COMPUTING PLAUSIBLE ROAD SURFACES IN 3D FROM 2D GEOMETRY

• US 20130328863A1
• Filed: 11/29/2012
• Published: 12/12/2013
• Est. Priority Date: 06/10/2012
• Status: Active Grant

• Current Assignee: Apple Inc.
• Original Assignee: Apple Inc.
• Inventors: Pirwani, Imran A.
• Granted Patent: US 9,208,601 B2
• Time in Patent Office: Days
• US Class Current: 345/419
• CPC Class Codes: G01C 21/26 specially adapted for navigation in a road network
• CPC Class Codes: G01C 21/3822 Road feature data, e.g. slope data
• CPC Class Codes: G01C 21/3867 Geometry of map features, e.g. shape points, polygons or for simplified maps
• CPC Class Codes: G06T 11/20 Drawing from basic elements, e.g. lines or circles
• CPC Class Codes: G06T 11/203 Drawing of straight lines or curves
• CPC Class Codes: G06T 15/00 3D [Three Dimensional] image rendering
• CPC Class Codes: G06T 17/00 Three dimensional [3D] modelling, e.g. data description of 3D objects
• CPC Class Codes: G06T 17/05 Geographic models

Abstract

Road network data can include two dimensional (2D) coordinates corresponding to junctions and non junctions in the road network. Height values for roads at junctions can be obtained from optimizing a cost function or as input. Height values for roads at non junction locations can be obtained from a height function defined using the height values for the junctions. Pitch, yaw, and roll vectors can be obtained for non junction locations using the height function, the 2D coordinates, and one or more road parameters, respectively. These vectors can define a coordinate frame for the road, along with which a width can provide points for defining polygons for the road. Road surface data can be constructed from the polygons. The polygons can be provided to a device display for rendering of a three dimensional image of navigation data.

Claims

1. A method for generating polygons of a road surface for a road network area that includes a plurality of junctions, the method comprising:

receiving a junction data set for each junction in the road network area, wherein each junction data set includes a first coordinate and a second coordinate;

receiving a non junction data set for each non junction location in the road network area, wherein each non junction location includes a first coordinate and a second coordinate, the non junction data set defining locations of road segments between junctions;

determining, by a computing device, height values of the road segments at each junction;

for each of a plurality road segments;

computing, by the computing device, a height function defining a change in height of the road segment between the corresponding two junctions;

for each non junction location of the road segment;

calculating a yaw vector using a two dimensional vector between the non junction location and a successive location, wherein a road element connects the non junction location and a successive location;

determining a pitch using the height function at the non junction location; and

determining a roll based on one or more road parameters; and

for each road element of the road segment;

constructing, by the computing device, a set of polygons based on;

a road width at the two locations which the road element is between,

the pitch at each of the two locations,

the yaw vector at each of the two locations, and

the roll at each of the two location.

2. The method of claim 1, wherein determining the pitch using the height function at a non junction location includes:

calculating a value of a first derivative of the height function at the non junction location.

3. The method of claim 1, wherein determining the pitch using the height function at a non junction location includes:

calculating height values at the non junction location and at the successive location using the height function;

calculating a different in the height values between the non junction location and the successive location.

4. The method of claim 1, wherein the height function includes:

a transform subfunction that receives, as input, a two dimensional distance t of a location from a start junction of a road segment to the location measured along the road segment in a two dimensional plane defined by the corresponding first and second coordinates and outputs a transformed distance t′

; and

a height subfunction h(t′

) that receives, as input, the transformed distance t′ and

outputs a height at the two dimensional distance t.

5. The method of claim 4, wherein determining the pitch using the height function at a non junction location includes:

determining the two-dimensional distance t corresponding to the non junction location;

calculating the transformed distance t′

of the non junction location by evaluating the transform subfunction; and

calculating a value of a first derivative of the height function h(t′

) at the transformed distance t′

.

6. The method of claim 4, wherein the transform subfunction includes a function l(t′

), where l(t′

)=a_lt′

³+b_lt′

²+c_lt′

+d_l, where a_l=−

2L_r+c_r,s+c_r,e, b_l=3Lr−

2c_r,s−

c_r,e, c_l=c_r,s, and d_l=0, wherein L_r is the length of the road segment r in two dimensions, and c_r,s and c_r,e are scalars that are functions of L_r, where t′

runs from 0 to 1, and

wherein t′

is determined from the equation l(t′

)=t·

L_r.

7. The method of claim 4, wherein the height subfunction h(t′

) of a road segment r is defined as;

h(t′

)=a_ht′

³+b_ht′

²+c_ht′

+d_h, where a_h=2h_s−

2h_e, b_h=−

3h_s+3h_e, c_h=0, and d_h=h_s, and wherein h_r,s is a height of start junction and h_r,e is a height of an end junction.

8. The method of claim 1, wherein the height function is defined to have a maximum slope at a median point between the two corresponding junctions.

9. The method of claim 8, wherein a sign of the curvature of the height function changes at the median point.

10. The method of claim 1, wherein the height function includes a cubic Hermite spline.

11. The method of claim 1, further comprising:

constructing, by the computing device, road surface data for each road of the road network area based on the set of polygons; and

transmitting, from the computing device to a controller, the road surface data for rendering a three-dimensional map of a part of the road network area.

12. The method of claim 1, wherein determining height values of the roads of each junction includes:

determining, by the computing device, height variables that provide on optimal value for a cost function based on the road data set for each junction, wherein height values of roads of a grade separated crossing are constrained;

to satisfy the stacking order of each road in the junction, and

to have a minimum distance between roads having consecutive stacking order values.

13. The method of claim 1, wherein determining height values of the roads of each junction includes receiving the height values at the computing device.

14. The method of claim 1, wherein the one or more road parameters for determining the roll at a non junction location include a speed limit of the road segment at the non junction location.

15. The method of claim 1, wherein the one or more road parameters for determining the roll at a non junction location include a curvature of the road segment at the non junction location.

16. The method of claim 15, wherein the roll β

at a non junction location p is computed as;

17. The method of claim 1, wherein the roll is computed after the yaw vector and the pitch.

18. The method of claim 17, wherein yaw vector is computer first and pitch vector second.

19. The method of claim 1, wherein each road segment is labeled with a road designation that is associated with junctions and non junction locations of the respective road segment.

20. The method of claim 1, wherein the junction data sets include a stacking order for at least a portion of the junctions, and wherein the plurality of junctions include a plurality of grade separated crossings, a grade separated crossing including at least two roads having a different stacking order signifying that the at least two roads have different heights.

25. The method of claim 17, wherein yaw vector is computed, then the pitch, and then the roll.

21. A computer product comprising a non-transitory computer readable medium storing a plurality of instructions that when executed control a computer system to generate polygons of a road surface for a road network area that includes a plurality of junctions, the instructions comprising:

receiving a junction data set for each junction in the road network area, wherein each junction data set includes a first coordinate and a second coordinate;

receiving a non junction data set for each non junction location in the road network area, wherein each non junction location includes a first coordinate and a second coordinate, the non junction data set defining locations of road segments between junctions;

determining height values of the road segments at each junction;

for each of a plurality road segments;

computing a height function defining a change in height of the road segment between the corresponding two junctions;

for each non junction location of the road segment;

calculating a yaw vector using a two dimensional vector between the non junction location and a successive location, wherein a road element connects the non junction location and a successive location;

determining a pitch using the height function at the non junction location; and

determining a roll based on one or more road parameters; and

for each road element of the road segment;

constructing a set of polygons based on;

a road width at the two locations which the road element is between,

the pitch at each of the two locations,

the yaw vector at each of the two locations, and

the roll at each of the two location.

22. The computer product of claim 21, wherein determining the pitch using the height function at a non junction location includes:

calculating a value of a first derivative of the height function at the non junction location.

23. The computer product of claim 21, wherein the height function includes:

a length subfunction l(t) that receives, as input, a two dimensional distance t of a location from a start junction of a road segment to the location measured along the road segment in a two dimensional plane defined by the corresponding first and second coordinates; and

a height subfunction h(t′

) that receives as input a three dimensional distance t′

of the location as determined from the length subfunction.

24. The computer product of claim 21, wherein the one or more road parameters for determining the roll at a non junction location include a speed limit and a curvature of the road segment at the non junction location.