Apparatus and methods for wrapping texture onto the surface of a virtual object

• US 20050128211A1
• Filed: 12/10/2003
• Published: 06/16/2005
• Est. Priority Date: 12/10/2003
• Status: Active Grant

• Current Assignee: 3D Systems, Inc. (3D Systems Corporation)
• Original Assignee: SensAble Technologies, Inc. (3D Systems Corporation)
• Inventors: Berger, Torsten, Shannon, Walter C. III, Chen, Elaine
• Granted Patent: US 7,889,209 B2
• Time in Patent Office: Days
• US Class Current: 345/582
• CPC Class Codes: G06T 11/001 Texturing; Colouring; Generation of texture or colour inpainting G06T5/77
• CPC Class Codes: G06T 15/04 Texture mapping
• CPC Class Codes: G06T 19/00 Manipulating 3D models or images for computer graphics
• CPC Class Codes: G09G 5/00 Control arrangements or circuits for visual indicators common to cathode-ray tube indicators and other visual indicators image data processing or generation, in general G06T

Abstract

The invention provides techniques for wrapping a two-dimensional texture conformally onto a surface of a three dimensional virtual object within an arbitrarily-shaped, user-defined region. The techniques provide minimum distortion and allow interactive manipulation of the mapped texture. The techniques feature an energy minimization scheme in which distances between points on the surface of the three-dimensional virtual object serve as set lengths for springs connecting points of a planar mesh. The planar mesh is adjusted to minimize spring energy, and then used to define a patch upon which a two-dimensional texture is superimposed. Points on the surface of the virtual object are then mapped to corresponding points of the texture. The invention also features a haptic/graphical user interface element that allows a user to interactively and intuitively adjust texture mapped within the arbitrary, user-defined region.

Claims

1. A method for mapping a location on a surface of a three-dimensional virtual object to a corresponding location on a two-dimensional texture, the method comprising the steps of:

(a) selecting a region on a surface of a three-dimensional virtual object;

(b) creating a first mesh comprising points corresponding to points within the selected region;

(c) creating a second mesh comprising points corresponding to points of the first mesh;

(d) adjusting the second mesh to improve a quality metric associated with an arrangement of points of the second mesh;

(e) relating the adjusted second mesh to a two-dimensional texture; and

(f) mapping a location in the selected region to a corresponding location in the texture.

2. The method of claim 1, wherein step (d) further comprises defining the quality metric using the first mesh.

3. The method of claim 1, wherein the first mesh and the second mesh have an identical number of points.

4. The method of claim 1, wherein the three-dimensional virtual object is represented in a first coordinate space and the two-dimensional texture is represented in a second coordinate space.

5. The method of claim 4, further comprising the steps of:

(g) defining a first geometric representation relating a first parameter space to the first coordinate space; and

(h) defining a second geometric representation relating the first parameter space to the second coordinate space.

6. The method of claim 5, wherein at least one of the first geometric representation and the second geometric representation is selected from the group consisting of a NURBS patch, a Bezier patch, a Cardinal spline patch, a Gregory patch, a bilinear patch, a bicubic patch, a polygon mesh, and a triangle mesh.

7. The method of claim 5, wherein at least one of the first geometric representation and the second geometric representation is interpolable.

8. The method of claim 5, wherein the mapping of step (f) comprises determining parameters of the first parameter space corresponding to the location in the selected region.

9. The method of claim 1, wherein the region in step (a) is a contiguous user-defined region.

10. The method of claim 1, wherein step (a) comprises selecting the region using a curve loop drawn on the surface of the virtual object by a user.

11. The method of claim 10, wherein the curve loop comprises a plurality of curves.

12. The method of claim 10, wherein the curve loop comprises four curves.

13. The method of claim 1, wherein the first mesh comprises substantially uniformly-spaced points.

14. The method of claim 1, wherein the second mesh consists of points lying within a plane.

15. The method of claim 1, wherein points of the second mesh are substantially uniformly spaced prior to the adjusting of step (d).

16. The method of claim 1, wherein step (d) comprises modeling at least a plurality of the points of the second mesh as connected by springs.

17. The method of claim 16, wherein step (d) comprises adjusting the second mesh to reduce an energy associated with the springs.

18. The method of claim 16, wherein step (d) comprises adjusting the second mesh in a step-wise manner to substantially minimize an energy associated with the springs.

19. The method of claim 16, wherein step (d) comprises modeling an interior point of the second mesh as connected to eight neighboring mesh points by eight springs.

20. The method of claim 16, wherein the springs comprise at least one linear spring.

21. The method of claim 16, wherein step (d) further comprises modeling at least one point using at least one torsional spring.

22. The method of claim 16, wherein step (d) comprises adjusting edge points of the second mesh.

23. The method of claim 16, wherein step (d) comprises using distances between neighboring points of the first mesh as set lengths for corresponding springs.

24. The method of claim 23, wherein the distances between neighboring points of the first mesh are shortest-path geodesic distances.

25. The method of claim 23, wherein the distances between neighboring points of the first mesh are approximate.

26. The method of claim 1, wherein step (b) comprises creating the first mesh from a representation of the surface of the virtual object using at least one of a Delaunay triangulation technique and a Voronoi diagram.

27. The method of claim 1, wherein step (e) comprises relating the adjusted second mesh to the two-dimensional texture using a transformation matrix.

28. The method of claim 27, wherein the transformation matrix accounts for at least one of a translation of the texture, a rotation of the texture, and a scaling of the texture.

29. A method for mapping a location on a surface of a virtual object to a corresponding location on a texture, the method comprising the steps of:

(a) selecting a region on a surface of a virtual object represented in a first coordinate space;

(b) defining a first patch corresponding to the selected region;

(c) tessellating the first patch to create a first mesh;

(d) creating a second mesh comprising points corresponding to points of the first mesh;

(e) adjusting the second mesh to improve a quality metric associated with an arrangement of points of the second mesh;

(f) defining a second patch using the second mesh;

(g) superimposing a texture onto the second patch, wherein the texture is represented in a second coordinate space; and

(h) mapping a location on the surface of the virtual object to a corresponding location on the texture.

30. The method of claim 29, wherein step (e) further comprises defining the quality metric using the first mesh.

31. The method of claim 29, wherein the texture comprises a tiled pattern, and wherein no boundary of a tile of the tiled pattern is constrained to align with a boundary of the region.

32. The method of claim 29, wherein the texture is an image, and wherein no boundary of the image is constrained to align with a boundary of the region.

33. The method of claim 29, wherein the first coordinate space is three-dimensional and the second coordinate space is two-dimensional.

34. The method of claim 33, wherein the first patch relates a first parameter space to the first coordinate space, and wherein the second patch relates the first parameter space to the second coordinate space.

35. The method of claim 34, wherein the first parameter space is a (u,v) parameter space.

36. The method of claim 34, wherein the second patch relates the first parameter space to the second coordinate space using a linear transformation between the first parameter space and a second parameter space.

37. The method of claim 34, wherein the second patch directly relates the first parameter space to the second coordinate space.

38. The method of claim 29, wherein the region in step (a) is a contiguous user-defined region.

39. The method of claim 29, wherein at least one of the first patch and the second patch is a NURBS patch.

40. The method of claim 29, wherein at least one of the first patch and the second patch is a member selected from the group consisting of a Bezier patch, a Cardinal spline patch, a Gregory patch, a bilinear patch, and a bicubic patch.

41. The method of claim 29, wherein at least one of the first patch and the second patch is interpolable.

42. The method of claim 29, wherein step (b) comprises the substeps of:

(i) generating an initial grid comprising grid points;

(ii) projecting at least a plurality of the grid points onto the surface of the virtual object;

(iii) modeling at least a plurality of the grid points as connected by springs;

(iv) adjusting at least a plurality of the grid points to decrease an energy associated with the springs; and

(v) defining a NURBS patch using at least a plurality of the grid points.

43. The method of claim 42, wherein step (b) further comprises the substep of:

(vi) repeating the projecting of substep (ii) and the adjusting of substep (iv) until the energy associated with the springs is substantially minimized.

44. The method of claim 42, wherein substep (iii) comprises modeling an interior grid point as connected to four neighboring grid points by four springs.

45. The method of claim 42, wherein substep (iv) comprises constraining grid points to lie on the surface of the object.

46. The method of claim 42, wherein each of the springs in substep (iii) has an identical set length.

47. The method of claim 42, wherein substep (v) comprises performing a least squares fit using the adjusted grid points.

48. The method of claim 29, wherein step (e) comprises modeling at least a plurality of the points of the second mesh as connected by springs having set lengths based on distances between corresponding points of the first mesh.

49. The method of claim 48, wherein step (e) comprises adjusting the second mesh in a step-wise manner to substantially minimize an energy associated with the springs.

50. The method of claim 48, wherein step (e) comprises modeling an interior point of the second mesh as connected to eight neighboring grid points by eight springs.

51. The method of claim 29, wherein the superimposing of step (g) comprises using a transformation matrix.

52. The method of claim 51, wherein the transformation matrix accounts for at least one of a translation of the texture, a rotation of the texture, and a scaling of the texture.

53. The method of claim 29, wherein step (h) further comprises assigning to the location on the surface of the virtual object a graphical value associated with the corresponding location on the texture.

54. The method of claim 53, wherein the graphical value is a color value.

55. The method of claim 53, wherein the graphical value represents an adjustment along a normal to the surface of the virtual object.

56. A method for wrapping a texture onto a surface of a three-dimensional virtual object, the method comprising the steps of:

(a) selecting an arbitrarily-shaped user-defined region of a surface of a three-dimensional virtual object; and

(b) for each of a plurality of locations in the region;

(i) mapping the location in the selected region to a corresponding location in a texture; and

(ii) assigning to the location in the selected region a graphical value associated with the location in the texture.

57. The method of claim 56, further comprising the step of:

(c) graphically rendering the virtual object.

58. The method of claim 57, further comprising the step of:

(d) modifying a voxel representation of the virtual object according to the graphical values assigned in step (b).

59. The method of claim 56, wherein the texture comprises a tiled pattern.

60. The method of claim 59, wherein no boundary of a tile of the tiled pattern is constrained to align with a boundary of the user-defined region.

61. The method of claim 59, further comprising the step of:

(c) graphically rendering the virtual object with the tiled pattern applied within the user-defined region.

62. The method of claim 56, wherein the graphical value is a color value.

63. The method of claim 56, wherein the texture comprises an embossing pattern and wherein the graphical value represents an adjustment along a normal to the surface of the virtual object.

64. The method of claim 63, further comprising the step of:

(c) graphically rendering the virtual object with the embossing pattern applied within the user-defined region.