Functions
for areas
surfit gridding rules

Functions

boolvec * area (const char *value="undef", const char *area_name="*", int inside=1)
 interpolate area value More...
 
boolvec * area_add (REAL value, REAL weight, const char *area_name="*", int inside=1)
 
boolvec * area_leq (REAL value, const char *area_name="*", REAL penalty_factor=0, int inside=1)
 
boolvec * area_geq (REAL value, const char *area_name="*", REAL penalty_factor=0, int inside=1)
 
boolvec * area_surf (const char *surf_name="*", const char *area_name="*", int inside=1)
 
boolvec * area_surf_add (const char *surf_name="*", REAL weight=1, const char *area_name="*", int inside=1)
 
boolvec * area_surf_leq (const char *surf_name="*", const char *area_name="*", REAL penalty_factor=0, int inside=1)
 
boolvec * area_surf_geq (const char *surf_name="*", const char *area_name="*", REAL penalty_factor=0, int inside=1)
 
boolvec * area_mean (REAL mean, const char *area_name="*", REAL penalty_factor=-2, int inside=1)
 
boolvec * area_wmean (REAL mean, const char *area_name="*", const char *surf_name="*", REAL penalty_factor=-2, int inside=1)
 
boolvec * area_completer (const char *area_name="*", REAL D1=1, REAL D2=2, REAL alpha=0, REAL w=1, int inside=1)
 
boolvec * area_completer_add (REAL weight=1, const char *area_name="*", REAL D1=1, REAL D2=2, REAL alpha=0, REAL w=1, int inside=1)
 
boolvec * area_hist (const char *area_name="*", const char *histogram_name="*", REAL penalty_factor=-1, int inside=1)
 

Detailed Description

Function Documentation

boolvec* surfit::area ( const char *  value = "undef",
const char *  area_name = "*",
int  inside = 1 
)

interpolate area value

Tcl syntax:
area value area_name inside
Description:
Using this rule the resulting surface approximates area with constant "value" in least squares meaning. Value can be set to any real number or "undef".
Parameters
valuereal number for surface approximation in area
area_namename of area dataset
insideif inside is equal to 1, then surface will be approximated inside area, else outside
Math:
This command adds the following functional to the functional sequence:

\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \sum_{p=1}^P \left( u_{i,j} - z \right)^2, \]

where (i,j) - indices of the cells in area, z - constant value
boolvec* surfit::area_add ( REAL  value,
REAL  weight,
const char *  area_name = "*",
int  inside = 1 
)
Tcl syntax:
area_add value weight area_name inside
Description:
This function modifies previous (modifiable) rule by adding the area rule with some weight. Use this rule if you don't know "value" exactly. Using this rule the resulting surface approximates area with "value" taking into account a previous (modifiable) rule.
Parameters
valuereal number for surface approximation in area
weightinformational weight for this rule
area_namename of area dataset
insideif inside is equal to 1, then surface will be approximated inside area, else outside
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,

\[ \Phi_1(u_{1,1},\ldots,u_{N,M}) = \sum_{p=1}^P \left( u_{i,j} - z \right)^2, \]

where (i,j) - indices of the cells in area, z - constant value
boolvec* surfit::area_completer ( const char *  area_name = "*",
REAL  D1 = 1,
REAL  D2 = 2,
REAL  alpha = 0,
REAL  w = 1,
int  inside = 1 
)
Tcl syntax:
area_completer area_name D1 D2 alpha w inside
Description
This rule implements completer rule inside or outside area
Parameters
area_namearea name
D1weight coefficient for rule that the resulting surface should tend to constant surface
D2weight coefficient for rule that the resulting surface should tend to plane surface
alphaanisotropy angle (degrees)
wanisotropy factor
insideif inside is equal to 1, then area_completer will work inside area, else outside
boolvec* surfit::area_completer_add ( REAL  weight = 1,
const char *  area_name = "*",
REAL  D1 = 1,
REAL  D2 = 2,
REAL  alpha = 0,
REAL  w = 1,
int  inside = 1 
)
Tcl syntax:
area_completer_add weight area_name D1 D2 alpha w inside
Description
This rule adds rule area_completer with informational "weight" to the previous rule.
Parameters
weightweight coefficient. This gridding rule will be added with this weight coefficient to previous gridding rule.
area_namearea name
D1weight coefficient for rule that the resulting surface should tend to constant surface
D2weight coefficient for rule that the resulting surface should tend to plane surface
alphaanisotropy angle (degrees)
wanisotropy factor
insideif inside is equal to 1, then area_completer will work inside area, else outside
boolvec* surfit::area_geq ( REAL  value,
const char *  area_name = "*",
REAL  penalty_factor = 0,
int  inside = 1 
)
Tcl syntax:
area_geq value area_name penalty_factor inside
Description:
This rule adds the surface condition - "the resulting surface in area should be greater than or equal to value".
Parameters
valueresulting surface values should be greater than or equal to this real number
area_namename of area dataset
penalty_factorparameter for penalty algorithm
insideif inside is equal to 1, then surface values should be greater than or equal to value inside area, else outside
Math:
This command adds the condition:

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

where (i,j) - indices of the cells in area, z - constant value
boolvec* surfit::area_hist ( const char *  area_name = "*",
const char *  histogram_name = "*",
REAL  penalty_factor = -1,
int  inside = 1 
)
Tcl syntax:
area_hist area_name histogram_name penalty_factor inside
Description
This rule adds the following condition: histogram of the resulting surface should be equal to the desired histogram inside (or outside) the area.
Parameters
area_namename of the area for histogram fitting
histogram_namename of the desired histogram
penalty_factorparameter for penalty algorithm
insideif inside is equal to 1, then area_hist will work inside area, else outside
boolvec* surfit::area_leq ( REAL  value,
const char *  area_name = "*",
REAL  penalty_factor = 0,
int  inside = 1 
)
Tcl syntax:
area_leq value area_name penalty_factor inside
Description:
This rule adds the surface condition - "the resulting surface in area should be lower than or equal to value".
Parameters
valueresulting surface values should be lower than or equal to this real number
area_namename of area dataset
penalty_factorparameter for penalty algorithm
insideif inside is equal to 1, then surface values should be lower than or equal to value inside area, else outside
Math:
This command adds the condition:

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

where (i,j) - indices of the cells in area, z - constant value
boolvec* surfit::area_mean ( REAL  mean,
const char *  area_name = "*",
REAL  penalty_factor = -2,
int  inside = 1 
)
Tcl syntax:
area_mean mean_value area_name penalty_factor inside
Description:
This rule adds the surface condition - "the resulting surface mean value in area should be equal to real number".
Math:
This command adds the condition:

\[ \frac {\sum\limits_{i,j} u_{i,j}} {Q} = m \]

where (i,j) - indices of the cells in area, Q - number of cells in area, m - desired mean value
boolvec* surfit::area_surf ( const char *  surf_name = "*",
const char *  area_name = "*",
int  inside = 1 
)
Tcl syntax:
area_surf surf_name mult inside
Description:
Using this rule the resulting surface approximates area in least squares meaning with values taken from the other surface.
Parameters
surf_namename of surface. Resulting surface will approximate this surface values inside (or outside) area.
area_namename of area dataset
insideif inside is equal to 1, then surface will be approximated inside area, else outside
Math:
This command adds the following functional to the functional sequence:

\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \sum_{p=1}^P \left( u_{i,j} - z(x_i, y_j) \right)^2, \]

where (i,j) - indices of the cells in area, $z(x_i, y_j)$ - surface value for the (i,j) cell.
boolvec* surfit::area_surf_add ( const char *  surf_name = "*",
REAL  weight = 1,
const char *  area_name = "*",
int  inside = 1 
)
Tcl syntax:
area_surf_add surf_name weight area_name inside
Description:
This function modifies previous (modifiable) rule by adding the area_surf rule with some weight. Using this rule the resulting surface approximates area with other surface "values" taking into account a previous (modifiable) rule.
Parameters
surf_namename of surface. Resulting surface will approximate this surface values inside (or outside) area.
weightinformational weight for this rule
area_namename of area dataset
insideif inside is equal to 1, then surface will be approximated inside area, else outside
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,

\[ \Phi_1(u_{1,1},\ldots,u_{N,M}) = \sum_{p=1}^P \left( u_{i,j} - z(x_i, y_j) \right)^2, \]

where (i,j) - indices of the cells in area, $z(x_i, y_j)$ - surface value for the (i,j) cell.
boolvec* surfit::area_surf_geq ( const char *  surf_name = "*",
const char *  area_name = "*",
REAL  penalty_factor = 0,
int  inside = 1 
)
Tcl syntax:
area_surf_geq surf_name area_name penalty_factor inside
Description:
This rule adds the surface condition - "the resulting surface in area should be greater than or equal to other surface".
Math:
This command adds the condition:

\[ u_{i,j} \geq f(x_{u_i},y_{u_j}) \]

where (i,j) - indices of the cells in area, $f(x_{u_i},y_{u_j})$ - surface value in the center of the cell.
boolvec* surfit::area_surf_leq ( const char *  surf_name = "*",
const char *  area_name = "*",
REAL  penalty_factor = 0,
int  inside = 1 
)
Tcl syntax:
area_surf_leq surf_name area_name penalty_factor inside
Description:
This rule adds the surface condition - "the resulting surface in area should be lower than or equal to other surface".
Math:
This command adds the condition:

\[ u_{i,j} \leq f(x_{u_i},y_{u_j}) \]

where (i,j) - indices of the cells in area, $f(x_{u_i},y_{u_j})$ - surface value in the center of the cell.
boolvec* surfit::area_wmean ( REAL  mean,
const char *  area_name = "*",
const char *  surf_name = "*",
REAL  penalty_factor = -2,
int  inside = 1 
)
Tcl syntax:
area_wmean weighted_mean_value area_name surf_name penalty_factor inside
Description:
This rule adds the surface condition - "the resulting surface weighted mean value in area should be equal to real number".
Math:
This command adds the condition:

\[ \frac {\sum\limits_{i,j} z(x_i,y_j) u_{i,j}} {z(x_i,y_j)} = m \]

where (i,j) - indices of the cells in area, $z(x_i,y_j)$ - weighted surface value for the (i,j) cell, m - desired weighted mean value


surfit: gridding and contouring software.