Exertion-aware path generation

1. A computing system, comprising:

at least one processor; and

at least one memory device having computer-executable instructions stored thereon that, in response to execution by the at least one processor, cause the computing system to:

generate a path based at least on first data defining a terrain, second data defining a target level of total work, and third data defining a target level of perceived difficulty;

generate a road surface along the path, wherein generating the road surface includes embedding metadata defining position-dependent resistance forces based on a physics model, the metadata controlling force feedback at virtual-reality equipment; and

supply the road surface to the virtual-reality equipment.

2. The computing system of claim 1 , wherein generating the path comprises determining a solution to an optimization problem with respect to a cost function based at least on the target level of total work and the target level of perceived difficulty, the solution defining the path.

3. The computing system of claim 2 , wherein the determining the solution comprises iteratively updating an initial path until a termination criterion is satisfied.

4. The computing system of claim 3 , wherein the iteratively updating the initial path comprises:

randomly selecting, by the computing system, a particular spatial transformation from a group of spatial transformations; and

updating, by the computing system, a current path by moving respective positions of a group of points on a plane according to the particular spatial transformation, the group of points defining a two-dimensional trajectory.

5. The computing system of claim 4 , the at least one memory device having further computer-executable instructions stored thereon that, in response to execution by the at least one processor, further cause the computing system to configure the updated current path as a next path using a probability based on a Metropolis criterion defined in terms of a ratio of an exponential function of the cost function evaluated at the updated current path and the exponential function evaluated at the current path.

6. The computing system of claim 3 , wherein the termination criterion dictates that an absolute change of the cost function is less than a defined percentage threshold over a defined number of past iterations.

7. The computing system of claim 1 , wherein the virtual-reality equipment comprises a VR computer, a VR head-mounted device (HMD) configured to provide at least visual data, and a bike having a haptic device configured to provide haptic feedback.

8. The computing system of claim 1 , wherein the path has an elevation profile along a trajectory on a plane, and wherein generating the road surface comprises:

approximating the elevation profile with a series of linear segments; and

planarizing a portion of a profile of the terrain about a centerline located at a position defined by a two-dimensional point in the trajectory and an elevation corresponding to the elevation profile at the two-dimensional point.

9. A computer-implemented method, comprising:

generating, by a computing system comprising at least one processor, a path based at least on first data defining a terrain, second data defining a target level of total work, and third data defining a target level of perceived difficulty;

generating, by the computing system, a road surface along the path, wherein generating the road surface includes embedding metadata defining position-dependent resistance forces based on a physics model, the metadata controlling force feedback at virtual-reality equipment; and

supplying, by the computing system, the road surface to the virtual-reality equipment.

10. The computer-implemented method of claim 9 , wherein the generating the path comprises determining a solution to an optimization problem with respect to a cost function based at least on the target level of total work and the target level of perceived difficulty, the solution defining the path.

11. The computer-implemented method of claim 10 , wherein the determining the solution comprises iteratively updating an initial path until a termination criterion is satisfied.

12. The computer-implemented method of claim 11 , wherein the iteratively updating the initial path comprises:

randomly selecting, by the computing system, a particular spatial transformation from a group of spatial transformations; and

updating, by the computing system, a current path by moving respective positions of a group of points on a plane according to the particular spatial transformation, the group of points defining a two-dimensional trajectory.

13. The computer-implemented method of claim 12 , further comprising configuring, by the computing system, the updated current path as a next path using a probability based on a Metropolis criterion defined in terms of a ratio of an exponential function of the cost function evaluated at the updated current path and the exponential function evaluated at the current path.

14. The computer-implemented method of claim 9 , wherein the path has an elevation profile along a trajectory on a plane, and wherein the generating the road surface comprises:

approximating, by the computing system, the elevation profile with a series of linear segments; and

planarizing a portion of a profile of the terrain about a centerline located at a position defined by a two-dimensional point in the trajectory and an elevation corresponding to the elevation profile at the two-dimensional point.

15. The computer-implemented method of claim 9 , further comprising generating, by the computing system, the path further based on one or more of fourth data defining a group of positions along the path to be intersected by the path or fifth data defining a group of positions along the path to be avoided by the path.

16. A computer-readable non-transitory storage medium having encoded thereon instructions that, in response to execution, cause a computing system to perform or facilitate operations comprising:

generating a path based at least on first data defining a terrain, second data defining a target level of total work, and third data defining a target level of perceived difficulty;

generating a road surface along the path, wherein generating the road surface includes embedding metadata defining position-dependent resistance forces based on a physics model, the metadata controlling force feedback at virtual-reality equipment; and

supplying the road surface to virtual-reality equipment.

17. The computer-readable non-transitory medium of claim 16 , wherein the generating the path comprises determining a solution to an optimization problem with respect to a cost function based at least on the target level of total work and the target level of perceived difficulty, the solution defining the path.

18. The computer-readable non-transitory medium of claim 17 , wherein the determining the solution comprises iteratively updating an initial path until a termination criterion is satisfied.

19. The computer-readable non-transitory medium of claim 18 , wherein the iteratively updating the initial path comprises,

randomly selecting, by the computing system, a particular spatial transformation from a group of spatial transformations; and

updating, by the computing system, a current path by moving respective positions of a group of points on a plane according to the particular spatial transformation, the group of points defining a two-dimensional trajectory.

20. The computer-readable non-transitory medium of claim 19 , the operations further comprising configuring, by the computing system, the updated current path as a next path using a probability based on a Metropolis criterion defined in terms of a ratio of an exponential function of the cost function evaluated at the updated current path and the exponential function evaluated at the current path.