Multi-dimensional graphing in two-dimensional space

Abstract

A method and system for displaying a function in two dimensions where the function is made up of numerous independent variables and at least one dependent variable. A new independent variable value can be defined having values which correspond to the multiple dependent variables. The variable values are read into a computer and the independent variables are then ranked by the user from fastest- to slowest-running variable. Each dependent variable corresponding to the new independent variable is plotted along the Y-axis. The independent variable values are plotted along the X-axis in a hierarchical manner. The hierarchical manner involves a nesting of fastest-running variables within slower-running variables. Rectangles are then drawn to correspond to each variable value. Each rectangle horizontally encloses the faster-running variables associated with it.

It is claimed: 
     
       1. A method using a system including a computer with a display for displaying a function in two dimensions, said display defined by an X-axis and a Y-axis wherein said function is comprised of .[.a plurality of.]. .Iadd.at least three discrete .Iaddend.independent variables and at least one dependent variable, each independent variable having associated values, the method comprising the steps of: a. defining a new independent variable for said dependent variables, said new independent .[.variables.]. .Iadd.variable .Iaddend.having associated values, each of said values representing one dependent variable;   b. reading the values associated with all of the independent variables;   c. selecting which independent variable is a fastest-running independent variable, and ranking the selected independent variable as the fastest-running independent variable;   d. selecting which independent variable is a next fastest-running independent variable, and ranking the selected independent variable as the next .[.faster.]. .Iadd.fastest.Iaddend.-running independent variable;   e. repeating step (d) until all independent variables are ranked, with a last ranked independent variable being a slowest-running independent variable;   f. determining a result for each value of .[.a.]. .Iadd.the .Iaddend.new independent variable and for all combinations of the values of all independent variables other than the new independent .[.variables.]. .Iadd.variable.Iaddend.;   g. plotting the results determined in step (f) .[.along.]. .Iadd.for at least one value of the new independent variable in .Iaddend.the Y-axis .Iadd.direction.Iaddend., with the corresponding values associated with all independent variables along the X-axis in a hierarchical manner, said plotting comprising the steps of: (1) .[.sequentially.]. displaying .Iadd.horizontally next to one another .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a first value of the next .[.faster.]. .Iadd.fastest.Iaddend.-running independent variable and a first value of each of the remaining independent variables;   (2) .[.sequentially.]. displaying .Iadd.horizontally next to one another, in a same manner as for the first value of the next fastest-running independent variable so as to preserve horizontal spacing of the fastest-running independent variable's values, .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a second value for the next fastest-running independent variable and a first value for each of the remaining independent variables.Iadd., the horizontally displaying next to one another of the results being in such a manner that the ranking of the independent variables remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking.Iaddend.;   (3) repeating steps (g)(2) for each remaining value of the next fastest-running independent variable;   (4) repeating steps (g)(1)-(g)(3) for each value of any remaining independent variable.Iadd., preserving horizontal spacings of any given independent variable's values for every occurrence in a nested hierarchy, .Iaddend.until completed for a last value of the slowest-running independent variable.Iadd., the horizontally displaying next to one another of the results being in such a manner that the ranking of the independent variables from fastest to slowest remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking.Iaddend.;     .[.h. displaying a group of rectangles, each rectangle having a first vertical extreme and a second vertical extreme, said rectangles horizontally enclosing the plotted results associated with an independent variable, said group of rectangles containing a nesting of rectangles of faster-running independent variables horizontally within the rectangles of slower-running independent variables according to the hierarchical manner in which the results associated with the independent variables are plotted;.]. and   .[.i.]. .Iadd.h.Iaddend.. repeating steps (f) and (g) for each remaining new independent variable .Iadd.value.Iaddend..   
     
     
       2. The method of claim .[.1.]. .Iadd.29 .Iaddend.wherein said group of rectangles .[.displayed in step (h).]. are comprised of different colored rectangles. 
     
     
       3. The method of claim 2 wherein each color represents a different independent variable. 
     
     
       4. The method of claim .[.1.]. .Iadd.29 .Iaddend.wherein said first vertical extreme of each rectangle is on the .[.Y-axis line.]. .Iadd.X-axis (Y=0) .Iaddend.and the second vertical extreme of the rectangle representing the fastest-running variable is at the point corresponding to .[.the value.]. .Iadd.a result .Iaddend.of each particular fastest-running variable .Iadd.value.Iaddend.. 
     
     
       5. The method of claim 4 wherein the second vertical extreme of each .Iadd.horizontally enclosing .Iaddend.rectangle is equal to the sum of the second vertical extremes of the .Iadd.horizontally enclosed .Iaddend.rectangles associated with .[.the next fastest-running.]. .Iadd.any faster-running independent .Iaddend.variable. 
     
     
       6. The method of claim 5 wherein the values of the dependent variables .[.are both.]. .Iadd.can include .Iaddend.positive and negative .Iadd.results.Iaddend.. 
     
     
       7. The method of claim .[.1.]. .Iadd.29 .Iaddend.comprising the further step of selecting which of the rectangles .[.displayed in step (h).]. is to be displayed first. 
     
     
       8. The method of claim 7 comprising the further step of selecting the order in which the remaining rectangles are displayed. 
     
     
       9. The method as set forth in claim .[.1.]. .Iadd.29  wherein the second vertical extreme of each rectangle is determined by a predetermined function. 
     
     
       10. The method of claim 9 wherein the predetermined function defines a subset of the nested rectangles. 
     
     
       11. The method of claim 10 wherein the nested rectangles correspond to .[.the next fastest-running.]. .Iadd.any faster-running independent .Iaddend.variable. 
     
     
       12. The method of claim 1, wherein more than one new independent variable is defined in step (a), each of said more than one new independent variables corresponding to a set of dependent variables, and each new independent variable having associated new values relating to .[.a property of said.]. corresponding dependent .[.variable.]. .Iadd.variables.Iaddend.. 
     
     
       13. A system using a computer for displaying a function in two dimensions on a display, said display defined by an X-axis and a Y-axis, wherein said function is comprised of .[.a plurality of.]. .Iadd.at least three discrete .Iaddend.independent variables and at least one dependent variable, each independent variable having associated values, the system comprising: a. defining means for defining a new independent variable for said dependent variables, said new independent .[.variables.]. .Iadd.variable .Iaddend.having associated values, each of said values representing one dependent variable;   b. reading means for reading the values associated with all of the independent variables;   c. first selecting means for selecting which independent variable is a fastest-running independent variable and ranking the selected independent variable as the fastest-running independent variable;   d. second selecting means for selecting which independent variable is a next fastest-running independent variable and ranking the selected independent variable as the next .[.faster.]. .Iadd.fastest.Iaddend.-running independent variable;   e. ranking means for repeating said selection of the next fastest-running independent variable until all independent variables are ranked with a last ranked independent variable being a slowest-running independent variable;   f. determining means for determining a result for each value of .[.a.]. .Iadd.the .Iaddend.new independent variable and for all combinations of the values of all remaining independent variables other than the new independent variable;   g. plotting means for plotting said results .[.along.]. .Iadd.for at least one value of the new independent variable in .Iaddend.the Y-axis .Iadd.direction .Iaddend.with the corresponding values associated with the independent variables along the X-axis in a hierarchical manner, said plotting means comprising: (1) first .[.sequentially.]. displaying means for .[.sequentially.]. displaying .Iadd.horizontally next to one another .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a first value of the next fastest-running independent variable and a first value of each of the remaining independent variables;   (2) second .[.sequentially.]. displaying means for .[.sequentially.]. displaying .Iadd.horizontally next to one another, in a same manner as for the first value of the next fastest-running independent variable so as to preserve horizontal spacing of the fastest-running independent variable's values and in such a manner that the ranking of the independent variables remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking, .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a second value of the next fastest-running independent variable and a first value for each of the remaining independent variables;   (3) first repeating means for repeating the .[.sequential.]. display .Iadd.of the results, horizontally next to one another, .Iaddend.by the second .[.sequentially.]. displaying means for each remaining value of the next fastest-running independent variable;   (4) second repeating means for repeating the .[.sequential.]. display by the first .[.sequentially.]. displaying means, by the second .[.sequentially.]. displaying means, and by the first repeating means for each value of any remaining independent variable.Iadd., preserving horizontal spacings of any given independent variable's values for every occurrence in a nested hierarchy and continuing in such a manner that the ranking of the independent variables from fastest to slowest remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking, .Iaddend.until completed for a last value of the slowest-running independent variable;     .[.h. group means for displaying a group of rectangles, each rectangle having a first vertical extreme and a second vertical extreme, said rectangles horizontally enclosing the plotted results associated with an independent variable, said group of rectangles containing a nesting of rectangles of faster-running independent variables within the rectangles of slower-running independent variables according to the hierarchical manner in which the results associated with the independent variables are plotted;.]. and   .[.i.]. .Iadd.h.Iaddend.. looping means for repeating the determining of the results by said determining means, and for repeating the plotting of the results by said plotting means for each remaining new independent variable .Iadd.value.Iaddend..   
     
     
       14. The method of claim .[.1.]. .Iadd.29 .Iaddend.further comprising, after .Iadd.the .Iaddend.step .[.(h).]. .Iadd.of displaying a group of rectangles.Iaddend., the step of: .[.(h2).]. graphically connecting the plotted result of each fastest running variable nested within a rectangle of the next fastest running variable.   
     
     
       15. The method of claim 14 further comprising, after .Iadd.the .Iaddend.step .[.(h).]. .Iadd.of graphically connecting.Iaddend., the step of: .[.(h3).]. graphically connecting the plotted result of a fastest running variable located within a rectangle of the next fastest running variable with the plotted result of a fastest running variable located within all other rectangles of the next fastest running variable.   
     
     
       16. The method of claim .[.1.]. .Iadd.29 .Iaddend.further comprising, after .Iadd.the .Iaddend.step .[.(h).]. .Iadd.of displaying a group of rectangles.Iaddend., the step of: .[.(h2).]. graphically connecting the plotted result of a fastest running variable located within a rectangle associated with a particular independent variable with a corresponding plotted result of a fastest running variable located within all other rectangles associated with the same independent variable.   
     
     
       17. The method of claim 16 further comprising, after .Iadd.the .Iaddend.step .[.(h2).]. .Iadd.of graphically connecting.Iaddend., the step of repeating .Iadd.the .Iaddend.step .[.(h2).]. .Iadd.of graphically connecting .Iaddend.for all independent variables. 
     
     
       18. The method of claim 14 wherein .Iadd.the .Iaddend.step .[.(h2).]. .Iadd.of graphically connecting .Iaddend.further includes graphically connecting the plotted results using a line. 
     
     
       19. The method of claim 14 wherein .Iadd.the .Iaddend.step .[.(h2).]. .Iadd.of graphically connecting .Iaddend.further includes graphically connecting the plotted results using a curve. 
     
     
       20. The method of claim .[.1.]. .Iadd.29 .Iaddend.wherein .Iadd.the .Iaddend.step .[.(h).]. .Iadd.of displaying a group of rectangles .Iaddend.further includes displaying the rectangles with each rectangle having a height equal to the difference between a maximum .Iadd.enclosed result .Iaddend.and .Iadd.a .Iaddend.minimum .[.value of the independent variable associated with the rectangle.]. .Iadd.enclosed result.Iaddend.. 
     
     
       21. The method of claim .[.1.]. .Iadd.29 .Iaddend.wherein .Iadd.the .Iaddend.step .[.(h).]. .Iadd.of displaying a group of rectangles .Iaddend.further includes graphically connecting the rectangles associated with a given independent variable. 
     
     
       22. The method of claim 21 wherein .Iadd.the .Iaddend.step .[.(h).]. .Iadd.of graphically connecting .Iaddend.further includes graphically connecting the rectangles at a corresponding point in each rectangle. 
     
     
       23. The method of claim 22 wherein the corresponding point is a top center point of each rectangle. 
     
     
       24. The method of claim 1 wherein the values read in step (b) comprise a grid. 
     
     
       25. The method of claim 24 wherein step (b) further includes the steps of: b1. reading a first value;   b2. reading a last value;   b3. reading an incremental value; and   b4. generating the grid using the incremental value to generate values between the first value and the last value to form the grid.   
     
     
       26. The method of claim 1 wherein step (g) further includes, after step (g)(4), the step of: (5) displaying the results of steps (g)(1) to (g)(4) together.   
     
     
       27. A method using a system including a computer with a display for displaying a function of at least .[.one.]. .Iadd.three .Iaddend.independent .[.variable.]. .Iadd.variables .Iaddend.and at least one dependent variable, .Iadd.each independent variable having associated values, .Iaddend.the method comprising the steps of: a. defining a new independent variable for said dependent variables, said new independent .[.variables.]. .Iadd.variable .Iaddend.having associated values;   b. reading the values .Iadd.associated with each independent variable.Iaddend.;   c. selecting which independent variable is a fastest-running independent variable, and ranking the selected independent variable as the fastest-running independent variable;   d. selecting which independent variable is a next fastest-running independent variable, and ranking the selected independent variable as the next fastest-running independent variable;   e. repeating step (d) until al independent variables are ranked;   f. determining a result for each value of .[.a.]. .Iadd.the .Iaddend.new independent variable and for all combinations of the values of all independent variables;   g. plotting the results determined in step (f) .Iadd.for at least one value of the new independent variable.Iaddend., said plotting comprising the steps of: (1) .[.sequentially.]. displaying .Iadd.horizontally next to one another .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a first value of the next fastest-running independent variable and a first value of each of the remaining independent variables;   (2) .[.sequentially.]. displaying .Iadd.horizontally next to one anther .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a second value of the next fastest-running independent variable and a first value for each of the remaining independent variables.Iadd., the horizontally displaying next to one another of the results being in such a manner that the ranking of the independent variables remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking.Iaddend.;   (3) repeating steps (g)(2) for each remaining value of the next fastest-running independent variable;   (4) repeating steps (g)(1)-(g)(3) for each value of any remaining independent variable.Iadd., the horizontally displaying next to one another of the results being in such a manner that the ranking of the independent variables from fastest to slowest remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking.Iaddend.;     .[.h. displaying a group of rectangles, said group of rectangles containing a nesting of rectangles of faster-running independent variables within the rectangles of slower-running independent variables;.]. and   .[.i.]. .Iadd.h.Iaddend.. repeating steps (f) and (g) for each remaining new independent variable .Iadd.value.Iaddend..   
     
     
       28. A system using a computer for displaying a function of at least .[.one.]. .Iadd.three .Iaddend.independent .[.variable.]. .Iadd.variables .Iaddend.and at least one dependent variable, .Iadd.each independent variable having associated values, .Iaddend.the system comprising: a. defining means for defining a new independent variable for said dependent variables, said new independent .[.variables.]. .Iadd.variable .Iaddend.having associated values;   b. reading means for reading the values .Iadd.associated with each independent variable.Iaddend.;   c. first selecting means for selecting which independent variable is a fastest-running independent variable and ranking the selected independent variable as the fastest-running independent variable;   d. second selecting means for selecting which independent variable is a next fastest-running independent variable and ranking the selected independent variable as the next fastest-running independent variable;   e. ranking means for repeating said selection of the next fastest-running independent variable until all independent variables are ranked;   f. determining means for determining a result for each value of .[.a.]. .Iadd.the .Iaddend.new independent variable and for all combinations of the values of all remaining independent variables;   g. plotting means for plotting said results .Iadd.for at least one value of the new independent variable.Iaddend., said plotting means comprising: (1) first .[.sequentially.]. displaying means for .[.sequentially.]. displaying .Iadd.horizontally next to one another .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a first value of the next fastest-running independent variable and a first value of each of the remaining independent variables;   (2) second .[.sequentially.]. displaying means for .[.sequentially.]. displaying .Iadd.horizontally next to one another in such a manner that the ranking of the independent variables remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking, .Iaddend.the .[.result.]. .Iadd.results .Iaddend.corresponding to the values associated with the fastest-running independent variable for a second value of the next fastest-running independent variable and a first value for each of the remaining independent variables;   (3) first repeating means for repeating the .[.sequential.]. display by the second .[.sequentially.]. displaying means for each remaining value of the next fastest-running independent variable;   (4) second repeating means for repeating the .[.sequential.]. display by the first .[.sequentially.]. displaying means, by the second .[.sequentially.]. displaying means, and by the first repeating means for each value of any remaining independent variable .Iadd.in such a manner that the ranking of the independent variables from fastest to slowest remains unchanged when using an extreme left of each result to determine the ranking as when using an extreme right of each result to determine the ranking, .Iaddend.until completed for a last value of the slowest-running independent variable;     .[.h. group means for displaying a group of rectangles, said group of rectangles containing a nesting of rectangles of faster-running independent variables within the rectangles of slower-running independent variables;.]. and   .[.i.]. .Iadd.h.Iaddend.. looping means for repeating the determining of the results by said determining means, and for repeating the plotting of the results by said plotting means for each remaining new independent variable .Iadd.value.Iaddend.. .Iadd.   
     
     
       29.  The method as set forth in claim 1, further comprising the step of: displaying a group of rectangles, each rectangle having a first vertical extreme and a second vertical extreme, with at least one of said first vertical extreme and said second vertical extreme being determined by a property of at least one horizontally enclosed result, said rectangles horizontally enclosing the plotted results associated with a faster-running independent variable. .Iaddend..Iadd.30. The system as set forth in claim 13, further comprising:   group means for displaying a group of rectangles, each rectangle having a first vertical extreme and a second vertical extreme, with at least one of said first vertical extreme and said second vertical extreme being determined by a property of at least one horizontally enclosed result, said rectangles horizontally enclosing the plotted results associated with a faster-running independent variable. .Iaddend..Iadd.31. The method as set forth in claim 27, further comprising the step of:   displaying a group of rectangles, each rectangle having a first vertical extreme and a second vertical extreme, with at least one of said first vertical extreme and said second vertical extreme being determined by a property of at least one horizontally enclosed result, said rectangle horizontally enclosing the plotted results associated with a faster-running independent variable. .Iaddend..Iadd.32. The system as set forth in claim 28, further comprising:   group means for displaying a group of rectangles, each rectangle having a first vertical extreme and a second vertical extreme, with at least one of said first vertical extreme and said second vertical extreme being determined by a property of at least one horizontally enclosed result, said rectangles horizontally enclosing the plotted results associated with a faster-running independent variable. .Iaddend.