiguous states of the USA but not for Canada or Alaska. For those areas you have to correct the NAD 27 datum first and then make the NAD7 to WGS84 move. Whereas for NAD83 to WGS84 the concept works for most of North America.

Just a comment on the diagram that is trying to illustrate a projection from a sphere. Rather that what is illustrated, imagine a light source at the center of the sphere. The shadow of the polygon "projected" onto a flat piece of paper outside of the sphere is in essence a type of projection. To me the diagram is implying a projection is like a reflected surface which is an incorrect way to visualize what is happening.

Also, at least in the ESRI world, georeferencing is not applying points to a sphere. Georeferencing is assigning a known planar (projected) coordinate system to either a raster or vector dataset that has originated from either a scanning or digitizing operation in which a 'local' coordinate system was first applied. "Local" in this case simply means the coordinates were made up with no reference to a real world coordinate system. That is, a map may have originally been hand digitized where the person decided the lower left coordinate of the map had an XY value of (0,0). Georeferencing is the process of assigning a set of real world (projected) coordinates to the original. If this process is applied to a photograph or scanned map then the georeferencing process will often warp the original image to fit within the set of reference points that have been assigned real world planar coordinates. This "georeference warping" is not the same as the distortions created when projecting from a sphere onto a plane. "Georeference warping" is all about correcting distortions produced by either the camera or scanner. When projecting a feature from a spherical surface to a planar surface there is always a distortion created in distance, area, scale, and bearing. You choose a projection to minimize one or more of these distortions, depending on the intended purpose of the map.

Just a comment on the diagram that is trying to illustrate a projection from a sphere. Rather that what is illustrated, imagine a light source at the center of the sphere. The shadow of the polygon "projected" onto a flat piece of paper outside of the sphere is in essence a type of projection. To me the diagram is implying a projection is like a reflected surface which is an incorrect way to visualize what is happening.

Also, at least in the ESRI world, georeferencing is not applying points to a sphere. Georeferencing is assigning a known planar (projected) coordinate system to either a raster or vector dataset that has originated from either a scanning or digitizing operation in which a 'local' coordinate system was first applied. "Local" in this case simply means the coordinates were made up with no reference to a real world coordinate system. That is, a map may have originally been hand digitized where the person decided the lower left coordinate of the map had an XY value of (0,0). Georeferencing is the process of assigning a set of real world (projected) coordinates to the original. If this process is applied to a photograph or scanned map then the georeferencing process will often warp the original image to fit within the set of reference points that have been assigned real world planar coordinates. This "georeference warping" is not the same as the distortions created when projecting from a sphere onto a plane. "Georeference warping" is all about correcting distortions produced by either the camera or scanner. When projecting a feature from a spherical surface to a planar surface there is always a distortion created in distance, area, scale, and bearing. You choose a projection to minimize one or more of these distortions, depending on the intended purpose of the map.

As to the strings on a ball illustration, rather than strings I would use pencils of various lengths that start from a point on the sphere and end on a flat piece of paper. The outer ends of the pencils represent the projected points. In a sense, changing the geographic coordinate system (datum for this discussion) is analogous to rotating the sphere on one more axis to a new position. The concept works only for isolated areas on the earth. That is for NAD27 to WGS84 it applies pretty well to the 48 contiguous states of the USA but not for Canada or Alaska. For those areas you have to correct the NAD 27 datum first and then make the NAD7 to WGS84 move. Whereas for NAD83 to WGS84 the concept works for most of North America.