點坐標進行3d轉動怎麼計算?

BDYCAD · 发表于 2005-2-1 20:34:00

如题: 我有一个点坐标值是 (150 55 100) , 我想把这个点绕x轴正转90度后的坐标值求出来. 不知用什么方法??

平时我们用的polar 涵数都是用来指定Ｘ　Ｙ平面的夹角来算点的. 可到3D旋转的可把我难到了. 没有做过. 不太了解. 所以请教各位大侠了

龙龙仔 · 发表于 2005-2-2 17:14:00

考学数吗?

;;这是3个旋转物件程序,ROTX ROTY ROTZ,
;;其中用了EA网友的矩阵平移
(defun C:ROTX (/ E C B)
(setq E (car (entsel)))
(setq C (getpoint "\n指定基准点: "))
(setq B (getreal "\n指定旋转角度: "))
(MATRIX_T E C B 'M_MX_BLKX)
(princ)
)(defun M_MX_BLKX (IP SX SY SZ RT)
(list
(list SX 0.0 0.0 (car IP))
(list 0.0 (* SY (cos RT)) (* SZ -1.0 (sin RT)) (cadr IP))
(list 0.0 (* SY (sin RT)) (* SZ (cos RT)) (caddr IP))
(list 0.0 0.0 0.0 1.0)
)
);;----------------------------------------------------------
(defun C:ROTY (/ E C B)
(setq E (car (entsel)))
(setq C (getpoint "\n指定基准点: "))
(setq B (getreal "\n指定旋转角度: "))
(MATRIX_T E C B 'M_MX_BLKY)
(princ)
)(defun M_MX_BLKY (IP SX SY SZ RT)
(list
(list (* SX (cos RT)) 0.0 (* SZ (sin RT)) (car IP))
(list 0.0 SY 0.0 (cadr IP))
(list (* SX -1.0 (sin RT)) 0.0 (* SZ (cos RT)) (caddr IP))
(list 0.0 0.0 0.0 1.0)
)
);;----------------------------------------------------------
(defun C:ROTZ (/ E C B)
(setq E (car (entsel)))
(setq C (getpoint "\n指定基准点: "))
(setq B (getreal "\n指定旋转角度: "))
(MATRIX_T E C B 'M_MX_BLKZ)
(princ)
);;先平移基准点再旋转物件
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; M_MX_BLK Creates matrix to multiple local point list by to obtain
;; a world coordinate point. Used when transforming coordinates inside
;; a block definition or similar structure.
;;
;; MATRIX is always 4x4
;; IP base point of block insertion [translation point]
;; SX..SZ scaling factors along the X,Y,Z axes.
;; RT rotation about Z axis in radians.
;;
(defun M_MX_BLKZ (IP SX SY SZ RT)
(list
(list (* SX (cos RT)) (* SY -1.0 (sin RT)) 0.0 (car IP))
(list (* SX (sin RT)) (* SY (cos RT)) 0.0 (cadr IP))
(list 0.0 0.0 SZ (caddr IP))
(list 0.0 0.0 0.0 1.0)
)
);;----------------------------------------------------------------------
(defun MATRIX_T (E PT AA M_MX_BLK / MATRIX)
(setq MATRIX '((1.0 0.0 0.0 0.0)
(0.0 1.0 0.0 0.0)
(0.0 0.0 1.0 0.0)
(0.0 0.0 0.0 1.0)
)
)
(vla-transformby
(vlax-ename->vla-object E)
(vlax-tmatrix
(EA:MATRIX_SETTRANSLATION
MATRIX
(mapcar '- '(0 0 0) PT)
)
)
)
(vla-transformby
(vlax-ename->vla-object E)
(vlax-tmatrix ((eval M_MX_BLK) '(0 0 0) 1 1 1 (DTOR AA)))
)
(vla-transformby
(vlax-ename->vla-object E)
(vlax-tmatrix
(EA:MATRIX_SETTRANSLATION
MATRIX
PT
)
)
)
);;----------------------------------------------------------------------
;;矩阵平移一个向量
(defun EA:MATRIX_SETTRANSLATION (MATRIX VE / M1 M2 M3)
(setq M1 (car MATRIX)
M2 (cadr MATRIX)
M3 (nth 2 MATRIX)
)
(list (list (car M1) (cadr M1) (nth 2 M1) (car VE))
(list (car M2) (cadr M2) (nth 2 M2) (cadr VE))
(list (car M3) (cadr M3) (nth 2 M3) (last VE))
'(0.0 0.0 0.0 1.0)
)
)(defun DTOR (VAL)
(* VAL (/ pi 180))
)

;;这是3个旋转物件程序,ROTX ROTY ROTZ,
;;其中用了EA网友的矩阵平移
(defun C:ROTX (/ E C B)
   (setq E (car (entsel)))
   (setq C (getpoint "\n指定基准点: "))
   (setq B (getreal "\n指定旋转角度: "))
   (MATRIX_T E C B 'M_MX_BLKX)
   (princ)
)(defun M_MX_BLKX (IP SX SY SZ RT)
   (list
       (list SX 0.0 0.0 (car IP))
       (list 0.0 (* SY (cos RT)) (* SZ -1.0 (sin RT)) (cadr IP))
       (list 0.0 (* SY (sin RT)) (* SZ (cos RT)) (caddr IP))
       (list 0.0 0.0 0.0 1.0)
   )
);;----------------------------------------------------------
(defun C:ROTY (/ E C B)
   (setq E (car (entsel)))
   (setq C (getpoint "\n指定基准点: "))
   (setq B (getreal "\n指定旋转角度: "))
   (MATRIX_T E C B 'M_MX_BLKY)
   (princ)
)(defun M_MX_BLKY (IP SX SY SZ RT)
   (list
       (list (* SX (cos RT)) 0.0 (* SZ (sin RT)) (car IP))
       (list 0.0 SY 0.0 (cadr IP))
       (list (* SX -1.0 (sin RT)) 0.0 (* SZ (cos RT)) (caddr IP))
       (list 0.0 0.0 0.0 1.0)
   )
);;----------------------------------------------------------
(defun C:ROTZ (/ E C B)
   (setq E (car (entsel)))
   (setq C (getpoint "\n指定基准点: "))
   (setq B (getreal "\n指定旋转角度: "))
   (MATRIX_T E C B 'M_MX_BLKZ)
   (princ)
);;先平移基准点再旋转物件
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; M_MX_BLK Creates matrix to multiple local point list by to obtain
;; a world coordinate point. Used when transforming coordinates inside
;; a block definition or similar structure.
;;
;; MATRIX is always 4x4
;;     IP   base point of block insertion [translation point]
;;     SX..SZ   scaling factors along the X,Y,Z axes.
;;     RT   rotation about Z axis in radians.
;;
(defun M_MX_BLKZ (IP SX SY SZ RT)
   (list
       (list (* SX (cos RT)) (* SY -1.0 (sin RT)) 0.0 (car IP))
       (list (* SX (sin RT)) (* SY (cos RT)) 0.0 (cadr IP))
       (list 0.0 0.0 SZ (caddr IP))
       (list 0.0 0.0 0.0 1.0)
   )
);;----------------------------------------------------------------------
(defun MATRIX_T  (E PT AA M_MX_BLK / MATRIX)
   (setq  MATRIX '((1.0 0.0 0.0 0.0)
     (0.0 1.0 0.0 0.0)
     (0.0 0.0 1.0 0.0)
     (0.0 0.0 0.0 1.0)
    )
   )
   (vla-transformby
       (vlax-ename->vla-object E)
       (vlax-tmatrix
           (EA:MATRIX_SETTRANSLATION
  MATRIX
  (mapcar '- '(0 0 0) PT)
           )
       )
   )
   (vla-transformby
       (vlax-ename->vla-object E)
       (vlax-tmatrix ((eval M_MX_BLK) '(0 0 0) 1 1 1 (DTOR AA)))
   )
   (vla-transformby
       (vlax-ename->vla-object E)
       (vlax-tmatrix
           (EA:MATRIX_SETTRANSLATION
  MATRIX
  PT
           )
       )
   )
);;----------------------------------------------------------------------
;;矩阵平移一个向量
(defun EA:MATRIX_SETTRANSLATION  (MATRIX VE / M1 M2 M3)
   (setq  M1 (car MATRIX)
  M2 (cadr MATRIX)
  M3 (nth 2 MATRIX)
   )
   (list  (list (car M1) (cadr M1) (nth 2 M1) (car VE))
  (list (car M2) (cadr M2) (nth 2 M2) (cadr VE))
  (list (car M3) (cadr M3) (nth 2 M3) (last VE))
  '(0.0 0.0 0.0 1.0)
   )
)(defun DTOR (VAL)
   (* VAL (/ pi 180))
)

Ea · 发表于 2005-2-3 19:15:00

[Power=1]

(defun ea:ZeroSmallNum (num)
(setq num (rtos num 2 24))
(distof
(if (or (wcmatch num "*e-*")
(wcmatch num "*E-*")
)
"0.0"
num
)
)
)
;;a 绕 x 轴旋转角， yb 绕 y 轴旋转角，zc 绕 z 轴旋转角
;;返回值单位矩阵
(defun ea:Matrix_xyz (xa yb zc)
(mapcar
'(lambda (x) (mapcar '(lambda (a) (ea:zerosmallnum a)) x))
(list
(list (* (cos yb) (cos zc))
(- (cos yb) (sin zc))
(- (sin yb))
0.
)
(list (- (* (sin xa) (sin yb) (sin zc)) (* (cos xa) (sin zc)))
(- (* (cos xa) (cos zc)) (* (sin xa) (sin yb) (sin zc)))
(* (sin xa) (cos yb))
0.
)
(list (+ (* (cos xa) (sin yb) (sin zc)) (* (sin xa) (sin yb)))
(- (- (* (cos xa) (sin yb) (sin zc))) (* (sin xa) (cos yb)))
(* (cos xa) (cos yb))
0.
)
'(0. 0. 0. 1.)
)
)
)

[/Power]

citykunan · 发表于 2005-2-4 11:37:00

两位高手的程序真实巧妙阿。

龙龙仔 · 发表于 2005-2-4 12:27:00

EA兄:再提供个使用例好吗? (defun C:ROT ()
(setq E (car (entsel)))
(setq C1 (getpoint "\n指定基准点: "))
(setq X (DTOR (getreal "\n指定X旋转角度: ")))
(setq Y (DTOR (getreal "\n指定Y旋转角度: ")))
(setq Z (DTOR (getreal "\n指定Z旋转角度: ")))
(setq MAT (EA:MATRIX_XYZ X Y Z))
;;不会用!! 8-(
;|
(vla-transformby
(vlax-ename->vla-object E)
(vlax-tmatrix
MAT
)
)|;
(princ)
) (defun DTOR (VAL)
(* VAL (/ pi 180))
)

Ea · 发表于 2005-2-4 12:37:00

龙龙仔发表于2005-2-4 12:27:00EA兄:再提供个使用例好吗? (defun C:ROT () (setq E (car (entsel))) (setq C1 (getpoint \"\n指定基准点: \")) (setq X (DTOR (getreal \"\n指定...

我很少有3D方面的应用，还得好好想想：）最好你有什么3D变换应用提供个例子（不要太复杂呀），结合起来写更好理解和应用。
另外如果使用矩阵应该还需要其他几个函数配合。这个矩阵是变换点的，不用作用到实体，CAD中不能使用非统一比例矩阵缩放变换。

BDYCAD · 发表于 2005-2-19 17:04:00

我的意图是想计算一排点转后的数据, 不是旋转对象用啊. 上面的程序我看的一头雾水. (SETQ M-POINT '((-0.5 -3.0 0.0) (2.19866 7.16542 0.0) (4.74952 17.6138 0.0) (5.95614 27.1406 0.0)
(5.77003 38.9947 0.0) (4.05484 49.3571 0.0) (-0.997759 67.4402 0.0)
(-5.78818 80.7516 0.0) (-8.85785 88.7957 0.0) (-13.0177 98.7803 0.0) (-20.5174 113.578 0.0))) 如这排点我想绕X轴转30度后变成的点或绕y轴转或绕z轴转其实绕z轴转就用polar涵数计算就好的. 难就是在X 轴和Y轴我想不通, 高手给我讲解下哦. 谢谢!!!

王咣生 · 发表于 2005-2-19 17:49:00

试一下这段程序:
(defun C:recC (/ pl L W ang p2)
(command "UCS" "w")
(setq pl (getpoint "\n Base point:")
L (getdist "\n Length:")
W (getdist pl "\n Width:")
ang (getangle pl "\n Angle:")
)
(command "UCS" "o" pl "ucs" "z" (* 180.0 (/ ang pi))) ;将用户坐标系统旋转ang角;
(command "PLINE" "0,0"
(list L 0)
(list L W)
(list 0 W)
"C")
(command "UCS" "w")
) 再试试这段程序:
(defun C:recC (/ pl L W ang p2)
(command "UCS" "w") (command "ucs" "x" (* 180.0 (/ 30 pi))) ;将用户坐标系统旋转ang角;
(command "point" (list 10 10)) ;点'(10 10 0)
(command "UCS" "w")
)
看看画出的点的坐标是多少,是否能满足你的需要?

yaopx0782 · 发表于 2005-2-20 09:29:00

8楼，程序我一下写不来，可以提供你经过三维旋转后点坐标的计算方法，你编程序应该是高手。

绕x轴的旋转a角度的变换矩阵为：

   1    0    0         0

   0    cos a    sin a           0

   0    -sin a    cos a    0

   0    0    0      1

绕y轴的旋转a角度的变换矩阵为：

   cos a    0    -sin a    0

   0 1      0    0

   sin a    0    cos a         0

   0         0         0           1

绕z轴的旋转a角度的变换矩阵为：

cos a    sin a    0         0

-sin a    cos a         0 0

     0         0         1    0

        0    0    0      1

然后，只需要用原坐标的n+1维向量，与上述变换矩阵相乘，就可以得到所需。

yaopx0782 · 发表于 2005-2-20 09:32:00

奔想回复7楼，写成了8楼，对不起。

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點坐標進行3d轉動怎麼計算?

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用UCS吧,

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