Methods and apparatus for navigating an image

1. A method, comprising:

receiving at a client terminal a plurality of pre-rendered images of varying zoom levels of a roadmap;

receiving one or more user navigation commands including zooming information at the client terminal; and

blending two or more of the pre-rendered images to obtain an intermediate image of an intermediate zoom level that corresponds with the zooming information of the navigation commands such that a display of the intermediate image on the client terminal provides the appearance of smooth navigation,

wherein at least some roads of the roadmap are scaled up and/or down in order to produce the plurality of pre-determined images, and the scaling is at least one of: (i) physically proportional to the zoom level; and (ii) non-physically proportional to the zoom level, and wherein the non-physically proportional scaling may be expressed by the following formula: p=d′·z a , where p is a linear size in pixels of one or more elements of the object at the zoom level, d′ is an imputed linear size of the one or more elements of the object in physical units, z is the zoom level in units of physical linear size/pixel, and a is a power law where a≠−1.

2. The method of claim 1 , wherein the physically proportional scaling may be expressed by the following formula: p=c·d/z, where p is a linear size in pixels of one or more elements of the object at the zoom level, c is a constant, d is a real or imputed linear size of the one or more elements of the object in physical units, and z is the zoom level in units of physical linear size/pixel.

3. The method of claim 1 , wherein at least one of d′ and a may vary for one or more elements of the object.

4. The method of claim 1 , wherein the power law is −1<a<0 within a range of zoom levels between z 0 and z 1 , where z 0 is of a lower physical linear size/pixel than z 1 .

5. The method of claim 4 , wherein at least one of z 0 and z 1 may vary for one or more roads of the roadmap.

6. The method of claim 1 , wherein:

the roads of the roadmap are of varying degrees of coarseness; and

the scaling of the roads in a given pre-rendered image are physically proportional or non-physically proportional based on at least one of: (i) a degree of coarseness of such roads; and (ii) the zoom level of the given pre-rendered image.

7. A method, comprising:

receiving at a client terminal a plurality of pre-rendered images of varying zoom levels of at least one object, at least some elements of the at least one object being scaled up and/or down in order to produce the plurality of pre-determined images, and the scaling being at least one of: (i) physically proportional to the zoom level; and (ii) non-physically proportional to the zoom level, wherein the zoom levels and the scaling of the pre-rendered images are selected such that respective linear sizes in pixels p of a given one or more of the elements of the object do not vary by more than a predetermined number of pixels as between one pre-rendered image and another pre-rendered image of higher resolution;

receiving one or more user navigation commands including zooming information at the client terminal;

blending two or more of the pre-rendered images to obtain an intermediate image of an intermediate zoom level that corresponds with the zooming information of the navigation commands; and

displaying the intermediate image on the client terminal.

8. The method of claim 7 , wherein the blending step includes performing at least one of alpha-blending, trilinear interpolation, and bicubic-linear interpolation.

9. The method of claim 7 , further comprising downsampling a lowest resolution one of the pre-rendered images to facilitate navigation to zoom levels beyond a zoom level of the lowest resolution one of the pre-rendered images.

10. The method of claim 7 , wherein:

the elements of the object are of varying degrees of coarseness; and

the scaling of the elements in a given pre-rendered image are physically proportional or non-physically proportional based on at least one of: (i) a degree of coarseness of such elements; and (ii) the zoom level of the given pre-rendered image.

11. The method of claim 10 , wherein:

the object is a roadmap, the elements of the object are roads, and the varying degrees of coarseness are road hierarchies; and

the scaling of a given road in a given pre-rendered image is physically proportional or non-physically proportional based on: (i) the road hierarchy of the given road; and (ii) the zoom level of the given pre-rendered image.

12. A method, comprising:

receiving at a client terminal a plurality of pre-rendered images of varying zoom levels of at least one object, at least some elements of the at least one object being scaled up and/or down in order to produce the plurality of pre-determined images, and the scaling being at least one of: (i) physically proportional to the zoom level; and (ii) non-physically proportional to the zoom level, wherein the non-physically proportional scaling may be expressed by the following formula: p=d′·z a , where p is a linear size in pixels of one or more elements of the object at the zoom level, d′ is an imputed linear size of the one or more elements of the object in physical units, z is the zoom level in units of physical linear size/pixel, and a is a power law where a≠−1;

receiving one or more user navigation commands including zooming information at the client terminal;

blending two or more of the pre-rendered images to obtain an intermediate image of an intermediate zoom level that corresponds with the zooming information of the navigation commands; and

displaying the intermediate image on the client terminal.

13. The method of claim 12 , wherein the physically proportional scaling may be expressed by the following formula: p=c·d/z, where p is a linear size in pixels of one or more elements of the object at the zoom level, c is a constant, d is a real or imputed linear size of the one or more elements of the object in physical units, and z is the zoom level in units of physical linear size/pixel.

14. The method of claim 12 , wherein at least one of d′ and a may vary for one or more elements of the object.

15. The method of claim 12 , wherein the power law is −1<a<0 within a range of zoom levels between z 0 and z 1 , where z 0 is of a lower physical linear size/pixel than z 1 .

16. The method of claim 15 , wherein at least one of z 0 and z 1 may vary for one or more elements of the object.

17. The method of claim 12 wherein the plurality of pre-rendered images are received by the client terminal over a packetized network.