euler: use enum and static values for EULER ORDER, remove some macros

this must be more robust and flexible api

CREDITS

@@ -65,3 +65,19 @@ https://forums.khronos.org/showthread.php/10651-Animation-TCB-Spline-Interpolati
 12. vec2 cross product
 http://allenchou.net/2013/07/cross-product-of-2d-vectors/
 
+13. Ken Shoemake's algorithm Implementation and Euler
+Ken Shoemake's algorithm impl. is taken from this repo by permission:
+  https://github.com/erich666/GraphicsGems/blob/master/gemsiv/euler_angle
+
+* -------------------------- GraphicsGems EULA ----------------------------- *
+|   http://www.realtimerendering.com/resources/GraphicsGems/                 |
+|                                                                            |
+| EULA: The Graphics Gems code is copyright-protected. In other words, you   |
+| cannot claim the text of the code as your own and resell it. Using the     |
+| code is permitted in any program, product, or library, non-commercial or   |
+| commercial. Giving credit is not required, though is a nice gesture.       |
+| The code comes as-is, and if there are any flaws or problems with any Gems |
+| code, nobody involved with Gems - authors, editors, publishers, or         |
+| webmasters - are to be held responsible. Basically, don't be a jerk, and   |
+| remember that anything free comes with no guarantee.                       |
+* -------------------------------- END --------------------------------------*/

include/cglm/euler.h

@@ -18,24 +18,160 @@
    enum glm_euler_seq
 
  Functions:
-   CGLM_INLINE glm_euler_seq glm_euler_order(int newOrder[3]);
-   CGLM_INLINE void glm_euler_angles(mat4 m, vec3 dest);
-   CGLM_INLINE void glm_euler(vec3 angles, mat4 dest);
-   CGLM_INLINE void glm_euler_xyz(vec3 angles, mat4 dest);
-   CGLM_INLINE void glm_euler_zyx(vec3 angles, mat4 dest);
-   CGLM_INLINE void glm_euler_zxy(vec3 angles, mat4 dest);
-   CGLM_INLINE void glm_euler_xzy(vec3 angles, mat4 dest);
-   CGLM_INLINE void glm_euler_yzx(vec3 angles, mat4 dest);
-   CGLM_INLINE void glm_euler_yxz(vec3 angles, mat4 dest);
-   CGLM_INLINE void glm_euler_by_order(vec3         angles,
-                                       glm_euler_seq ord,
-                                       mat4         dest);
+   CGLM_INLINE glm_eul_mat4(vec3 ea, int order, mat4 dest)
  */
 
 #ifndef cglm_euler_h
 #define cglm_euler_h
 
 #include "common.h"
+#include "util.h"
+
+/* ---------- Notice for Ken Shoemake's algorithm Implementation -------------*
+ | Ken Shoemake's algorithm impl. is taken from this repo by permission:      |
+ |   https://github.com/erich666/GraphicsGems/blob/master/gemsiv/euler_angle  |
+ |                                                                            |
+ | cglm doesn't claim the ownership of GraphicsGems source codes              |
+ | and the algorithm itself. But cglm may change variable names or some piece |
+ | of codes in order to apply optimizations or to make it usable in cglm.     |
+ |                                                                            |
+ | Related issue: https://github.com/recp/cglm/issues/30                      |
+ |                                                                            |
+ * -------------------------- GraphicsGems EULA ----------------------------- *
+ | Related EULA for GraphicsGems can be found at below, plus in CREDITS:      |
+ |   http://www.realtimerendering.com/resources/GraphicsGems/                 |
+ |                                                                            |
+ | EULA: The Graphics Gems code is copyright-protected. In other words, you   |
+ | cannot claim the text of the code as your own and resell it. Using the     |
+ | code is permitted in any program, product, or library, non-commercial or   |
+ | commercial. Giving credit is not required, though is a nice gesture.       |
+ | The code comes as-is, and if there are any flaws or problems with any Gems |
+ | code, nobody involved with Gems - authors, editors, publishers, or         |
+ | webmasters - are to be held responsible. Basically, don't be a jerk, and   |
+ | remember that anything free comes with no guarantee.                       |
+ * -------------------------------- END --------------------------------------*/
+
+/* Order type constants, constructors, extractors
+ * There are 24 possible conventions, designated by:
+ *	  o EulAxI = axis used initially
+ *	  o EulPar = parity of axis permutation
+ *	  o EulRep = repetition of initial axis as last
+ *	  o EulFrm = frame from which axes are taken
+ * Axes I,J,K will be a permutation of X,Y,Z.
+ * Axis H will be either I or K, depending on EulRep.
+ * Frame S takes axes from initial static frame.
+ * If ord = (AxI=X, Par=Even, Rep=No, Frm=S), then
+ * {a,b,c,ord} means Rz(c)Ry(b)Rx(a), where Rz(c)v
+ * rotates v around Z by c radians.			    
+*/
+
+#define EulRep(ord)  (((unsigned)(ord)>>1)&1)
+#define EulFrm(ord)  ((unsigned)(ord)&1)
+#define EulPar(ord)  (((unsigned)(ord)>>2)&1)
+
+/*! this code is merely a quick (and legal!) way to set arrays,
+    EulSafe being 0,1,2,0 */
+#define EulSafe	     "\000\001\002\000"
+#define EulNext	     "\001\002\000\001"
+#define EulAxI(ord)  ((int)(EulSafe[(((unsigned)(ord)>>3)&3)]))
+#define EulAxJ(ord)  ((int)(EulNext[EulAxI(ord)+(EulPar(ord)==EulParOdd)]))
+#define EulAxK(ord)  ((int)(EulNext[EulAxI(ord)+(EulPar(ord)!=EulParOdd)]))
+#define EulAxH(ord)  ((EulRep(ord)==EulRepNo)?EulAxK(ord):EulAxI(ord))
+
+/*! EulGetOrd unpacks all useful information about order simultaneously. */
+#define EulGetOrd(ord,i,j,k,h,n,s,f)                                          \
+  {unsigned o=(unsigned)ord;f=o&1;o>>=1;s=o&1;o>>=1;\
+    n=o&1;o>>=1;i=EulSafe[o&3];j=EulNext[i+n];k=EulNext[i+1-n];h=s?k:i;}
+
+typedef enum glm_eul_order {
+  /*! Static axes */
+  GLM_EUL_XYZs  = 0,
+  GLM_EUL_XYXs  = 2,
+  GLM_EUL_XZYs  = 4,
+  GLM_EUL_XZXs  = 6,
+  GLM_EUL_YZXs  = 8,
+  GLM_EUL_YZYs  = 10,
+  GLM_EUL_YXZs  = 12,
+  GLM_EUL_YXYs  = 14,
+  GLM_EUL_ZXYs  = 16,
+  GLM_EUL_ZXZs  = 18,
+  GLM_EUL_ZYXs  = 20,
+  GLM_EUL_ZYZs  = 22,
+  
+  /*! Rotating axes */
+  GLM_EUL_ZYXr  = 1,
+  GLM_EUL_XYXr  = 3,
+  GLM_EUL_YZXr  = 5,
+  GLM_EUL_XZXr  = 7,
+  GLM_EUL_XZYr  = 9,
+  GLM_EUL_YZYr  = 11,
+  GLM_EUL_ZXYr  = 13,
+  GLM_EUL_YXYr  = 15,
+  GLM_EUL_YXZr  = 17,
+  GLM_EUL_ZXZr  = 19,
+  GLM_EUL_XYZr  = 21,
+  GLM_EUL_ZYZr  = 23
+} glm_eul_order;
+
+/*!
+ * @brief build matrix from euler angles
+ *
+ * @param[in]  ea     [Xangle, Yangle, Zangle]
+ * @param[out] dest   rotation matrix
+ */
+CGLM_INLINE
+void
+glm_eul_mat4(vec3 ea, glm_eul_order order, mat4 dest) {
+  float ti, tj, th, ci, cj, ch, si, sj, sh, cc, cs, sc, ss;
+  int   i, j, k, h, parOdd, repYes, frmR;
+
+  EulGetOrd(order, i, j, k, h, parOdd, repYes, frmR);
+  
+  if (frmR == 1)
+    glm_swapf(&ea[0], &ea[2]);
+  
+  if (parOdd == 1)
+    glm_vec3_negate(ea);
+  
+  ti = ea[0]; tj = ea[1]; th = ea[2];
+  
+  ci = cosf(ti);  cj = cosf(tj);
+  ch = cosf(th);  si = sinf(ti);
+  sj = sinf(tj);  sh = sinf(th);
+  
+  cc = ci * ch;  cs = ci * sh;
+  sc = si * ch;  ss = si * sh;
+  
+  if (repYes == 1) {
+    dest[i][i] =  cj;
+    dest[i][j] =  sj * si;
+    dest[i][k] =  sj * ci;
+    dest[j][i] =  sj * sh;
+    dest[j][j] = -cj * ss + cc;
+    dest[j][k] = -cj * cs - sc;
+    dest[k][i] = -sj * ch;
+    dest[k][j] =  cj * sc + cs;
+    dest[k][k] =  cj * cc - ss;
+  } else {
+    dest[i][i] =  cj * ch;
+    dest[i][j] =  sj * sc - cs;
+    dest[i][k] =  sj * cc + ss;
+    dest[j][i] =  cj * sh;
+    dest[j][j] =  sj * ss + cc;
+    dest[j][k] =  sj * cs - sc;
+    dest[k][i] = -sj;
+    dest[k][j] =  cj * si;
+    dest[k][k] =  cj * ci;
+  }
+  
+  dest[3][0] = 0.f;
+  dest[3][1] = 0.f;
+  dest[3][2] = 0.f;
+  dest[0][3] = 0.f;
+  dest[1][3] = 0.f;
+  dest[2][3] = 0.f;
+  dest[3][3] = 1.f;
+}
 
 /*!
  * if you have axis order like vec3 orderVec = [0, 1, 2] or [0, 2, 1]...