Visualization of spatial distributions

1. A mapping method for identifying density of one or more parameters of interest positioned within a boundary, comprising:

determining at least one geographical boundary about a geographical location of interest, the at least one geographical boundary is free of any self-intersections;

dividing the at least one geographical boundary into a plurality of regions of interests, each region of interest is defined by a start point and an end point on the at least one geographical boundary, wherein the end point associated with one region of interest coincides with a start point of a neighboring region of interest wherein the region of interest falls within the at least one geographical boundary, wherein dividing the at least one geographical boundary is based on:

for each of the segments of the plurality:

providing a first tangent line to the at least one boundary at the start point and a second tangent line to the at least one boundary at the end point providing a first circle from a first center disposed on a first perpendicular line extended inwardly from the first tangent line such that the first circle is tangent against the at least one geographical boundary at the start point and also tangent against the at least one geographical boundary at a first point with the first circle having a minimum length first diameter;

providing a second circle from a second center disposed on a second perpendicular line extended inwardly from the second tangent line such that the second circle is tangent against the at least one geographical boundary at the endpoint and also tangent against the at least one geographical boundary at a second point with the second circle having a minimum length second diameter; and

defining the region of interest for the start point and the end point formed by a polygon with four vertices consisting of the start point, the end point, the first center, and the second center;

for each of the plurality of regions of interest:

calculating at least one parameter of interest within the region of interest; and

graphically presenting a segment between the start point and the end point on the at least one geographical boundary with a line thickness proportional to the calculation results.

2. The method of claim 1 , wherein the step of dividing the at least one geographical boundary is based on a predetermined division of the at least one geographical boundary into the plurality of regions of interests.

3. The method of claim 1 , wherein the step of calculating the at least one parameter of interest is based on integration.

4. The method of claim 1 , further comprising:

smoothing transitions from one segment of the plurality of regions of interest to another.

5. The method of claim 4 , wherein the smoothing is based on a moving average.

6. The method of claim 1 , the step of determining at least one geographical boundary is based on i) a predetermined boundary; ii) convex hull; or iii) concave hull.

7. The method of claim 1 , wherein the line thickness is based on a thickness scale.

8. The method of claim 1 , wherein the thickness of each segment is inward pointing towards the interior of the at least one geographical boundary.

9. The method of claim 8 , wherein a curve fitting function is applied to transitions between segments of varying thicknesses.

10. A mapping method for identifying density of one or more parameters of interest positioned outside a boundary, comprising:

receiving at least one predetermined geographical boundary about a geographical location of interest, the at least one geographical boundary is free of any self-intersections;

dividing the at least one geographical boundary into a plurality of regions of interests, each region of interest is defined by a start point and an end point on the at least one geographical boundary, wherein the end point associated with one region of interest coincides with a start point of a neighboring region of interest, wherein the region of interest falls outside the at least one geographical boundary, wherein dividing the at least one geographical boundary is based on:

for each of the segments of the plurality:

providing a first tangent line to the at least one boundary at the start point and a second tangent line to the at least one boundary at the end point providing a first vertex disposed on a first perpendicular line extended outwardly from the first tangent line at the start point, the first vertex is a predetermined distance (D) away from the start point;

providing a second vertex disposed on a second perpendicular line extended outwardly from the second tangent line at the end point, the second vertex is D distance away from the end point; and

defining the region of interest for the start point and the end point formed by a polygon with four vertices consisting of the start point, the end point, the first vertex, and the second vertex;

for each of the plurality of regions of interest:

calculating at least one parameter of interest within the region of interest; and

graphically presenting a segment between the start point and the end point on the at least one geographical boundary with a line thickness proportional to the calculation results.

11. The method of claim 10 , wherein the step of dividing the at least one geographical boundary is based on a predetermined division of the at least one geographical boundary into the plurality of regions of interests.

12. The method of claim 10 , wherein the step of calculating the at least one parameter of interest is based on integration.

13. The method of claim 10 , further comprising:

smoothing transitions from one segment of the plurality of regions of interest to another.

14. The method of claim 13 , wherein the smoothing is based on a moving average.

15. The method of claim 14 , wherein the moving average is based on a window having between three points and 300 points.

16. The method of claim 1 , wherein the line thickness is based on a thickness scale.

17. The method of claim 1 , wherein the thickness of each segment is outward pointing away from the interior of the at least one geographical boundary.

18. The method of claim 17 , wherein a curve fitting function is applied to transitions between segments of varying thicknesses.