Contour triangulation system and method

• US 20070253617A1
• Filed: 04/27/2006
• Published: 11/01/2007
• Est. Priority Date: 04/27/2006
• Status: Active Grant

• Current Assignee: MAKO Surgical Corporation (Stryker Corporation)
• Original Assignee: MAKO Surgical Corporation (Stryker Corporation)
• Inventors: Wu, Min, Arata, Louis
• Granted Patent: US 7,623,702 B2
• Time in Patent Office: Days
• US Class Current: 382/154
• CPC Class Codes: G06T 17/20 Finite element generation, e.g. wire-frame surface description, tesselation

Abstract

A method and apparatus for reconstructing a surface shape of an object having contour lines, includes assigning points to each contour line. A first triangulation scheme is performed with respect to respective points on two adjacently-positioned contour lines, to determine a first surface shape for a portion of the object corresponding to the two contour lines. The first surface shape is checked to determine if the first surface shape is in error. If the first surface shape is not in error, the first surface shape is outputted for the portion of the object as determined by the first triangulation scheme, as a reconstructed surface shape for that portion of the object. If the first surface shape is in error, a second triangulation scheme is performed with respect to the respective points on the two contour lines, to determine a second surface shape for that portion of the object, and the second surface shape is outputted for that portion of the object as determined by the second triangulation scheme, as a reconstructed surface shape.

Claims

1. A method of reconstructing a surface shape of an object from a plurality of contour lines, comprising:

obtaining the plurality of contour lines by scanning the object to obtain scan data and segmenting the scan data;

assigning points to each of the plurality of contour lines obtained from the segmented scan data, wherein each of the contour lines is closed and non-intersecting with respect to others of the contour lines;

performing a first triangulation scheme with respect to respective points on two adjacently-positioned contour lines, to determine a first surface shape for a portion of the object corresponding to the two adjacently-positioned contour lines;

checking the first surface shape to determine if the first surface shape is in error;

if the first surface shape is not in error, outputting the first surface shape for the portion of the object as determined by the first triangulation scheme, as a reconstructed surface shape for the portion of the object; and

if the first surface shape is in error,

performing a second triangulation scheme with respect to the respective points on the two adjacently-positioned contour lines, to determine a second surface shape for the portion of the object corresponding to the two adjacently-positioned contour lines; and

outputting the second surface shape for the portion of the object as determined by the second triangulation scheme, as a reconstructed surface shape for the portion of the object.

2. The method according to claim 1, wherein the first triangulation scheme is a shortest distance scheme, and wherein the second triangulation scheme is a closest orientation scheme.

3. The method according to claim 1, wherein the scanning step is accomplished by performing a CT scan of the object.

4. The method according to claim 1, wherein the object includes a bone structure of a patient.

5. The method according to claim 1, further comprising:

performing either or both of the first triangulation scheme or the second triangulation scheme with respect to respective points on each two adjacently-positioned contour lines of the plurality of contour lines, in order to obtain a full reconstructed surface shape of the object.

6. The method according to claim 1, wherein one of the first triangulation scheme and the second triangulation scheme includes a shortest distance triangulation scheme comprising:

a) for each point on the first contour line, determining a point on the second contour line that is closest to the point on the first contour line;

b) setting a first triangle leg as a line that connects the point on the second contour line that is closest to the point on the first contour line;

c) comparing a first distance from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second distance from an adjacent point on the second contour line to the point on the first contour line;

d) based on the comparing step, setting a second triangle leg as a line that connects the shorter one of the first and second distances, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

e) repeating steps a) through d) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

7. The method according to claim 1, wherein one of the first triangulation scheme and the second triangulation scheme includes a closest orientation triangulation scheme comprising:

a) for each point on the first contour line, determining an orientation of a centroid vector of the point on the first contour line to each contour point on the second contour line;

b) determining a closest orientation of the centroid vector of the point on the first contour line to a centroid vector of a point on the second contour line;

c) repeating steps a) and b) until a closest orientation for all points on the first contour line have been determined;

d) setting a first triangle leg as a line that connects the point on the second contour line that has the closest orientation to the point on the first contour line;

e) comparing a first orientation from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second orientation from an adjacent point on the second contour line to the point on the first contour line;

f) based on the comparing step, setting a second triangle leg as a line that connects the closest orientation of the first and second orientations, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

g) repeating steps d) through f) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

8. The method according to claim 6, wherein the other of the first triangulation scheme and the second triangulation scheme includes a closest orientation triangulation scheme comprising:

a) for each point on the first contour line, determining an orientation of a centroid vector of the point on the first contour line to each contour point on the second contour line;

b) determining a closest orientation of the centroid vector of the point on the first contour line to a centroid vector of a point on the second contour line;

c) repeating steps a) and b) until a closest orientation for all points on the first contour line have been determined;

d) setting a first triangle leg as a line that connects the point on the second contour line that has the closest orientation to the point on the first contour line;

e) comparing a first orientation from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second orientation from an adjacent point on the second contour line to the point on the first contour line;

f) based on the comparing step, setting a second triangle leg as a line that connects the closest orientation of the first and second orientations, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

g) repeating steps d) through f) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

9. The method according to claim 1, further comprising:

creating a model of the object from multiple pairs of triangulated contours, wherein the multiple pairs of triangulated contours are stacked on top of each other.

10. The method according to claim 9, further comprising:

closing top and bottom contours of the stacked triangulated contours by using a respective centroid point as an apex of multiple triangles each formed from adjacent points on the respective top and bottom contours.

11. The method according to claim 1, wherein the checking step comprises:

a) for each point on the first contour line, determining a point on the second contour line that is closest to the point on the first contour line;

b) setting a first triangle leg as a line that connects the point on the second contour line that is closest to the point on the first contour line;

c) comparing a first distance from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second distance from an adjacent point on the second contour line to the point on the first contour line;

d) based on the comparing step, setting a second triangle leg as a line that connects the shorter one of the first and second distances, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line;

e) checking the orientation of the centroid vector for the point on the first contour line to the centroid vector for the point on the second contour line, if orientation is larger than 90 degrees, the surface shape is in error, otherwise the surface shape is correct;

wherein the orientation is determined by computing a dot product of the centroid vector of the point on the first contour line with the centroid vector of the point on the second contour line, wherein the negative dot product corresponds to the orientation larger than 90 degrees;

f) repeating steps a) through e) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

12. A method of reconstructing a surface shape of an object from a plurality of contour lines, comprising:

obtaining the plurality of contour lines by scanning the object to obtain scan data and segmenting the scan data;

assigning points to each of the plurality of contour lines obtained from the segmented scan data, wherein each of the contour lines is closed and non-intersecting with respect to others of the contour lines;

performing a shortest distance triangulation scheme with respect to respective points on two adjacently-positioned contour lines that correspond to first and second contour lines, to determine a first surface shape for a portion of the object corresponding to the first and second contour lines,

wherein the shortest distance triangulation scheme comprises;

a) for each point on the first contour line, determining a point on the second contour line that is closest to the point on the first contour line;

b) setting a first triangle leg as a line that connects the point on the second contour line that is closest to the point on the first contour line;

c) comparing a first distance from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second distance from an adjacent point on the second contour line to the point on the first contour line;

d) based on the comparing step, setting a second triangle leg as a line that connects the shorter one of the first and second distances, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

e) repeating steps a) through d) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

13. The method according to claim 12, wherein the scanning step is accomplished by performing a CT scan of the object.

14. The method according to claim 12, wherein the object includes a bone structure of a patient.

15. The method according to claim 12, further comprising:

creating a model of the object from multiple pairs of triangulated contours, wherein the multiple pairs of triangulated contours are stacked on top of each other.

16. The method according to claim 15, further comprising:

closing top and bottom contours of the stacked triangulated contours by using a respective centroid point as an apex of multiple triangles each formed from adjacent points on the respective top and bottom contours.

17. A method of reconstructing a surface shape of an object from a plurality of contour lines, comprising:

obtaining the plurality of contour lines by scanning the object to obtain scan data and segmenting the scan data;

assigning points to each of the plurality of contour lines obtained from the segmented scan data, wherein each of the contour lines is closed and non-intersecting with respect to others of the contour lines;

performing a closest orientation triangulation scheme with respect to respective points on two adjacently-positioned contour lines that correspond to first and second contour lines, to determine a first surface shape for a portion of the object corresponding to the first and second contour lines,

wherein the closest orientation triangulation scheme comprises;

a) for each point on the first contour line, determining an orientation of a centroid vector of the point on the first contour line to each contour point on the second contour line;

b) determining a closest orientation of the centroid vector of the point on the first contour line to a centroid vector of a point on the second contour line;

c) repeating steps a) and b) until a closest orientation for all points on the first contour line have been determined;

d) setting a first triangle leg as a line that connects the point on the second contour line that has the closest orientation to the point on the first contour line;

e) comparing a first orientation from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second orientation from an adjacent point on the second contour line to the point on the first contour line;

f) based on the comparing step, setting a second triangle leg as a line that connects the closest orientation of the first and second orientations, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

g) repeating steps d) through f) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

18. The method according to claim 17, wherein the scanning step is accomplished by performing a CT scan of the object.

19. The method according to claim 17, wherein the object includes a bone structure of a patient.

20. The method according to claim 17, wherein the closest orientation of the centroid vector of the point on the first contour line to the centroid vector of a point on the second contour line is determined by computing a dot product of the centroid vector of the point on the first contour line with a centroid vector of each point on the second contour line, wherein the point on the second contour line having the smallest dot product corresponds to the closest orientation.

21. The method according to claim 17, further comprising:

creating a model of the object from multiple pairs of triangulated contours, wherein the multiple pairs of triangulated contours are stacked on top of each other.

22. The method according to claim 21, further comprising:

closing top and bottom contours of the stacked triangulated contours by using a respective centroid point as an apex of multiple triangles each formed from adjacent points on the respective top and bottom contours.

23. A computer program product executable on a computer and configured to compute a surface shape of an object, the computer program product, when executed on the computer, performing the steps of:

obtaining a plurality of contour lines by scanning the object to obtain scan data and segmenting the scan data;

assigning points to each of the plurality of contour lines obtained from the segmented scan data, wherein each of the contour lines is closed and non-intersecting with respect to others of the contour lines;

performing a first triangulation scheme with respect to respective points on two adjacently-positioned contour lines, to determine a first surface shape for a portion of the object corresponding to the two adjacently-positioned contour lines;

checking the first surface shape to determine if the first surface shape is in error;

if the first surface shape is not in error, outputting the first surface shape for the portion of the object as determined by the first triangulation scheme, as a reconstructed surface shape for the portion of the object; and

if the first surface shape is in error,

performing a second triangulation scheme with respect to the respective points on the two adjacently-positioned contour lines, to determine a second surface shape for the portion of the object corresponding to the two adjacently-positioned contour lines; and

outputting the second surface shape for the portion of the object as determined by the second triangulation scheme, as a reconstructed surface shape for the portion of the object.

24. The computer program product according to claim 23, wherein the first triangulation scheme is a shortest distance scheme, and wherein the second triangulation scheme is a closest orientation scheme.

25. The computer program product according to claim 23, wherein the scanning step is accomplished by performing a CT scan of the object.

26. The computer program according to claim 23, wherein the object includes a bone structure of a patient.

27. The computer program product according to claim 23, further comprising:

performing either or both of the first triangulation scheme or the second triangulation scheme with respect to respective points on each two adjacently-positioned contour lines of the plurality of contour lines, in order to obtain a full reconstructed surface shape of the object.

28. The computer program product according to claim 23, wherein one of the first triangulation scheme and the second triangulation scheme includes a shortest distance triangulation scheme comprising:

a) for each point on the first contour line, determining a point on the second contour line that is closest to the point on the first contour line;

b) setting a first triangle leg as a line that connects the point on the second contour line that is closest to the point on the first contour line;

c) comparing a first distance from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second distance from an adjacent point on the second contour line to the point on the first contour line;

d) based on the comparing step, setting a second triangle leg as a line that connects the shorter one of the first and second distances, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

e) repeating steps a) through d) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

29. The computer program product according to claim 23, wherein one of the first triangulation scheme and the second triangulation scheme includes a closest orientation triangulation scheme comprising:

a) for each point on the first contour line, determining an orientation of a centroid vector of the point on the first contour line to each contour point on the second contour line;

b) determining a closest orientation of the centroid vector of the point on the first contour line to a centroid vector of a point on the second contour line;

c) repeating steps a) and b) until a closest orientation for all points on the first contour line have been determined;

d) setting a first triangle leg as a line that connects the point on the second contour line that has the closest orientation to the point on the first contour line;

e) comparing a first orientation from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second orientation from an adjacent point on the second contour line to the point on the first contour line;

f) based on the comparing step, setting a second triangle leg as a line that connects the closest orientation of the first and second orientations, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

g) repeating steps d) through f) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

30. The computer program product according to claim 28, wherein the other of the first triangulation scheme and the second triangulation scheme includes a closest orientation triangulation scheme comprising:

a) for each point on the first contour line, determining an orientation of a centroid vector of the point on the first contour line to each contour point on the second contour line;

b) determining a closest orientation of the centroid vector of the point on the first contour line to a centroid vector of a point on the second contour line;

c) repeating steps a) and b) until a closest orientation for all points on the first contour line have been determined;

d) setting a first triangle leg as a line that connects the point on the second contour line that has the closest orientation to the point on the first contour line;

e) comparing a first orientation from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second orientation from an adjacent point on the second contour line to the point on the first contour line;

f) based on the comparing step, setting a second triangle leg as a line that connects the closest orientation of the first and second orientations, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

g) repeating steps d) through f) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

31. The computer program product according to claim 23, further comprising:

creating a model of the object from multiple pairs of triangulated contours, wherein the multiple pairs of triangulated contours are stacked on top of each other.

32. The computer program product according to claim 31, further comprising:

closing top and bottom contours of the stacked triangulated contours by using a respective centroid point as an apex of multiple triangles each formed from adjacent points on the respective top and bottom contours.

33. The computer program product according to claim 23, wherein the checking step comprises:

a) for each point on the first contour line, determining a point on the second contour line that is closest to the point on the first contour line;

b) setting a first triangle leg as a line that connects the point on the second contour line that is closest to the point on the first contour line;

c) comparing a first distance from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second distance from an adjacent point on the second contour line to the point on the first contour line;

d) based on the comparing step, setting a second triangle leg as a line that connects the shorter one of the first and second distances, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line;

e) checking the orientation of the centroid vector for the point on the first contour line to the centroid vector for the point on the second contour line, if orientation is larger than 90 degrees, the surface shape is in error, otherwise the surface shape is correct;

wherein the orientation is determined by computing a dot product of the centroid vector of the point on the first contour line with the centroid vector of the point on the second contour line, wherein the negative dot product corresponds to the orientation larger than 90 degrees;

f) repeating steps a) through e) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

34. A computer program product executable on a computer and configured to compute a surface shape of an object, the computer program product, when executed on the computer;

performing the steps of;

obtaining a plurality of contour lines by scanning the object to obtain scan data and segmenting the scan data;

assigning points to each of the plurality of contour lines obtained from the segmented scan data, wherein each of the contour lines is closed and non-intersecting with respect to others of the contour lines;

performing a shortest distance triangulation scheme with respect to respective points on two adjacently-positioned contour lines that correspond to first and second contour lines, to determine a first surface shape for a portion of the object corresponding to the first and second contour lines,

wherein the shortest distance triangulation scheme comprises;

a) for each point on the first contour line, determining a point on the second contour line that is closest to the point on the first contour line;

b) setting a first triangle leg as a line that connects the point on the second contour line that is closest to the point on the first contour line;

c) comparing a first distance from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second distance from an adjacent point on the second contour line to the point on the first contour line;

d) based on the comparing step, setting a second triangle leg as a line that connects the shorter one of the first and second distances, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

e) repeating steps a) through d) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

35. The computer program product according to claim 34, wherein the scanning step is accomplished by performing a CT scan of the object.

36. The computer program product according to claim 34, wherein the object includes a bone structure of a patient.

37. The computer program product according to claim 34, further comprising:

creating a model of the object from multiple pairs of triangulated contours, wherein the multiple pairs of triangulated contours are stacked on top of each other.

38. The computer program product according to claim 37, further comprising:

closing top and bottom contours of the stacked triangulated contours by using a respective centroid point as an apex of multiple triangles each formed from adjacent points on the respective top and bottom contours.

39. A computer program product executable on a computer and configured to compute a surface shape of an object, the computer program product, when executed on the computer, performing the steps of:

obtaining a plurality of contour lines by scanning the object to obtain scan data and segmenting the scan data;

assigning points to each of the plurality of contour lines obtained from the segmented scan data, wherein each of the contour lines is closed and non-intersecting with respect to others of the contour lines;

performing a closest orientation triangulation scheme with respect to respective points on two adjacently-positioned contour lines that correspond to first and second contour lines, to determine a first surface shape for a portion of the object corresponding to the first and second contour lines,

wherein the closest orientation triangulation scheme comprises;

a) for each point on the first contour line, determining an orientation of a centroid vector of the point on the first contour line to each contour point on the second contour line;

b) determining a closest orientation of the centroid vector of the point on the first contour line to a centroid vector of a point on the second contour line;

c) repeating steps a) and b) until a closest orientation for all points on the first contour line have been determined;

d) setting a first triangle leg as a line that connects the point on the second contour line that has the closest orientation to the point on the first contour line;

e) comparing a first orientation from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second orientation from an adjacent point on the second contour line to the point on the first contour line;

f) based on the comparing step, setting a second triangle leg as a line that connects the closest orientation of the first and second orientations, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line; and

g) repeating steps d) through f) by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.

40. The computer program product according to claim 39, wherein the scanning step is accomplished by performing a CT scan of the object.

41. The computer program product according to claim 39, wherein the object includes a bone structure of a patient.

42. The computer program product according to claim 39, wherein the closest orientation of the centroid vector of the point on the first contour line to the centroid vector of a point on the second contour line is determined by computing a dot product of the centroid vector of the point on the first contour line with a centroid vector of each point on the second contour line, wherein the point on the second contour line having the smallest dot product corresponds to the closest orientation.

43. The computer program product according to claim 39, further comprising:

creating a model of the object from multiple pairs of triangulated contours, wherein the multiple pairs of triangulated contours are stacked on top of each other.

44. The computer program product according to claim 43, further comprising:

closing top and bottom contours of the stacked triangulated contours by using a respective centroid point as an apex of multiple triangles each formed from adjacent points on the respective top and bottom contours.

45. An apparatus for reconstructing a surface shape of an object from a plurality of contour lines, comprising:

a scanner unit configured to obtain the plurality of contour lines by scanning the object to obtain scan data and to segment the scan data;

an assigning unit configured to assign points to each of the plurality of contour lines obtained from the segmented scan data, wherein each of the contour lines is closed and non-intersecting with respect to others of the contour lines;

a first triangulation computation unit configured to perform a first triangulation scheme with respect to respective points on two adjacently-positioned contour lines, to determine a first surface shape for a portion of the object corresponding to the two adjacently-positioned contour lines;

a checking unit configured to check the first surface shape to determine if the first surface shape is in error;

a second triangulation computation unit configured to perform a second triangulation scheme with respect to the respective points on the two adjacently-positioned contour lines, to determine a second surface shape for the portion of the object corresponding to the two adjacently-positioned contour lines; and

an output and display unit configured to output and display either the first surface shape as output by the first triangulation computation unit or the second surface shape as output by the second triangulation computation unit, as a reconstructed surface shape for the portion of the object.

46. The apparatus according to claim 45, wherein the first triangulation computation unit performs a shortest distance triangulation, and wherein the second triangulation computation unit performs a closest orientation triangulation.

47. The apparatus according to claim 45, wherein the scanner unit includes a CT scanner.

48. The apparatus according to claim 45, wherein the object includes a bone structure of a patient.

49. The apparatus according to claim 45, further comprising:

an object model creating unit configured to create a model of the object from multiple pairs of triangulated contours, wherein the multiple pairs of triangulated contours are stacked on top of each other.

50. The apparatus according to claim 49, wherein the object model creating unit creates top and bottom portions of the model by closing top and bottom contours of the stacked triangulated contours by using a respective centroid point as an apex of multiple triangles each formed from adjacent points on the respective top and bottom contours.

51. The apparatus according to claim 45, wherein the checking unit comprises:

means for determining, for each point on the first contour line, a point on the second contour line that is closest to the point on the first contour line;

means for setting a first triangle leg as a line that connects the point on the second contour line that is closest to the point on the first contour line;

means for comparing a first distance from the point on the second contour line to an adjacent point on the first contour line that is adjacent the point on the first contour line, to a second distance from an adjacent point on the second contour line to the point on the first contour line;

means for setting, based on the comparing step, a second triangle leg as a line that connects the shorter one of the first and second distances, and setting a third triangle leg as a line that connects either the point and the adjacent point on the first contour line, or the point and the adjacent point on the second contour line;

means for checking the orientation of the centroid vector for the point on the first contour line to the centroid vector for the point on the second contour line, if orientation is larger than 90 degrees, the surface shape is in error, otherwise the surface shape is correct;

wherein the orientation is determined by computing a dot product of the centroid vector of the point on the first contour line with the centroid vector of the point on the second contour line, wherein the negative dot product corresponds to the orientation larger than 90 degrees,

wherein the checking unit performs checking by moving to a next point in either a clockwise direction or a counterclockwise direction on either the first contour line or the second contour line, until all points on the first and second contour lines have been connected to another point on the other of the first and second contour lines.