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Computer-implemented methods and systems for displaying nodes on a display device, wherein the nodes have a hierarchical context. Positional information associated with a plurality of nodes is used to generate a display for the nodes in response to a change in focal position. The generated node dis

Computer-implemented methods and systems for displaying nodes on a display device, wherein the nodes have a hierarchical context. Positional information associated with a plurality of nodes is used to generate a display for the nodes in response to a change in focal position. The generated node display maintains hierarchical contextual information about the nodes.

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It is claimed as the invention: 1. A computer-implemented method for displaying nodes on a display device, wherein the nodes have a hierarchical context, said method comprising: receiving positional information associated with a plurality of nodes; using the positional information to generate a dis

It is claimed as the invention: 1. A computer-implemented method for displaying nodes on a display device, wherein the nodes have a hierarchical context, said method comprising: receiving positional information associated with a plurality of nodes; using the positional information to generate a display for the nodes in response to a change in focal position; wherein the using of the positional information includes performing an angular transformation upon the plurality of nodes' node positional information in order to angularly displace each of the plurality of nodes; wherein a conal transformation is performed upon the angularly transformed node positional information in order to generate a three-dimensional conal layout of the nodes; wherein generating the display for the nodes in response to a change in focal position includes displaying the generated conal layout of the nodes; wherein the generated display includes displaying each of the plurality of nodes whose positional information was used in performing the angular transformation; wherein the generated conal layout of the nodes maintains hierarchical contextual information about the nodes; wherein the angular transformation and the conal transformation were performed upon the nodes when generating the display for the nodes in response to the change in focal position; wherein said performing an angular transformation upon the plurality of nodes' node positional information comprises: determining a focus theta angle that defines direction from a focus node to a root node; determining nodal offsets with respect to center of the display; determining geometric distances from the center; for the geometric distances that are not zero, determining theta angles that are equal to a trigonometric transformation of the determined geometric distances; comparing the determined theta angles with the determined focus theta angle in order to determine relative theta angles for the nodes; wherein the relative theta angles are determined differently based upon whether: a theta angle for a node is less than the focus theta angle, a theta angle for a node is equal to the focus theta angle, or a theta angle for a node is greater than the focus theta angle; if a determined relative theta angle has a positive value, then determining a second theta angle for a node based upon a first equation; wherein the first equation determines a second theta angle for a node that is equal to: -(1+dt)*(FocusTheta-minAng)/(dt+1/relTheta)+FocusTheta; wherein the dt for a node in the first equation is indicative of an angular distortion strength factor; wherein the FocusTheta for a node in the first equation is indicative of the focus theta angle determined for the node; wherein the relTheta for a node in the first equation is indicative of the relative theta angle determined for the node; if a determined relative theta angle has a zero value, then determining a second theta angle for a node based upon a second equation; wherein the second equation determines a second theta angle that is equal to a focus theta angle for a node; if a determined relative theta angle has a negative value, then determining a second theta angle for a node based upon a third equation; wherein the third equation determines for a node a second theta angle that is equal to: (1+dt)*(maxAng-FocusTheta)/(dt+1/relTheta)+FocusTheta; wherein the dt for a node in the third equation is indicative of an angular distortion strength factor; wherein the FocusTheta for a node in the third equation is indicative of the focus theta angle determined for the node; wherein the relTheta for a node in the third equation is indicative of the relative theta angle determined for the node; wherein the maxAng and the minAng for a node define angle of the conal layout; wherein the three-dimensional conal layout of the nodes is generated using the determined second theta angles for the nodes. 2. The method of claim 1, wherein the hierarchical context conveys parent-child relationships in the display of the nodes. 3. The method of claim 1, wherein the change in focal position results in viewing at least several nodes in greater detail. 4. The method of claim 1, wherein the change in focal position is caused by a user. 5. The method of claim 1, wherein the focal position is a location on a display screen specified by a user through an interface device. 6. The method of claim 1, wherein the change in focal position is caused by a software program. 7. The method of claim 1, wherein the focal position indicates a location of interest as specified by a user. 8. The method of claim 1, wherein the focal position is located at center of the display. 9. The method of claim 1, wherein the focal position is not located at center of the display. 10. The method of claim 1, wherein the new node positions are provided to a software program. 11. The method of claim 1, wherein the generated display displays the nodes along arcs of concentric circles. 12. The method of claim 1, wherein a plurality of subsequently generated displays maintain the nodes in a three-dimensional conal layout. 13. The method of claim 12, wherein conal transformations were performed upon the nodes for use in maintaining the nodes in a three-dimensional conal layout in the plurality of subsequently generated displays. 14. The method of claim 12, wherein the conal transformations maintain the nodes in three-dimensional conal layouts while magnifying the area around the focal position and in a direction of interest. 15. The method of claim 1, wherein the nodes convey information. 16. The method of claim 1, wherein the angular transformation includes a non-linear angular expansion. 17. The method of claim 16, wherein the non-linear angular expansion includes receiving first positions for locating a first node and a second node on the display device, wherein the first node and second node are separated from each other and are equidistant from a predetermined center position on the display device; wherein second positions are determined for the first node and second node such that angular shift of the first node from its first position to its second position is different in magnitude than angular shift of the second node from its first position to its second position, wherein the angular shifts for the first node and second node are determined based upon a focus position; wherein the focus position indicates a position of interest on the display device; wherein the angular shifts for the first node and second node are with respect to the center position; and wherein the first node and second node are displayed on the display device based upon the determined second positions for the first node and second node. 18. The method of claim 1, further comprising: calculating an angular distortion strength based on focal position; using the calculated angular distortion strength when performing the angular transformation. 19. The method of claim 1, wherein the received positional information include nodes arranged in arch-shaped levels of a cone, further comprising: calculating conal fisheye lens strength based on the distance from apex of the cone along its center axis; using the calculated conal fisheye lens strength when performing the conal transformation. 20. The method of claim 1, wherein the conal transformation includes a conal fisheye distortion to the nodes wherein the conal transformation causes the reduction of the density of nodes along direction of the interest and increases density of nodes at edges of an arch. 21. The method of claim 20, wherein the angular transformation pushes away the nodes on an arch from direction of interest towards edges of the conal layout of the nodes. 22. The method of claim 21, wherein nodes in the conal layout appear in arch-shaped levels of the cone, wherein the pushing of the nodes on an arch allows the node's hierarchical context to be maintained. 23. The method of claim 22, wherein strength of conal transformation is varied with the minimum value at the apex of the cone to the maximum at the arch along the base of the cone. 24. The method of claim 1, wherein parameters are provided to determine which nodes are displayed with full level of detail. 25. The method of claim 1, wherein the generated node display is a dense node-link diagram that graphically represents hierarchical data. 26. The method of claim 1, wherein the generated node display is for use in a data mining software application. 27. The method of claim 1, wherein the generated node display is for use in a decision tree. 28. The method of claim 1, wherein the generated node display is for use in an organizational chart. 29. The method of claim 1, wherein the generated node display is for use in an OLAP (Online Analytical Processing) data viewer. 30. The method of claim 1, wherein the generated node display is for use in a decision tree, organizational chart, and OLAP (Online Analytical Processing) data viewer. 31. A computer-implemented apparatus for displaying nodes on a display device, wherein the nodes have a hierarchical context, said apparatus comprising: means for receiving positional information associated with a plurality of nodes; means for performing an angular transformation using the plurality of nodes' node positional information in order to angularly displace each of the plurality of nodes; means for performing a conal transformation using the angularly transformed node positional information in order to generate a three-dimensional conal node layout; wherein display of the generated conal node layout on the display device maintains hierarchical contextual information about the nodes; wherein the display includes displaying each of the plurality of nodes whose node positional information was used in performing the angular transformation; wherein said performing an angular transformation using the plurality of nodes' node positional information comprises: determining a focus theta angle that defines direction from a focus node to a root node; determining nodal offsets with respect to center of the display; determining geometric distances from the center; for the geometric distances that are not zero, determining theta angles that are equal to a trigonometric transformation of the determined geometric distances; comparing the determined theta angles with the determined focus theta angle in order to determine relative theta angles for the nodes; wherein the relative theta angles are determined differently based upon whether: a theta angle for a node is less than the focus theta angle, a theta angle for a node is equal to the focus theta angle, or a theta angle for a node is greater than the focus theta angle; if a determined relative theta angle has a positive value, then determining a second theta angle for a node based upon a first equation; wherein the first equation determines a second theta angle for a node that is equal to: -(1+dt)*(FocusTheta-minAng)/(dt-1/relTheta)+FocusTheta; wherein the dt for a node in the first equation is indicative of an angular distortion strength factor; wherein the FocusTheta for a node in the first equation is indicative of the focus theta angle determined for the node; wherein the relTheta for a node in the first equation is indicative of the relative theta angle determined for the node; if a determined relative theta angle has a zero value, then determining a second theta angle for a node based upon a second equation; wherein the second equation determines a second theta angle that is equal to a focus theta angle for a node; if a determined relative theta angle has a negative value, then determining a second theta angle for a node based upon a third equation; wherein the third equation determines for a node a second theta angle that is equal to: (1+dt)*(maxAng-FocusTheta)/(dt+1/relTheta)+FocusTheta; wherein the dt for a node in the third equation is indicative of an angular distortion strength factor; wherein the FocusTheta for a node in the third equation is indicative of the focus theta angle determined for the node; wherein the relTheta for a node in the third equation is indicative of the relative theta angle determined for the node: wherein the maxAng and the minAng for a node define angle of the conal layout: wherein the three-dimensional conal layout of the nodes is generated using the determined second theta angles for the nodes. 32. A computer-implemented apparatus for displaying nodes on a display device based upon a change in focal position, wherein the nodes have a hierarchical arrangement, apparatus comprising: computer instructions configured to receive positional information associated with a plurality of nodes; node calculator computer instructions configured to use the positional information to generate a display for the nodes in response to a change in focal position; wherein the node calculator computer instructions are configured to perform an angular transformation upon the plurality of nodes' positional information in order to angularly displace each of the plurality of nodes; wherein the node calculator computer instructions are configured to perform a conal transformation upon the angularly transformed positional information in order to generate a three-dimensional conal layout of the nodes on the display in response to the change in focal position; wherein the generated node layout display maintains the hierarchical arrangement; wherein the generated node layout display includes displaying each of the plurality of nodes whose positional information was used in performing the angular transformation; wherein the node calculator computer instructions are configured to perform an angular transformation by: determining a focus theta angle that defines direction from a focus node to a root node; determining nodal offsets with respect to center of the disp1ay; determining geometric distances from the center; for the geometric distances that are not zero, determining theta angles that are equal to a trigonometric transformation of the determined geometric distances; comparing the determined theta angles with the determined focus theta angle in order to determine relative theta angles for the nodes; wherein the relative theta angles are determined differently based upon whether: a theta angle for a node is less than the focus theta angle, a theta angle for a node is equal to the focus theta angle, or a theta angle for a node is greater than the focus theta angle; if a determined relative theta angle has a positive value, then determining a second theta angle for a node based upon a first equation; wherein the first equation determines a second theta angle for a node that is equal to: (1+dt)*(FocusTheta-minAng)/(dt-1/relTheta)+FocusTheta; wherein the dt for a node in the first equation is indicative of an angular distortion strength factor; wherein the FocusTheta for a node in the first equation is indicative of the focus theta angle determined for the node; wherein the relTheta for a node in the first equation is indicative of the relative theta angle determined for the node; if a determined relative theta angle has a zero value, then determining a second theta angle for a node based upon a second equation; wherein the second equation determines a second theta angle that is equal to a focus theta angle for a node; if a determined relative theta angle has a negative value, then determining a second theta angle for a node based upon a third equation; wherein the third equation determines for a node a second theta angle that is equal to: (1+dt)*(maxAng-FocusTheta)/(dt+1/relTheta)+FocusTheta; wherein the dt for a node in the third equation is indicative of an angular distortion strength factor; wherein the FocusTheta for a node in the third equation is indicative of the focus theta angle determined for the node; wherein the relTheta for a node in the third equation is indicative of the relative theta angle determined for the node; wherein the maxAng and the minAng for a node define angle of the conal layout: wherein the three-dimensional conal layout of the nodes is generated using the determined second theta angles for the nodes. 33. The method of claim 1, wherein the received positional information associated with the plurality of nodes contains information indicating that the plurality of nodes are in a three-dimensional conal layout.