Main Page | Modules | Data Structures | File List | Data Fields | Globals | Related Pages

splines.h File Reference

#include <volume_io.h>

Include dependency graph for splines.h:

Include dependency graph

Go to the source code of this file.

Defines

#define LINEAR_COEF_00   1.0
#define LINEAR_COEF_01   0.0
#define LINEAR_COEF_10   -1.0
#define LINEAR_COEF_11   1.0
#define LINEAR_COEF_0(v0, v1)   (v0)
#define LINEAR_COEF_1(v0, v1)   ((v1) - (v0))
#define LINEAR_UNIVAR(v0, v1, u)   ( (v0) + (u) * ((v1) - (v0)) )
#define QUADRATIC_COEF_00   0.5
#define QUADRATIC_COEF_01   0.5
#define QUADRATIC_COEF_02   0.0
#define QUADRATIC_COEF_10   (-1.0)
#define QUADRATIC_COEF_11   1.0
#define QUADRATIC_COEF_12   0.0
#define QUADRATIC_COEF_20   0.5
#define QUADRATIC_COEF_21   (-1.0)
#define QUADRATIC_COEF_22   0.5
#define QUADRATIC_COEF_OF_V0(u)
#define QUADRATIC_COEF_OF_V1(u)
#define QUADRATIC_COEF_OF_V2(u)
#define COMPUTE_QUADRATIC_COEFFS(u, c0, c1, c2)
#define QUADRATIC_UNIVAR(v0, v1, v2, u)
#define QUADRATIC_DERIV_COEF_OF_V0(u)
#define QUADRATIC_DERIV_COEF_OF_V1(u)
#define QUADRATIC_DERIV_COEF_OF_V2(u)
#define COMPUTE_QUADRATIC_DERIV_COEFFS(u, c0, c1, c2)
#define QUADRATIC_UNIVAR_DERIV(v0, v1, v2, u)
#define QUADRATIC_DERIV2_COEF_OF_V0(u)   ( 2.0 * QUADRATIC_COEF_20 )
#define QUADRATIC_DERIV2_COEF_OF_V1(u)   ( 2.0 * QUADRATIC_COEF_21 )
#define QUADRATIC_DERIV2_COEF_OF_V2(u)   ( 2.0 * QUADRATIC_COEF_22 )
#define COMPUTE_QUADRATIC_DERIV2_COEFFS(u, c0, c1, c2)
#define QUADRATIC_UNIVAR_DERIV2(v0, v1, v2, u)
#define DOT3(a1, b1, c1, a2, b2, c2)   ( (a1) * (a2) + (b1) * (b2) + (c1) * (c2) )
#define MULT3(r1, r2, r3, v1, v2, v3, v00, v01, v02, v10, v11, v12, v20, v21, v22)
#define QUADRATIC_BIVAR(v00, v01, v02, v10, v11, v12, v20, v21, v22, u_parm, v_parm, val)
#define QUADRATIC_BIVAR_DERIV(v00, v01, v02, v10, v11, v12, v20, v21, v22, u, v, val, du, dv)
#define QUADRATIC_BIVAR_DERIV2(v00, v01, v02, v10, v11, v12, v20, v21, v22, u_parm, v_parm, val, du, dv, duu, duv, dvv)
#define QUADRATIC_TRIVAR(c, u_parm, v_parm, w_parm, val)
#define QUADRATIC_TRIVAR_DERIV(c, u_parm, v_parm, w_parm, val, du, dv, dw)
#define QUADRATIC_TRIVAR_DERIV2(c, u_parm, v_parm, w_parm, val, du, dv, dw, duu, duv, duw, dvv, dvw, dww)
#define CUBIC_COEF_00   0.0
#define CUBIC_COEF_01   1.0
#define CUBIC_COEF_02   0.0
#define CUBIC_COEF_03   0.0
#define CUBIC_COEF_10   (-0.5)
#define CUBIC_COEF_11   0.0
#define CUBIC_COEF_12   0.5
#define CUBIC_COEF_13   0.0
#define CUBIC_COEF_20   1.0
#define CUBIC_COEF_21   (-2.5)
#define CUBIC_COEF_22   2.0
#define CUBIC_COEF_23   (-0.5)
#define CUBIC_COEF_30   (-0.5)
#define CUBIC_COEF_31   1.5
#define CUBIC_COEF_32   (-1.5)
#define CUBIC_COEF_33   0.5
#define CUBIC_COEF_OF_V0(u)
#define CUBIC_COEF_OF_V1(u)
#define CUBIC_COEF_OF_V2(u)
#define CUBIC_COEF_OF_V3(u)
#define COMPUTE_CUBIC_COEFFS(u, c0, c1, c2, c3)
#define CUBIC_UNIVAR(v0, v1, v2, v3, u)
#define CUBIC_DERIV_COEF_OF_V0(u)
#define CUBIC_DERIV_COEF_OF_V1(u)
#define CUBIC_DERIV_COEF_OF_V2(u)
#define CUBIC_DERIV_COEF_OF_V3(u)
#define COMPUTE_CUBIC_DERIV_COEFFS(u, c0, c1, c2, c3)
#define CUBIC_UNIVAR_DERIV(v0, v1, v2, v3, u)
#define CUBIC_DERIV2_COEF_OF_V0(u)
#define CUBIC_DERIV2_COEF_OF_V1(u)
#define CUBIC_DERIV2_COEF_OF_V2(u)
#define CUBIC_DERIV2_COEF_OF_V3(u)
#define COMPUTE_CUBIC_DERIV2_COEFFS(u, c0, c1, c2, c3)
#define CUBIC_UNIVAR_DERIV2(v0, v1, v2, v3, u)
#define DOT4(a1, b1, c1, d1, a2, b2, c2, d2)   ( (a1) * (a2) + (b1) * (b2) + (c1) * (c2) + (d1) * (d2) )
#define MULT4(r1, r2, r3, r4, w1, w2, w3, w4, v)
#define CUBIC_BIVAR(cv, u_parm, v_parm, val)
#define CUBIC_BIVAR_DERIV(cv, u_parm, v_parm, val, du, dv)
#define CUBIC_BIVAR_DERIV2(cv, u_parm, v_parm, val, du, dv, duu, duv, dvv)
#define CUBIC_TRIVAR(c, u_parm, v_parm, w_parm, val)
#define CUBIC_TRIVAR_DERIV(c, u_parm, v_parm, w_parm, val, deriv_u, deriv_v, deriv_w)
#define CUBIC_TRIVAR_DERIV2(c, u_parm, v_parm, w_parm, val, deriv_u, deriv_v, deriv_w, deriv_uu, deriv_uv, deriv_uw, deriv_vv, deriv_vw, deriv_ww)

Define Documentation

#define COMPUTE_CUBIC_COEFFS (  u,
c0,
c1,
c2,
c3   ) 
 

Value:

{ \
              (c0) = CUBIC_COEF_OF_V0( u ); \
              (c1) = CUBIC_COEF_OF_V1( u ); \
              (c2) = CUBIC_COEF_OF_V2( u ); \
              (c3) = CUBIC_COEF_OF_V3( u ); \
          }

Definition at line 415 of file splines.h.

#define COMPUTE_CUBIC_DERIV2_COEFFS (  u,
c0,
c1,
c2,
c3   ) 
 

Value:

{ \
              (c0) = CUBIC_DERIV2_COEF_OF_V0( u ); \
              (c1) = CUBIC_DERIV2_COEF_OF_V1( u ); \
              (c2) = CUBIC_DERIV2_COEF_OF_V2( u ); \
              (c3) = CUBIC_DERIV2_COEF_OF_V3( u ); \
          }

Definition at line 473 of file splines.h.

#define COMPUTE_CUBIC_DERIV_COEFFS (  u,
c0,
c1,
c2,
c3   ) 
 

Value:

{ \
              (c0) = CUBIC_DERIV_COEF_OF_V0( u ); \
              (c1) = CUBIC_DERIV_COEF_OF_V1( u ); \
              (c2) = CUBIC_DERIV_COEF_OF_V2( u ); \
              (c3) = CUBIC_DERIV_COEF_OF_V3( u ); \
          }

Definition at line 446 of file splines.h.

#define COMPUTE_QUADRATIC_COEFFS (  u,
c0,
c1,
c2   ) 
 

Value:

{ \
              (c0) = QUADRATIC_COEF_OF_V0( u ); \
              (c1) = QUADRATIC_COEF_OF_V1( u ); \
              (c2) = QUADRATIC_COEF_OF_V2( u ); \
          }

Definition at line 62 of file splines.h.

#define COMPUTE_QUADRATIC_DERIV2_COEFFS (  u,
c0,
c1,
c2   ) 
 

Value:

{ \
              (c0) = QUADRATIC_DERIV2_COEF_OF_V0( u ); \
              (c1) = QUADRATIC_DERIV2_COEF_OF_V1( u ); \
              (c2) = QUADRATIC_DERIV2_COEF_OF_V2( u ); \
          }

Definition at line 103 of file splines.h.

#define COMPUTE_QUADRATIC_DERIV_COEFFS (  u,
c0,
c1,
c2   ) 
 

Value:

{ \
              (c0) = QUADRATIC_DERIV_COEF_OF_V0( u ); \
              (c1) = QUADRATIC_DERIV_COEF_OF_V1( u ); \
              (c2) = QUADRATIC_DERIV_COEF_OF_V2( u ); \
          }

Definition at line 84 of file splines.h.

#define CUBIC_BIVAR (  cv,
u_parm,
v_parm,
val   ) 
 

Value:

{ \
         Real  wv0, wv1, wv2, wv3; \
         Real  v0, v1, v2, v3; \
 \
         COMPUTE_CUBIC_COEFFS( v_parm, wv0, wv1, wv2, wv3 ); \
 \
         MULT4( v0, v1, v2, v3, wv0, wv1, wv2, wv3,cv); \
 \
         (val) = CUBIC_UNIVAR( v0, v1, v2, v3, u_parm ); \
     }

Definition at line 497 of file splines.h.

#define CUBIC_BIVAR_DERIV (  cv,
u_parm,
v_parm,
val,
du,
dv   ) 
 

Value:

{ \
         Real  wu0, wu1, wu2, wu3; \
         Real  wv0, wv1, wv2, wv3; \
         Real  wdv0, wdv1, wdv2, wdv3; \
         Real  v0, v1, v2, v3; \
         Real  dv0, dv1, dv2, dv3; \
 \
         COMPUTE_CUBIC_COEFFS( u_parm, wu0, wu1, wu2, wu3 ); \
         COMPUTE_CUBIC_COEFFS( v_parm, wv0, wv1, wv2, wv3 ); \
         COMPUTE_CUBIC_DERIV_COEFFS( v_parm, wdv0, wdv1, wdv2, wdv3 ); \
 \
         MULT4(  v0,  v1,  v2,  v3,  wv0,  wv1,  wv2,  wv3,cv); \
         MULT4( dv0, dv1, dv2, dv3, wdv0, wdv1, wdv2, wdv3,cv); \
 \
         (dv) = DOT4( wu0, wu1, wu2, wu3, dv0, dv1, dv2, dv3 ); \
         (du) = CUBIC_UNIVAR_DERIV( v0, v1, v2, v3, u_parm ); \
         (val) = DOT4( wu0, wu1, wu2, wu3, v0, v1, v2, v3 ); \
     }

Definition at line 509 of file splines.h.

#define CUBIC_BIVAR_DERIV2 (  cv,
u_parm,
v_parm,
val,
du,
dv,
duu,
duv,
dvv   ) 
 

Value:

{ \
         Real  wu0, wu1, wu2, wu3; \
         Real  wdu0, wdu1, wdu2, wdu3; \
         Real  wv0, wv1, wv2, wv3; \
         Real  wdv0, wdv1, wdv2, wdv3; \
         Real  wdvv0, wdvv1, wdvv2, wdvv3; \
         Real  v0, v1, v2, v3; \
         Real  dv0, dv1, dv2, dv3; \
         Real  dvv0, dvv1, dvv2, dvv3; \
 \
         COMPUTE_CUBIC_COEFFS( u_parm, wu0, wu1, wu2, wu3 ); \
         COMPUTE_CUBIC_DERIV_COEFFS( u_parm, wdu0, wdu1, wdu2, wdu3 ); \
         COMPUTE_CUBIC_COEFFS( v_parm, wv0, wv1, wv2, wv3 ); \
         COMPUTE_CUBIC_DERIV_COEFFS( v_parm, wdv0, wdv1, wdv2, wdv3 ); \
         COMPUTE_CUBIC_DERIV2_COEFFS( v_parm, wdvv0, wdvv1, wdvv2, wdvv3 ); \
 \
         MULT4( v0, v1, v2, v3, wv0, wv1, wv2, wv3,cv); \
         MULT4( dv0, dv1, dv2, dv3, wdv0, wdv1, wdv2, wdv3,cv); \
         MULT4( dvv0, dvv1, dvv2, dvv3, wdvv0, wdvv1, wdvv2, wdvv3,cv); \
 \
         (val) = DOT4( wu0, wu1, wu2, wu3,   v0,   v1,   v2,   v3 ); \
         (dv)  = DOT4( wu0, wu1, wu2, wu3,  dv0,  dv1,  dv2,  dv3 ); \
         (dvv) = DOT4( wu0, wu1, wu2, wu3, dvv0, dvv1, dvv2, dvv3 ); \
         (du)  = DOT4( wdu0, wdu1, wdu2, wdu3, v0, v1, v2, v3 ); \
         (duv) = DOT4( wdu0, wdu1, wdu2, wdu3, dv0, dv1, dv2, dv3 ); \
         (duu) = CUBIC_UNIVAR_DERIV2( v0, v1, v2, v3, u_parm ); \
     }

Definition at line 529 of file splines.h.

#define CUBIC_COEF_00   0.0
 

Definition at line 374 of file splines.h.

#define CUBIC_COEF_01   1.0
 

Definition at line 375 of file splines.h.

#define CUBIC_COEF_02   0.0
 

Definition at line 376 of file splines.h.

#define CUBIC_COEF_03   0.0
 

Definition at line 377 of file splines.h.

#define CUBIC_COEF_10   (-0.5)
 

Definition at line 379 of file splines.h.

#define CUBIC_COEF_11   0.0
 

Definition at line 380 of file splines.h.

#define CUBIC_COEF_12   0.5
 

Definition at line 381 of file splines.h.

#define CUBIC_COEF_13   0.0
 

Definition at line 382 of file splines.h.

#define CUBIC_COEF_20   1.0
 

Definition at line 384 of file splines.h.

#define CUBIC_COEF_21   (-2.5)
 

Definition at line 385 of file splines.h.

#define CUBIC_COEF_22   2.0
 

Definition at line 386 of file splines.h.

#define CUBIC_COEF_23   (-0.5)
 

Definition at line 387 of file splines.h.

#define CUBIC_COEF_30   (-0.5)
 

Definition at line 389 of file splines.h.

#define CUBIC_COEF_31   1.5
 

Definition at line 390 of file splines.h.

#define CUBIC_COEF_32   (-1.5)
 

Definition at line 391 of file splines.h.

#define CUBIC_COEF_33   0.5
 

Definition at line 392 of file splines.h.

#define CUBIC_COEF_OF_V0 (  u   ) 
 

Value:

( CUBIC_COEF_00 + (u) * ( \
            CUBIC_COEF_10 + (u) * (\
            CUBIC_COEF_20 + (u) * \
            CUBIC_COEF_30)) )

Definition at line 394 of file splines.h.

#define CUBIC_COEF_OF_V1 (  u   ) 
 

Value:

( CUBIC_COEF_01 + (u) * ( \
            CUBIC_COEF_11 + (u) * (\
            CUBIC_COEF_21 + (u) * \
            CUBIC_COEF_31)) )

Definition at line 399 of file splines.h.

#define CUBIC_COEF_OF_V2 (  u   ) 
 

Value:

( CUBIC_COEF_02 + (u) * ( \
            CUBIC_COEF_12 + (u) * (\
            CUBIC_COEF_22 + (u) * \
            CUBIC_COEF_32)) )

Definition at line 404 of file splines.h.

#define CUBIC_COEF_OF_V3 (  u   ) 
 

Value:

( CUBIC_COEF_03 + (u) * ( \
            CUBIC_COEF_13 + (u) * (\
            CUBIC_COEF_23 + (u) * \
            CUBIC_COEF_33)) )

Definition at line 409 of file splines.h.

#define CUBIC_DERIV2_COEF_OF_V0 (  u   ) 
 

Value:

( 2.0 * CUBIC_COEF_20 + (u) * \
             6.0 * CUBIC_COEF_30 )

Definition at line 460 of file splines.h.

#define CUBIC_DERIV2_COEF_OF_V1 (  u   ) 
 

Value:

( 2.0 * CUBIC_COEF_21 + (u) * \
             6.0 * CUBIC_COEF_31 )

Definition at line 463 of file splines.h.

#define CUBIC_DERIV2_COEF_OF_V2 (  u   ) 
 

Value:

( 2.0 * CUBIC_COEF_22 + (u) * \
             6.0 * CUBIC_COEF_32 )

Definition at line 466 of file splines.h.

#define CUBIC_DERIV2_COEF_OF_V3 (  u   ) 
 

Value:

( 2.0 * CUBIC_COEF_23 + (u) * \
             6.0 * CUBIC_COEF_33 )

Definition at line 469 of file splines.h.

#define CUBIC_DERIV_COEF_OF_V0 (  u   ) 
 

Value:

(        CUBIC_COEF_10 + (u) * \
           (2.0 * CUBIC_COEF_20 + (u) * \
            3.0 * CUBIC_COEF_30 ) )

Definition at line 429 of file splines.h.

#define CUBIC_DERIV_COEF_OF_V1 (  u   ) 
 

Value:

(        CUBIC_COEF_11 + (u) * \
           (2.0 * CUBIC_COEF_21 + (u) * \
            3.0 * CUBIC_COEF_31 ) )

Definition at line 433 of file splines.h.

#define CUBIC_DERIV_COEF_OF_V2 (  u   ) 
 

Value:

(        CUBIC_COEF_12 + (u) * \
           (2.0 * CUBIC_COEF_22 + (u) * \
            3.0 * CUBIC_COEF_32 ) )

Definition at line 437 of file splines.h.

#define CUBIC_DERIV_COEF_OF_V3 (  u   ) 
 

Value:

(        CUBIC_COEF_13 + (u) * \
           (2.0 * CUBIC_COEF_23 + (u) * \
            3.0 * CUBIC_COEF_33 ) )

Definition at line 441 of file splines.h.

#define CUBIC_TRIVAR (  c,
u_parm,
v_parm,
w_parm,
val   ) 
 

Value:

{ \
         Real  wv0, wv1, wv2, wv3; \
         Real  ww0, ww1, ww2, ww3; \
         Real  v00, v01, v02, v03, v10, v11, v12, v13; \
         Real  v20, v21, v22, v23, v30, v31, v32, v33; \
         Real  v0, v1, v2, v3; \
 \
         COMPUTE_CUBIC_COEFFS( v_parm, wv0, wv1, wv2, wv3 ); \
         COMPUTE_CUBIC_COEFFS( w_parm, ww0, ww1, ww2, ww3 ); \
 \
         MULT4( v00, v01, v02, v03, ww0, ww1, ww2, ww3,GLUE(c,0));\
         MULT4( v10, v11, v12, v13, ww0, ww1, ww2, ww3,GLUE(c,1));\
         MULT4( v20, v21, v22, v23, ww0, ww1, ww2, ww3,GLUE(c,2));\
         MULT4( v30, v31, v32, v33, ww0, ww1, ww2, ww3,GLUE(c,3));\
 \
         MULT4( v0, v1, v2, v3, wv0, wv1, wv2, wv3,v); \
 \
         (val) = CUBIC_UNIVAR( v0, v1, v2, v3, u_parm ); \
    }

Definition at line 558 of file splines.h.

#define CUBIC_TRIVAR_DERIV (  c,
u_parm,
v_parm,
w_parm,
val,
deriv_u,
deriv_v,
deriv_w   ) 
 

Definition at line 579 of file splines.h.

#define CUBIC_TRIVAR_DERIV2 (  c,
u_parm,
v_parm,
w_parm,
val,
deriv_u,
deriv_v,
deriv_w,
deriv_uu,
deriv_uv,
deriv_uw,
deriv_vv,
deriv_vw,
deriv_ww   ) 
 

Definition at line 620 of file splines.h.

#define CUBIC_UNIVAR (  v0,
v1,
v2,
v3,
u   ) 
 

Value:

( (v0) * CUBIC_COEF_OF_V0(u) + \
       (v1) * CUBIC_COEF_OF_V1(u) + \
       (v2) * CUBIC_COEF_OF_V2(u) + \
       (v3) * CUBIC_COEF_OF_V3(u) )

Definition at line 423 of file splines.h.

#define CUBIC_UNIVAR_DERIV (  v0,
v1,
v2,
v3,
u   ) 
 

Value:

( (v0) * CUBIC_DERIV_COEF_OF_V0(u) + \
       (v1) * CUBIC_DERIV_COEF_OF_V1(u) + \
       (v2) * CUBIC_DERIV_COEF_OF_V2(u) + \
       (v3) * CUBIC_DERIV_COEF_OF_V3(u) )

Definition at line 454 of file splines.h.

#define CUBIC_UNIVAR_DERIV2 (  v0,
v1,
v2,
v3,
u   ) 
 

Value:

Definition at line 481 of file splines.h.

#define DOT3 (  a1,
b1,
c1,
a2,
b2,
c2   )     ( (a1) * (a2) + (b1) * (b2) + (c1) * (c2) )
 

Definition at line 115 of file splines.h.

#define DOT4 (  a1,
b1,
c1,
d1,
a2,
b2,
c2,
d2   )     ( (a1) * (a2) + (b1) * (b2) + (c1) * (c2) + (d1) * (d2) )
 

Definition at line 487 of file splines.h.

#define LINEAR_COEF_0 (  v0,
v1   )     (v0)
 

Definition at line 29 of file splines.h.

#define LINEAR_COEF_00   1.0
 

Definition at line 24 of file splines.h.

#define LINEAR_COEF_01   0.0
 

Definition at line 25 of file splines.h.

#define LINEAR_COEF_1 (  v0,
v1   )     ((v1) - (v0))
 

Definition at line 31 of file splines.h.

#define LINEAR_COEF_10   -1.0
 

Definition at line 26 of file splines.h.

#define LINEAR_COEF_11   1.0
 

Definition at line 27 of file splines.h.

#define LINEAR_UNIVAR (  v0,
v1,
u   )     ( (v0) + (u) * ((v1) - (v0)) )
 

Definition at line 34 of file splines.h.

#define MULT3 (  r1,
r2,
r3,
v1,
v2,
v3,
v00,
v01,
v02,
v10,
v11,
v12,
v20,
v21,
v22   ) 
 

Value:

{ (r1) = DOT3( v1, v2, v3, v00, v01, v02 ); \
           (r2) = DOT3( v1, v2, v3, v10, v11, v12 ); \
           (r3) = DOT3( v1, v2, v3, v20, v21, v22 ); \
         }

Definition at line 118 of file splines.h.

#define MULT4 (  r1,
r2,
r3,
r4,
w1,
w2,
w3,
w4,
v   ) 
 

Value:

{ (r1) = DOT4(w1,w2,w3,w4,GLUE(v,00),GLUE(v,01),GLUE(v,02),GLUE(v,03));\
         (r2) = DOT4(w1,w2,w3,w4,GLUE(v,10),GLUE(v,11),GLUE(v,12),GLUE(v,13));\
         (r3) = DOT4(w1,w2,w3,w4,GLUE(v,20),GLUE(v,21),GLUE(v,22),GLUE(v,23));\
         (r4) = DOT4(w1,w2,w3,w4,GLUE(v,30),GLUE(v,31),GLUE(v,32),GLUE(v,33));\
       }

Definition at line 490 of file splines.h.

#define QUADRATIC_BIVAR (  v00,
v01,
v02,
v10,
v11,
v12,
v20,
v21,
v22,
u_parm,
v_parm,
val   ) 
 

Value:

{ \
         Real  wv0, wv1, wv2; \
         Real  v0, v1, v2; \
 \
         COMPUTE_QUADRATIC_COEFFS( v_parm, wv0, wv1, wv2 ); \
 \
         MULT3( v0, v1, v2, wv0, wv1, wv2, \
                 v00, v01, v02, v10, v11, v12, v20, v21, v22 ); \
 \
         (val) = QUADRATIC_UNIVAR( v0, v1, v2, u_parm ); \
     }

Definition at line 124 of file splines.h.

#define QUADRATIC_BIVAR_DERIV (  v00,
v01,
v02,
v10,
v11,
v12,
v20,
v21,
v22,
u,
v,
val,
du,
dv   ) 
 

Value:

{ \
         Real  wu0, wu1, wu2; \
         Real  wv0, wv1, wv2; \
         Real  wdv0, wdv1, wdv2; \
         Real  v0, v1, v2; \
         Real  dv0, dv1, dv2; \
 \
         COMPUTE_QUADRATIC_COEFFS( u_parm, wu0, wu1, wu2 ); \
         COMPUTE_QUADRATIC_COEFFS( v_parm, wv0, wv1, wv2 ); \
         COMPUTE_QUADRATIC_DERIV_COEFFS( v_parm, wdv0, wdv1, wdv2 ); \
 \
         MULT3( v0, v1, v2, wv0, wv1, wv2, \
                 v00, v01, v02, v10, v11, v12, v20, v21, v22 ); \
\
         MULT3( dv0, dv1, dv2, wdv0, wdv1, wdv2, \
                 v00, v01, v02, v10, v11, v12, v20, v21, v22 ); \
 \
         (dv) = DOT3( wu0, wu1, wu2, dv0, dv1, dv2 ); \
         (du) = QUADRATIC_UNIVAR_DERIV( v0, v1, v2, u_parm ); \
         (val) = DOT3( wu0, wu1, wu2, v0, v1, v2 ); \
     }

Definition at line 137 of file splines.h.

#define QUADRATIC_BIVAR_DERIV2 (  v00,
v01,
v02,
v10,
v11,
v12,
v20,
v21,
v22,
u_parm,
v_parm,
val,
du,
dv,
duu,
duv,
dvv   ) 
 

Value:

{ \
         Real  wu0, wu1, wu2; \
         Real  wdu0, wdu1, wdu2; \
         Real  wv0, wv1, wv2; \
         Real  wdv0, wdv1, wdv2; \
         Real  wdvv0, wdvv1, wdvv2; \
         Real  v0, v1, v2; \
         Real  dv0, dv1, dv2; \
         Real  dvv0, dvv1, dvv2; \
 \
         COMPUTE_QUADRATIC_COEFFS( u_parm, wu0, wu1, wu2 ); \
         COMPUTE_QUADRATIC_DERIV_COEFFS( u_parm, wdu0, wdu1, wdu2 ); \
         COMPUTE_QUADRATIC_COEFFS( v_parm, wv0, wv1, wv2 ); \
         COMPUTE_QUADRATIC_DERIV_COEFFS( v_parm, wdv0, wdv1, wdv2 ); \
         COMPUTE_QUADRATIC_DERIV2_COEFFS( v_parm, wdvv0, wdvv1, wdvv2 ); \
 \
         MULT3( v0, v1, v2, wv0, wv1, wv2, \
                 v00, v01, v02, v10, v11, v12, v20, v21, v22 ); \
         MULT3( dv0, dv1, dv2, wdv0, wdv1, wdv2, \
                 v00, v01, v02, v10, v11, v12, v20, v21, v22 ); \
         MULT3( dvv0, dvv1, dvv2, wdvv0, wdvv1, wdvv2, \
                 v00, v01, v02, v10, v11, v12, v20, v21, v22 ); \
 \
         (val) = DOT3( wu0, wu1, wu2,   v0,   v1,   v2 ); \
         (dv)  = DOT3( wu0, wu1, wu2,  dv0,  dv1,  dv2 ); \
         (dvv) = DOT3( wu0, wu1, wu2, dvv0, dvv1, dvv2 ); \
         (du)  = DOT3( wdu0, wdu1, wdu2, v0, v1, v2 ); \
         (duv) = DOT3( wdu0, wdu1, wdu2, dv0, dv1, dv2 ); \
         (duu) = QUADRATIC_UNIVAR_DERIV2( v0, v1, v2, u_parm ); \
     }

Definition at line 160 of file splines.h.

#define QUADRATIC_COEF_00   0.5
 

Definition at line 39 of file splines.h.

#define QUADRATIC_COEF_01   0.5
 

Definition at line 40 of file splines.h.

#define QUADRATIC_COEF_02   0.0
 

Definition at line 41 of file splines.h.

#define QUADRATIC_COEF_10   (-1.0)
 

Definition at line 42 of file splines.h.

#define QUADRATIC_COEF_11   1.0
 

Definition at line 43 of file splines.h.

#define QUADRATIC_COEF_12   0.0
 

Definition at line 44 of file splines.h.

#define QUADRATIC_COEF_20   0.5
 

Definition at line 45 of file splines.h.

#define QUADRATIC_COEF_21   (-1.0)
 

Definition at line 46 of file splines.h.

#define QUADRATIC_COEF_22   0.5
 

Definition at line 47 of file splines.h.

#define QUADRATIC_COEF_OF_V0 (  u   ) 
 

Value:

Definition at line 49 of file splines.h.

#define QUADRATIC_COEF_OF_V1 (  u   ) 
 

Value:

Definition at line 53 of file splines.h.

#define QUADRATIC_COEF_OF_V2 (  u   ) 
 

Value:

Definition at line 57 of file splines.h.

#define QUADRATIC_DERIV2_COEF_OF_V0 (  u   )     ( 2.0 * QUADRATIC_COEF_20 )
 

Definition at line 96 of file splines.h.

#define QUADRATIC_DERIV2_COEF_OF_V1 (  u   )     ( 2.0 * QUADRATIC_COEF_21 )
 

Definition at line 98 of file splines.h.

#define QUADRATIC_DERIV2_COEF_OF_V2 (  u   )     ( 2.0 * QUADRATIC_COEF_22 )
 

Definition at line 100 of file splines.h.

#define QUADRATIC_DERIV_COEF_OF_V0 (  u   ) 
 

Value:

Definition at line 74 of file splines.h.

#define QUADRATIC_DERIV_COEF_OF_V1 (  u   ) 
 

Value:

Definition at line 77 of file splines.h.

#define QUADRATIC_DERIV_COEF_OF_V2 (  u   ) 
 

Value:

Definition at line 80 of file splines.h.

#define QUADRATIC_TRIVAR (  c,
u_parm,
v_parm,
w_parm,
val   ) 
 

Value:

{ \
         Real  wv0, wv1, wv2; \
         Real  ww0, ww1, ww2; \
         Real  v00, v01, v02, v10, v11, v12, v20, v21, v22; \
         Real  v0, v1, v2; \
 \
         COMPUTE_QUADRATIC_COEFFS( v_parm, wv0, wv1, wv2 ); \
         COMPUTE_QUADRATIC_COEFFS( w_parm, ww0, ww1, ww2 ); \
 \
         MULT3( v00, v01, v02, ww0, ww1, ww2, \
                 GLUE(c,000), GLUE(c,001), GLUE(c,002), \
                 GLUE(c,010), GLUE(c,011), GLUE(c,012), \
                 GLUE(c,020), GLUE(c,021), GLUE(c,022) ); \
         MULT3( v10, v11, v12, ww0, ww1, ww2, \
                 GLUE(c,100), GLUE(c,101), GLUE(c,102), \
                 GLUE(c,110), GLUE(c,111), GLUE(c,112), \
                 GLUE(c,120), GLUE(c,121), GLUE(c,122) ); \
         MULT3( v20, v21, v22, ww0, ww1, ww2, \
                 GLUE(c,200), GLUE(c,201), GLUE(c,202), \
                 GLUE(c,210), GLUE(c,211), GLUE(c,212), \
                 GLUE(c,220), GLUE(c,221), GLUE(c,222) ); \
 \
         MULT3( v0, v1, v2, wv0, wv1, wv2, \
                 v00, v01, v02, v10, v11, v12, v20, v21, v22 ); \
 \
         (val) = QUADRATIC_UNIVAR( v0, v1, v2, u_parm ); \
    }

Definition at line 192 of file splines.h.

#define QUADRATIC_TRIVAR_DERIV (  c,
u_parm,
v_parm,
w_parm,
val,
du,
dv,
dw   ) 
 

Definition at line 221 of file splines.h.

#define QUADRATIC_TRIVAR_DERIV2 (  c,
u_parm,
v_parm,
w_parm,
val,
du,
dv,
dw,
duu,
duv,
duw,
dvv,
dvw,
dww   ) 
 

Definition at line 279 of file splines.h.

#define QUADRATIC_UNIVAR (  v0,
v1,
v2,
u   ) 
 

Value:

( (v0) * QUADRATIC_COEF_OF_V0(u) + \
       (v1) * QUADRATIC_COEF_OF_V1(u) + \
       (v2) * QUADRATIC_COEF_OF_V2(u) )

Definition at line 69 of file splines.h.

#define QUADRATIC_UNIVAR_DERIV (  v0,
v1,
v2,
u   ) 
 

Value:

Definition at line 91 of file splines.h.

#define QUADRATIC_UNIVAR_DERIV2 (  v0,
v1,
v2,
u   ) 
 

Value:

Definition at line 110 of file splines.h.

Generated on Wed Jul 28 09:11:20 2004 for BICPL by doxygen 1.3.7