[ARX程序]：如何计算AcGeCircArc3d的refVec?

rave

AcGeCircArc3d的refVec是如何计算的?

XDSoft

关于参考向量的问题，涉及到ACAD的弧对象保存角度的方法，还有一个地方就是AcGeVector3d::angleTo中也会遇到，下面给你贴两篇资料，你理解下

1. 
   
2. [FONT=courier new]
   
3. Angles in AcDbArc and AcGeCircArc2d  
   
4. ID    13119  
   
5. Applies to:    AutoCAD 2000
   
6. AutoCAD 2000I
   
7. AutoCAD 2002
   
8. 
   
9. Date    1/29/2002  
   
10. 
    
11. This document is part of    AcGe (Geometry Library)     
    
12. 
    
13. 
    
14. Question
    
15. I use the AutoCAD RECTANG command to draw an unrotated rectangle with the
    
16. FILLET option. When prompted for the startAng and endAng of the resulting
    
17. AcDbPolyline's corner arcs, the values are always 0 and 90 degree. However, if
    
18. the polyline is selected and LIST is typed the values for startAng and endAng
    
19. are displayed correctly with only the upper-right corner sweeping from 90 to 0
    
20. degrees. Why ?
    
21. Answer
    
22. The LIST command and entity definition data for an arc uses AcDbArc class
    
23. information, whereas a polyline provides AcGeCircArc2d information.
    
24. 
    
25. Querying the arcs of a filleted rectangle, which is represented as a polyline
    
26. entity, pPoly:
    
27. 
    
28. 
    
29. int n = pPoly->numVerts();
    
30. AcGeCircArc2d arc; AcGeVector2d dir;
    
31. 
    
32. for (int i=0; i < n; i++) {
    
33.     if (pPoly->segType(i) != AcDbPolyline::kArc)
    
34.         continue;
    
35.     if ((es = pPoly->getArcSegAt(i, arc)) == Acad::eOk) {
    
36.         dir =  arc.refVec();
    
37.         acutPrintf("\nVertex %d:\tstartang= %f \t endang= %f \trefvec=
    
38. {%i %i}",
    
39.             i, arc.startAng(), arc.endAng(), (int)dir[0],
    
40. (int)dir[1]);
    
41.     }
    
42. }
    
43. 
    
44. Printed results are:
    
45. Vertex 0: startang= 0.000000 endang= 1.570796 refvec= {-1 0}
    
46. Vertex 2: startang= 0.000000 endang= 1.570796 refvec= {0 1}
    
47. Vertex 4: startang= 0.000000 endang= 1.570796 refvec= {1 0}
    
48. Vertex 6: startang= 0.000000 endang= 1.570796 refvec= {0 -1}
    
49. 
    
50. This is the expected result because the angles are measured with respect to the
    
51. arc's reference vector, which in this case is always oriented to contain the
    
52. startpoint of the arc. Therefore, vertex 0 is the upper left arc (corner) of an
    
53. unrotated rectangle. Its reference vector of [-1 0] proceeds from the arc's
    
54. center point along the -x axis in WCS. The startpoint of the arc then lies on
    
55. this reference vector, and thus the start angle from the reference vector is 0.
    
56. The arc's endpoint is found 1.57 rads away from the startpoint/reference vector
    
57. in a + clockwise direction.
    
58. 
    
59. The start and end angles for an AcDbArc are invariably measured in respect to
    
60. the +x axis. Also, the positive direction for rotation is considered to be
    
61. counter-clockwise. Vertex 0, the upper-left corner will then list a start
    
62. angle=180 and an end angle=90.
    
63. [/FONT]

复制代码

XDSoft

下面这个是关于AcGeVector3d::angleTo() 的参考向量的理解。

1. 
   
2. [FONT=courier new]
   
3. 
   
4. AcGeVector3d::angleTo() explained  
   
5. ID    45178  
   
6. Applies to:    AutoCAD 2000
   
7. 
   
8. Date    6/21/2000  
   
9. 
   
10. This document is part of    ObjectARX   ObjectARX Technical Newsletter - December 1999     
    
11. 
    
12. 
    
13. Question
    
14. The method AcGeVector3d::angleTo(const AcGeVector3d &vec, const AcGeVector3d&
    
15. refVec) const is described as follows in the ARXREF.HLP:
    
16. 
    
17. "Returns the angle between this vector and the vector 'vec' in the range [0, 2 *
    
18. PI]; If ( refVec.dotProduct(crossProduct(vec)) >=  0.0 ) the return value
    
19. coincides with the return value of the function angleTo( vec ). Otherwise the
    
20. return value is 2*PI  minus the return value of the function angleTo( vec )."
    
21. 
    
22. What exactly is meant when passing as refVec?
    
23. Answer
    
24. According to the online documentation, there are two overloaded functions for
    
25. angleTo().
    
26. 
    
27. One is:
    
28. double AcGeVector3d::angleTo( const AcGeVector3d& vec) const;
    
29. Returns the angle between this vector and the vector vec in the range [0, Pi].
    
30. 
    
31. Another is:
    
32. double AcGeVector3d::angleTo(const AcGeVector3d& vec, const AcGeVector3d&
    
33. refVec) const;
    
34. Returns the angle between this vector and the vector vec in the range [0, 2 x
    
35. Pi].
    
36. 
    
37. If (refVec.dotProduct(crossProduct(vec)) >= 0.0), then the return value
    
38. coincides with the return value of the function angleTo(vec). Otherwise, the
    
39. return value is 2 x Pi minus the return value of the function angleTo(vec).
    
40. 
    
41. Therefore, the return angle's range is different. That's exactly why the refVec
    
42. is needed. Dot Product, as you know, is a method to find out how parallel two
    
43. lines are. The result of the calculation is a scalar. This is most useful if you
    
44. use unit vectors (get a number between -1 and 1), such as our usage here
    
45. (vectors).
    
46. |x1| |x2|
    
47. 
    
48. |y1| . |y2| = (x1 * x2) + (y1 * y2) + (z1 * z2)
    
49. 
    
50. |z1| |z2|
    
51. Cross Product  is the process of multiplying two vectors together to get a
    
52. normal to the plane they describe with the Vector (0,0,0).
    
53. |x1| |x2| |y1*z2 - z1*y2|
    
54. 
    
55. |y1| x |y2| = |z1*x2 - x1*z2|
    
56. 
    
57. |z1| |z2| |x1*y2 - y1*x2|
    
58. Therefore, in the code,
    
59. refVec.dotProduct(crossProduct(vec))
    
60. it first checks the angle between the normal (for the plane which 'this' vector
    
61. and 'vec' vector is on) and the refVec. As it states, if
    
62. (refVec.dotProduct(crossProduct(vec)) >= 0.0), then the return value coincides
    
63. with the return value of the function angleTo(vec). Otherwise the return value
    
64. is 2 x Pi minus the return value of the function angleTo(vec).
    
65. 
    
66. You can actually use the normal vector for the plane that 'this' vector is on,
    
67. as the refVec, to check the 'vec'. Of course, you can choose other vectors that
    
68. are not the same as the normal vector depends on your application needs.
    
69. [/FONT]

复制代码

XDSoft

给你贴两个函数，在AcGeCircArc3d和AcDbArc间转换。

1. 
   
2. [FONT=courier new]
   
3. 
   
4. void convertArc2Arc( AcGeCircArc3d*pGeArc, AcDbArc*&pDbArc )
   
5. 
   
6. {
   
7.        
   
8.         AcGePoint3d center = pGeArc->center();
   
9.        
   
10.         AcGeVector3d normal = pGeArc->normal();
    
11.        
    
12.         AcGeVector3d refVec = pGeArc->refVec();
    
13.        
    
14.         AcGePlane plane = AcGePlane(center, normal);
    
15.        
    
16.         double ang = refVec.angleOnPlane(plane);
    
17.        
    
18.         pDbArc = new AcDbArc(center, normal, pGeArc->radius(),pGeArc->startAng() + ang, pGeArc->endAng() + ang );
    
19.        
    
20. }
    
21. 
    
22. 
    
23. 
    
24. void convertArc2Arc( AcDbArc*pDbArc, AcGeCircArc3d*&pGeArc)
    
25. 
    
26. {
    
27.        
    
28.         pGeArc = new AcGeCircArc3d(
    
29.                
    
30.                 pDbArc->center(),
    
31.                
    
32.                 pDbArc->normal(),
    
33.                
    
34.                 pDbArc->normal().perpVector(),
    
35.                
    
36.                 pDbArc->radius(),
    
37.                
    
38.                 pDbArc->startAngle(),
    
39.                
    
40.                 pDbArc->endAngle());
    
41.        
    
42. }
    
43. 
    
44. [/FONT]

复制代码

XDSoft

由 NORMAL 法向量，得到refVec 参考向量，实际就是X轴。

pDbArc->normal().perpVector()

对于世界座标系，Z=0,0,1,那么X轴＝1,0,0