博文
Research note of Experiment in migration by computer
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The areas between migration, or other movement, occurs are connected by a "band" whose width represents the quantity moved.
1)Ideally a desirable parsing strategy is one which yields only a linear growth in the number of movements needing to shown. Wherei the geographical space is considered to be continuous, not broken into data collection units, and the table no longer finite. This lead one to methods of movement depiction more analogous to those used in fluid dynamic. These continuous techniques are also useful for movement tables of large but finite size although the present discussion is limited to more conventional mapping methods.
2) The ealiest computer drawn flow maps are those of the Chicago Area Transportation Study. A special cathod ray tube system, "the cartographatron", was constructed to display several million "desire lines".
3)In addition to the computer N by N movement table, one is required to have a map showing the boundaries of the data collection on the movement map.
Weighted geographic centroids of these regions are calculated and used as rectangular coordinates for the initial and terminal points of the flow lines.
a small offset from these origin-destination points is generally desireable in order to avoid excessive overlap where flow bands come together.
a) The simplest graphic is the rectangular flow band with width proportional to the flow and stretching from starting centroid to ending cetroid, and representing all of the two-ray flow from place A to place B and from place B to place A, a combined total.
it is necessary to choose a scale of flow magnitudes, and this choice clearly impacts the impression obtained from the map.
As a default option, convenion but not necessarily correct, the computer program fixes the width of the largest flow band, making it equal to the distance between the closest centroid pair on the map.
b) Should the width of the flow band be proportional to the magnitude of the movement?
One alternative is to make all flow bands the same width, and then to use a variable intensity shading to represent the magnitude, as on choropleth maps, or to use a color variation to indicate the intensity of movements.
Alternatively, the shading density times the area shaded (length times width of band) can be made proportional to the movements, this option corresponding to the notion that visual intensity should be proportional to density times area.
Or the bands can be chosen to have their area(width times length) proportional to the movement magnitudes, the idea again being that eys responds to area and not just width.
c) In order to be able to represent the movement from place A to place B as something distinct from the movement in the reverse direction we require an asymmetric symbol, the flow arrow being the classic form. Generally there will be N*(N-1) of these, when the self-moves are omited.
difficult graphical problem, not really solved.
--A major difficulty lies in showing the simultaneous two directional movement along the single path coonecting places A and B. Half-barbed arrows, each of whose width is proportional to the respective movement, which about or which are separated by a small gap, do not seem very effective visually, nor does putting the smaller flow arrow on top of the larger one work very well.
--Another difficulty stems from the First Law of Geography, "near places interact more than distant places." Thus the large movements are often between close places on the map, where there is little room to draw anything. A common cartographic technique used to overcome this problem is to choose a base map, which enlarges area of high areas of high data density.
--The graphical simplicity of the maps is greatly enhanced if the arrows or bands are shown with overlap deletion.
The intitial guess was that we should have arrows representing the smaller flows cress over the top of the larger flows. The reverse in fact seems prefered. WHY?
The map clutter seems reduced for a given size of from-to table, and the more important (larger) movements become more noticeable.
d) The number of migration, which need to be shown, can be reduced in a number of ways.
(1) Instead of showing the entire N-squared possible migrations on one map, all of the N-1 movements from one place, or to one place, can be shown, in gross or net form.
These possibilities will yield 4N distinct maps from one single N by N from-to table.
(2) Another, classical, method is to delete all of the movements below some threshold quantity. The problem lies in determing this threshold level.
The optinal deletion strategy is to remove all movements whose magnitude is less than that of the average table entry. This delecately balances the deletion of individual migration streams with retention of movement volumes.
(3) Arbitrary thresholds can now be relaced by the optimal cut-off value, and this simple rule greatly reduces the map clutter while still providing a faithful representation of the geographic situation.
An alternative is to use a theoretical model to produce a table of "expected" movements and then to show only those movements which are significantly different from these expectations
(4) Collapsing a migration table to a smaller size by combining adjacent (geographically contiguous) place is a common technique.
If it must be done it probably should be done in such a manner as to reduce the variance of the resolution.
(5) Simplifying a from-to table can also be done by allowing movement to take place only between geographically adjacent places.
(6) Instead of drawing arrows from centroid to centroid an interesting variation would now be to place the arrows to just cross the borders of the immediately adjacent regions.
Open serveral research problems:
1. Spherical nature of the earth being taken into account
From a computational point view it is immaterial whether the data table is of within-city movements, or between the provinces of a country, or between several countries within a region, but truly international movement is different because the spherical nature of the earth has not been taken into account.
One can imagine drawing the flow arrows along great circles on an oblique orthographic view of hemisphere; the map projection problem becomes even more difficult when a movement pattern over the entire world must be shown.
2.The migration data is often desired to look at the difference between two tables, at distinct time period, or for populations partitioned by age, sex, or other charateristics, or to compare a theoretically computed table with an observed table.
3. Finally, completely different display techniques seem called for in more dynamic situations when one has a movement table which is regularly updated; by decade, by year, or by month.
Real cartographic animation
4. Commuting data also lend themsleves to this type of depiction.
converting residental street addresses into geodetic coordinates, and combining this with resent advances in high volume data storage and processing capabilities.
Point-to-Point rather than area-to-area movements are more expected.
https://blog.sciencenet.cn/blog-204718-277555.html
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下一篇：The condition of science growth
1)Ideally a desirable parsing strategy is one which yields only a linear growth in the number of movements needing to shown. Wherei the geographical space is considered to be continuous, not broken into data collection units, and the table no longer finite. This lead one to methods of movement depiction more analogous to those used in fluid dynamic. These continuous techniques are also useful for movement tables of large but finite size although the present discussion is limited to more conventional mapping methods.
2) The ealiest computer drawn flow maps are those of the Chicago Area Transportation Study. A special cathod ray tube system, "the cartographatron", was constructed to display several million "desire lines".
3)In addition to the computer N by N movement table, one is required to have a map showing the boundaries of the data collection on the movement map.
Weighted geographic centroids of these regions are calculated and used as rectangular coordinates for the initial and terminal points of the flow lines.
a small offset from these origin-destination points is generally desireable in order to avoid excessive overlap where flow bands come together.
a) The simplest graphic is the rectangular flow band with width proportional to the flow and stretching from starting centroid to ending cetroid, and representing all of the two-ray flow from place A to place B and from place B to place A, a combined total.
it is necessary to choose a scale of flow magnitudes, and this choice clearly impacts the impression obtained from the map.
As a default option, convenion but not necessarily correct, the computer program fixes the width of the largest flow band, making it equal to the distance between the closest centroid pair on the map.
b) Should the width of the flow band be proportional to the magnitude of the movement?
One alternative is to make all flow bands the same width, and then to use a variable intensity shading to represent the magnitude, as on choropleth maps, or to use a color variation to indicate the intensity of movements.
Alternatively, the shading density times the area shaded (length times width of band) can be made proportional to the movements, this option corresponding to the notion that visual intensity should be proportional to density times area.
Or the bands can be chosen to have their area(width times length) proportional to the movement magnitudes, the idea again being that eys responds to area and not just width.
c) In order to be able to represent the movement from place A to place B as something distinct from the movement in the reverse direction we require an asymmetric symbol, the flow arrow being the classic form. Generally there will be N*(N-1) of these, when the self-moves are omited.
difficult graphical problem, not really solved.
--A major difficulty lies in showing the simultaneous two directional movement along the single path coonecting places A and B. Half-barbed arrows, each of whose width is proportional to the respective movement, which about or which are separated by a small gap, do not seem very effective visually, nor does putting the smaller flow arrow on top of the larger one work very well.
--Another difficulty stems from the First Law of Geography, "near places interact more than distant places." Thus the large movements are often between close places on the map, where there is little room to draw anything. A common cartographic technique used to overcome this problem is to choose a base map, which enlarges area of high areas of high data density.
--The graphical simplicity of the maps is greatly enhanced if the arrows or bands are shown with overlap deletion.
The intitial guess was that we should have arrows representing the smaller flows cress over the top of the larger flows. The reverse in fact seems prefered. WHY?
The map clutter seems reduced for a given size of from-to table, and the more important (larger) movements become more noticeable.
d) The number of migration, which need to be shown, can be reduced in a number of ways.
(1) Instead of showing the entire N-squared possible migrations on one map, all of the N-1 movements from one place, or to one place, can be shown, in gross or net form.
These possibilities will yield 4N distinct maps from one single N by N from-to table.
(2) Another, classical, method is to delete all of the movements below some threshold quantity. The problem lies in determing this threshold level.
The optinal deletion strategy is to remove all movements whose magnitude is less than that of the average table entry. This delecately balances the deletion of individual migration streams with retention of movement volumes.
(3) Arbitrary thresholds can now be relaced by the optimal cut-off value, and this simple rule greatly reduces the map clutter while still providing a faithful representation of the geographic situation.
An alternative is to use a theoretical model to produce a table of "expected" movements and then to show only those movements which are significantly different from these expectations
(4) Collapsing a migration table to a smaller size by combining adjacent (geographically contiguous) place is a common technique.
If it must be done it probably should be done in such a manner as to reduce the variance of the resolution.
(5) Simplifying a from-to table can also be done by allowing movement to take place only between geographically adjacent places.
(6) Instead of drawing arrows from centroid to centroid an interesting variation would now be to place the arrows to just cross the borders of the immediately adjacent regions.
Open serveral research problems:
1. Spherical nature of the earth being taken into account
From a computational point view it is immaterial whether the data table is of within-city movements, or between the provinces of a country, or between several countries within a region, but truly international movement is different because the spherical nature of the earth has not been taken into account.
One can imagine drawing the flow arrows along great circles on an oblique orthographic view of hemisphere; the map projection problem becomes even more difficult when a movement pattern over the entire world must be shown.
2.The migration data is often desired to look at the difference between two tables, at distinct time period, or for populations partitioned by age, sex, or other charateristics, or to compare a theoretically computed table with an observed table.
3. Finally, completely different display techniques seem called for in more dynamic situations when one has a movement table which is regularly updated; by decade, by year, or by month.
Real cartographic animation
4. Commuting data also lend themsleves to this type of depiction.
converting residental street addresses into geodetic coordinates, and combining this with resent advances in high volume data storage and processing capabilities.
Point-to-Point rather than area-to-area movements are more expected.
https://blog.sciencenet.cn/blog-204718-277555.html
上一篇：RDF
下一篇：The condition of science growth
