Matrix 创建复合旋转矩阵时出错

我第一次把这个问题贴在Math.Stackexchange上，但是那里的人建议这是解决这个问题的正确地方

我试图沿着多个轴旋转球体上的一组点，以获得特定的方向。我用Fortran编写了同样的代码，如果我将点旋转到任意一个方向，转换似乎工作得很好。但一旦我指定了不止一个旋转轴，解决方案就会出错。大多数点，也许除了极端的点，都超出了球体的体积

我的代码（与问题相关）如下：

DO iSlice = 1, nSlices

 IF(iSlice<10) THEN
    WRITE(string1,'("slice",i1.1,".dat")'), iSlice
 ELSE
    WRITE(string1,'("slice",i2.2,".dat")'), iSlice
 END IF

!PRINT*,string1
OPEN (1, file = string1)
DO j = 1,4
    READ(1,*) z(j),y(j),t(j)
END DO
READ(1,*) temp
x(1:4) = -1.*temp
CLOSE (1)

!Transform the nodal positions as desired
CALL init_Trans
CALL form_translate(-1.*CG)
IF (iRotz) THEN
    ang =  (the3*pi/180.0)*(nSlices-iSlice)/(nSlices-1)
    r_axis = '-rz'
    PRINT*,'angz = ',ang*180./pi
    CALL form_rotate(r_axis,ang)
END IF
IF (iRoty) THEN
    ang =  (the2*pi/180.0)*(nSlices-iSlice)/(nSlices-1)
    r_axis = '-ry'
    PRINT*,'angy = ',ang*180./pi
    CALL form_rotate(r_axis,ang)
END IF
IF (iRotx) THEN
    ang =  (the1*pi/180.0)*(nSlices-iSlice)/(nSlices-1)
    r_axis = '-rx'
    PRINT*,'angx = ',ang*180./pi
    CALL form_rotate(r_axis,ang)
END IF
CALL form_translate(CG)
CALL transform 

WRITE(fout,'(A,I2)')'SLICE: ',iSlice
DO i = 1, 4
    WRITE(fout,71) xnew(i), ynew(i), znew(i), t(i)
END DO
WRITE(fout,*)''

DO i = 1, 4
    WRITE(fout_tec,'(3(D25.17,1X))') xnew(i), ynew(i), znew(i)
END DO

END DO

 SUBROUTINE init_Trans
 USE global_param, ONLY: Trans
 IMPLICIT NONE

 INTEGER :: i,j
! This subroutine initializes the final Transformation matrix as a 4x4 identity matrix
!--------------------------------------------------------------------------------------!
 Trans (:,:) = 0
 DO i = 1, 4
 Trans(i,i) = 1 
 END DO

 END SUBROUTINE init_Trans
! -------------------------------------------------------------------------------------------- !

 SUBROUTINE form_translate (D_MOVE)
 USE global_param, ONLY: Trans
 IMPLICIT NONE

 INTERFACE 

 SUBROUTINE mat_prod(M1, M2, M3)
 REAL, DIMENSION(:,:), INTENT(IN) :: M1, M2
 REAL, DIMENSION(:,:), INTENT(OUT) :: M3
 END SUBROUTINE

 END INTERFACE

 REAL, DIMENSION(3), INTENT(IN) :: D_MOVE
 REAL, DIMENSION(4,4) :: T, Temp 

 INTEGER :: i, j

! Initialize Translation Matrix
!-------------------------------!
! WRITE(*,*)'FORMULATING TRANSLATION MATRIX...'
 DO i = 1, 3
     DO j = 1, 3
         IF (i .eq. j) THEN
           T(i,j) = 1.0; 
         ELSE
           T(i,j) = 0.0; 
         END IF
     END DO
      T(i,4) = D_MOVE(i)
 END DO
 T(4,4) = 1.0;

 CALL mat_prod(T,Trans,Temp)
 Trans = Temp

 END SUBROUTINE form_translate 
! -------------------------------------------------------------------------------------------- !


 SUBROUTINE form_rotate(r_axis, theta)

 USE global_param, ONLY: Trans
 IMPLICIT NONE

 INTERFACE 

 SUBROUTINE mat_prod(M1, M2, M3)
 REAL, DIMENSION(:,:), INTENT(IN) :: M1, M2
 REAL, DIMENSION(:,:), INTENT(OUT) :: M3
 END SUBROUTINE

 END INTERFACE

 REAL, INTENT(IN) :: theta
 REAL, DIMENSION(4,4) :: R, Temp

 CHARACTER(LEN = 3), INTENT(IN) :: r_axis

 INTEGER :: i,j

 SELECT CASE (r_axis)

 CASE('-rx')
 !    WRITE(*,*)'FORMULATING X-ROTATION MATRIX...'
     ! Initialize x-Rotation matrix
     !----------------------------!
     DO i = 2,3
         DO j = 2, 3
             IF (i .eq. j) THEN
        R(i,j) = cos(theta)
         ELSE
            R(i,j) = ((-1)**(i-1))*sin(theta)
             END IF
         END DO 
     END DO

     DO i = 1, 4, 3
         DO j = 1, 4, 3
             IF (i .eq. j) R(i,j) = 1.0
         END DO
     END DO

 CASE('-ry')
 !    WRITE(*,*)'FORMULATING Y-ROTATION MATRIX...'
     ! Initialize y-Rotation matrix
     !----------------------------!
     DO i = 1,3,2
         R(i,i) = cos(theta)
     IF (mod(i+1,4) .eq. 0) THEN
        R(i,4-i) = -sin(theta)
     ELSE
        R(i,4-i) = sin(theta)
     END IF 
     END DO

     DO i = 2, 4, 2
         R(i,i) = 1.0
     END DO

 CASE('-rz')
 !    WRITE(*,*)'FORMULATING Z-ROTATION MATRIX...'
     ! Initialize z-Rotation matrix
     !----------------------------!
     DO i = 1,2
         DO j = 1, 2
             IF (i .eq. j) THEN
                R(i,j) = cos(theta)
         ELSE
            R(i,j) = ((-1)**i)*sin(theta)
             END IF
         END DO 
     END DO

     DO i = 3, 4
         DO j = 3, 4
             IF (i .eq. j) R(i,j) = 1.0
         END DO
     END DO

 END SELECT

     CALL mat_prod(R,Trans,Temp)
     Trans = Temp
     DO i = 1, 4
        PRINT*,Trans(i,:)   
     END DO
 END SUBROUTINE form_rotate
! -------------------------------------------------------------------------------------------- !


 SUBROUTINE transform
! Transform coordinates of each point using p_new = Tran*p
!----------------------------------------------------------!
 USE global_param
 IMPLICIT NONE

 INTERFACE 

 SUBROUTINE mat_prod(M1, M2, M3)
 REAL, DIMENSION(:,:), INTENT(IN) :: M1, M2
 REAL, DIMENSION(:,:), INTENT(OUT) :: M3
 END SUBROUTINE

 END INTERFACE

 REAL, DIMENSION(4,1) :: p, p_new
 INTEGER :: i,j

 p(4,1) = 1.0
 DO i = 1, n_nodes
     p(1,1) = x(i); p(2,1) = y(i); p(3,1) = z(i)
     CALL mat_prod(Trans, p, p_new)
     xnew(i) = p_new(1,1); ynew(i) = p_new(2,1); znew(i) = p_new(3,1)
 END DO

 END SUBROUTINE transform

我已经尝试创建一个复合旋转矩阵，以便可以同时处理沿两个轴产生的旋转。我想这就是我出错的地方，因为代码对于围绕单个轴旋转点很有效。有人能帮我解决这个问题吗

---

非常感谢

什么是

mat_prod

？您是否可以使用自己的卷替换

matmul

？查看轴角度公式如果问题仍然存在，您可以尝试。在使用4x4变换矩阵时，您可能会发现更多有用信息。我可能会建议你先处理3x3表单，如果你真的被卡住了，以后再添加平移。@Stefan，如果你要进行大量的旋转连接，四元数是有用的，但在单个连接中这应该不是问题。