gridding rules for contours
[surfit gridding rules]


Functions

bool surfit::contour (const char *cntr_name_or_position="0")
bool surfit::contour_add (REAL weight, const char *cntr_name_or_position="0")
bool surfit::contour_leq (const char *cntr_name_or_position="0", REAL mult=0.001)
bool surfit::contour_geq (const char *cntr_name_or_position="0", REAL mult=0.001)

Function Documentation

bool contour (  const char *  cntr_name_or_position = "0"  ) 
 

Tcl syntax:
contour "cntr_name_or_position"
Description:
Using this rule the resulting surface approximates contour values.
Parameters:
cntr_name_or_position contour name, or contour position number.
Math:
This command adds the following functional to the functional sequence:

\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \sum_i \sum_j \left( u_{i,j} - z_{i,j} \right)^2, \]

where (i,j) - indices of the cells cross with contour, $ z_{i,j} $ - contour mean value for the (i,j) cell.

Examples:
contour.tcl.

bool contour_add (  REAL  weight,
const char *  cntr_name_or_position = "0"
) 
 

Tcl syntax:
contour_add weight "cntr_name_or_position"
Description:
This rule modifies a previous (modifiable) rule by adding the contour rule with some weight. Use this rule if you don't know contour values exactly. Using this rule the resulting surface approximates contour taking into account a previous (modifiable) rule.
Parameters:
weight informational weight for this rule
cntr_name_or_position contour name, or contour position number.
Math:
This command modifies previous functional $ \Phi_0 $ by adding $ \Phi_1 $:

\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \Phi_0(u_{1,1},\ldots,u_{N,M}) + w\Phi_1(u_{1,1},\ldots,u_{N,M}), \]

where $ w $ - informational weight,

\[ \Phi_1(u_{1,1},\ldots,u_{N,M}) = \sum_i \sum_j \left( u_{i,j} - z_{i,j} \right)^2, \]

where (i,j) - indices of the cells cross with contour, $ z_{i,j} $ - contour mean value for the (i,j) cell.

Examples:
contour.tcl, map_hor_frac.tcl, and map_ver_frac.tcl.

bool contour_geq (  const char *  cntr_name_or_position = "0",
REAL  mult = 0.001
) 
 

Tcl syntax:
contour_geq "cntr_name_or_position" mult
Description:
This rule adds the surface condition - "the resulting surface at contour should be greater than or equal to contour values". In case of the penalty algorithm algorithm bad convergence or unexpected (wrong) result, you should carefully review your conditions and if they are correct, try to change "mult" parameter.
Parameters:
cntr_name_or_position contour name, or contour position number.
mult multiplier parameter for penalty algorithm algorithm
Math:
This command adds the condition:

\[ u_{i,j} \geq z_{i,j} \]

where (i,j) - indices of the cells cross with contour, $z_{i,j}$ - contour mean value for the (i,j) cell

Examples:
contour_ineq.tcl.

bool contour_leq (  const char *  cntr_name_or_position = "0",
REAL  mult = 0.001
) 
 

Tcl syntax:
contour_leq "cntr_name_or_position" mult
Description:
This rule adds the surface condition - "the resulting surface at contour should be lower than or equal to the contour values". In case of the penalty algorithm algorithm bad convergence or unexpected (wrong) result, you should carefully review your conditions and if they are correct, try to change "mult" parameter.
Parameters:
cntr_name_or_position contour name, or contour position number.
mult multiplier parameter for penalty algorithm algorithm
Math:
This command adds the condition:

\[ u_{i,j} \leq z_{i,j} \]

where (i,j) - indices of the cells cross with contour, $z_{i,j}$ - contour mean value for the (i,j) cell

Examples:
contour_ineq.tcl.


surfit: open source gridding and contouring software.